GestaltU - The Research Portal for Darwin Investment Strategies

The Whole is Greater than the Sum of the Parts

2013-05-14T13:10:00.000-07:00

One of the most mind-blowing implications of portfolio theory is that a well conceived portfolio has the potential to be much better, in terms of risk adjusted performance, than what we might expect from the sum of the individual portfolio holdings.

Not incidentally, the name of our blog - GestaltU - relates directly to this concept. Contrary to the dominant framework of reductionism, which decries that the most effective way to understand something is to understand its parts, Gestalt theory asserts that many things can not be understood by understanding the components, because the 'whole' is greater than the sum of the parts.

This is more obvious in some fields than others. For example, can a person intuit the qualities of water from an understanding of the properties of hydrogen and oxygen (without a deep understanding of quantum mechanics)? Can you effectively comprehend the experience of carrot cake from an understanding of the ingredients?

The famous World Wildlife Found logo is an example of a Gestalt because the brain identifies that the conglomeration of irregular black shapes in the image is actually a panda bear. It is not the shapes themselves, but the orientation of the shapes and how they fit together that communicates the salient information contained in the image.

Most investors pay much more attention to the process of identifying the individual characteristics of the assets they want to own than they commit to the process of identifying how well the assets might fit together in a portfolio. But what if the individual characteristics of the assets are less important than the way they work together?

We've been meaning to get a post up on this topic for a while, but a recent paper published by Cass Business School and sponsored by institutional consultant AonHewitt provided the ammunition we've been looking for. Their paper, which is in two parts, is called 'An evaluation of equity indices". Part 1 examines 'Heuristic and optimized weighting schemes' and Part 2. explores 'Fundamental Weighting Schemes'. This framework works beautifully to illustrate the relative importance of portfolio optimization versus fundamental stock selection because it compares the realized excess risk adjusted performance of pure risk-based optimization methods to methods based on traditional fundamental security selection.

Note that the authors used a universe of the top 1000 stocks by market cap in each year from 1968 - 2012.

In Part 1., the researchers describe a variety of ways to dynamically generate optimal stock portfolios where there is no effort to emphasize individual return characteristics at the security level. Rather, portfolios were assembled purely on the basis of how constituent stocks were expected to contribute to the overall risk of the portfolio, based on observations of the variance/covariance matrix over a trailing 60 month window. The authors then compared the performance of these optimized portfolios to the ubiquitous market capitalization weighted index, and the more competitive equal weight portfolio.

It is beyond the scope of this article to describe the characteristics of the different optimizations applied by the authors (we highly recommend that you download the paper and read about the various optimizations), but Table 1. summarizes the results.

Table 1. Portfolio optimization results

Source: Cass Business School, 2013

Part 2. explores a variety of fundamental based methods of creating portfolios that emphasize the stocks with attractive fundamental characteristics. The authors create portfolios where stocks are weighted by qualities like dividends, cashflows, book values, and sales to see how these fundamentally weighted portfolios compare to the traditional market cap and equal weight indices.

Table 2. Fundamental weighting results

Source: Cass Business School, 2013

It is interesting to compare the two methods of portfolio formation. Note that the best portfolio optimization method (in terms of Sharpe ratio), MVP (minimum variance), delivered 10.8% returns with volatility of 11.2% and a maximum drawdown over the full period of -32.5%. On the other hand, the best fundamental weighting method, Sales-weighted (Sharpe was tied with Dividend weighted, so used Sortino to break the tie), delivered returns of 11.4% with a volatility of 16.2% and a maximum drawdown of -52.6%. Note that the Sharpe ratio of the MVP strategy was 0.5 compared with 0.42 for the Sales-Weighted strategy, and the Sortino ratios were 0.59 and 0.53 respectively.

How is it that optimization alone can deliver better risk adjusted performance without any fundamental information about the relative prospects for portfolio constituents? Part of the answer is that optimization tends to indirectly tilt portfolios toward factors that are well known for adding excess returns over time.

The following table quantifies the annualized difference between the return to the factor exposure of the alternative index relative to the market-cap index. You can see that the optimized portfolio derives meaningful alpha from a small-cap bias relative to the market-cap index. This is unsurprising. What is more surprising is that the optimizations tend to tilt portfolios toward the Fama French Value factor, and away from the momentum factor.

Table 3. The Returns to Factor Exposures

Source: Cass Business School, 2013

Clearly there is an opportunity to combine fundamental stock-picking factors with robust portfolio optimization to deliver better results than either method alone - another Gestalt!

The following table is taken from an S&P Capital IQ presentation published in December 2010. The authors imposed factor tilts on a minimum variance portfolio derived from constituents of the S&P 1500, with the results in Table 4. Note improved Return/Risk ratios from a combination of FF Value and Earnings Quality tilt portfolios with minimum variance optimization.

Table 4. Minimum Variance with Factor Tilts

Source: Capital IQ, 2010

Investors should take note of the opportunity for better risk-adjusted returns by considering more holistic methods of stock-picking rather than concentrating so much time and effort on identifying individual stocks with prospective characteristics. The whole really can be better than the sum of the parts.

Darwin Investment Strategies Website Update

2013-04-16T09:40:00.001-07:00

Come check out our new website:

www.darwinstrategies.ca

Make sure to check out our Strategies page, and especially our whitepaper on Adapative Asset Allocation:

What the Bull Giveth, the Bear Taketh Away

2013-04-14T17:48:00.001-07:00

Those who cannot remember the past are condemned to repeat it. - Santayana

The question of whether to commit new funds to stocks here is nuanced and complex, not least because it isn't obvious that traditional alternatives - bonds or cash - offer any better value. We are very near all-time low interest rates across most developed government bond markets, credit spreads are near all-time tights, and rates are negative out to 5 or more years in real terms. If these options are representative of the complete opportunity set, then one might be justified in apportioning some capital to equities, if only because it is difficult to identify which investment stinks most profoundly.

However, those who do choose to allocate to equities should be aware of where we are relative to other bull-bear cycles throughout history. We have rambled-on about the poor prospects for equity returns over the next 10 - 20 years in many prior articles (see here for a full analysis, and here for a summary of research from other respected firms), but the true authority on stock market valuation is John Hussman. We would strongly encourage readers to investigate Dr. Hussman's Weekly Market Comments for all the gory details.

This article approaches the issue from a completely new direction than our other work and the work of Dr. Hussman. It is mostly constructed as a thought experiment that explores the logic of compounding, but the conclusion is troubling for those currently overweight U.S. equities.

For the purpose of the study below, we examined the S&P 500 price series from Shiller's publicly available database to understand the duration and magnitude of all bull and bear market periods in U.S. stocks since 1871. We defined a bear market as a drop in prices of at least 20% from any peak, and which lasted at least 3 months. Bull markets were then defined as a rise of at least 50% from the bottom of a bear market, over a period lasting at least 6 months.

Chart 1 and Table 1 describe every bull market since 1871 in the S&P, including duration and magnitude information. The lesson from this analysis is uninspiring for equity bulls, as we will see. The core hurdle is that the current bull market has (through end of February) already delivered 105% of gains, against the median 124% bull market run through history (using monthly data). Of course, this means that, should this bull market deliver an average surge, investors can hope for less than 20% more growth from this cycle. Further, given that the median bull market has historically lasted 50 months, and we are currently in our 49th bull month, we are about due for a wipeout.

Chart 1. Bull Markets since 1871

Source: Shiller (2013)

Table 1. Bull Markets since 1871 - Statistics

Source: Shiller (2013)

It's troubling enough that the current bull market has already delivered 85% of the gains, and lasted about as long, as the median historical bull market. More disconcerting still is the fact that, when the bear market comes, as Chart 2. and Table 2. demonstrate, it is likely to wipe out 38% of all prior gains. And this has profound mathematical implications for current equity investors.

Chart 2. Bear Markets since 1871

Source: Shiller (2013)

Table 2. Bear Markets since 1871 - Statistics

Source: Shiller (2013)

Portfolio growth is governed by the mathematics of compounding, which means that, for example, a 100% gain is erased by a 50% loss, and a 50% loss requires a 100% gain to get back to even. Applying the same principles to where we are in the current bull/bear cycle is illuminating.

If we assume that the next bear market will deliver losses in-line with what we have experienced from bear markets through history, then at the bottom of the next bear market investors will have lost 38% of their portfolio value. The question is, how much must current investors expect stocks to gain before peaking to justify owning them here instead of waiting to purchase them in the next bear market?

The most unbiased estimate of the magnitude of the next bear market is the historical median of 38%. Using the math of compounding, we can determine that a 38% loss requires a 61% gain to break-even [1 / (1 - 38%)]. Logically then, and by extension, investors who choose to hold stocks today must expect gains of at least 61% in order to rationalize their investment; otherwise they would eliminate the anxiety of riding the equity roller-coaster and simply invest in cash, waiting to pounce on stocks at equivalent or lower value at some point during the next bear market.

Figure 1. Example of potential equity roller coaster decision

Note that this argument is not meant to justify any sort of typical 'market timing' approach; most of these are rubbish and very difficult to adhere to for a variety of emotional reasons. Rather, it is a compelling argument for investors to seek out truly different sources of returns, such as tactical alpha strategies, CTAs, or diversified risk strategies inclusive of a wide variety of assets.

Valuation Based Equity Market Forecasts - Q1 2013 Update

2013-04-11T12:13:00.002-07:00

We endorse the decisive evidence that markets and economies are complex, dynamic systems which are not reducible to normal cause-effect analysis. However, we are willing to acknowledge the likelihood that the future is likely to rhyme with the past. Thus, we believe there is substantial value in applying simple statistical models to discover average estimates of what the future may hold over meaningful investment horizons (10+ years), while acknowledging the wide range of possibilities that exist around these averages.

To be crystal clear, the commentary below makes no assertions about whether markets will carry on higher from current levels. Expensive markets can get much more expensive in the intermediate term, and investors need look no further back than the late 2000s for just such an example. However, the physics of investing in expensive markets is that, at some point in the future, perhaps years from now, the market has a very high probability of trading back below current prices; perhaps far below. More importantly, investors must recognize that buying stocks at very expensive valuations will necessarily lead to future returns over the subsequent 10 - 20 years that are far below average.

There are several reasons why it may be useful to have a more robust estimate of future expected returns on stocks:

People who are approaching retirement need to estimate probable returns in order to budget how much they need to save.

A retiree's level of sustainable income is largely dictated by expected returns over the early years of retirement.

Investors of all types must make an informed decision about how best to allocate their capital among various investment opportunities.

Many studies have attempted to quantify the relationship between Shiller PE and future stock returns. Shiller PE smoothes away the spikes and troughs in corporate earnings which occur as a result of the business cycle by averaging inflation-adjusted earnings over rolling historical 10-year windows.

This study contributes substantially to research on smoothed earnings and Shiller PE by adding three new valuation indicators: the Q-Ratio, total market capitalization to GNP, and deviations from the long-term price trends. The Q-Ratio measures how expensive stocks are relative to the replacement value of corporate assets. Market capitalization to GNP accounts for the aggregate value of U.S. publicly traded business as a porportion of the size of the economy. In 2001, Warren Buffett wrote an article in Fortune where he states, "The ratio has certain limitations in telling you what you need to know. Still, it is probably the best single measure of where valuations stand at any given moment." Lastly, deviations from the long-term trend of the S&P inflation adjusted price series indicate how 'stretched' values are above or below their long-term averages.

These three measures take on further gravity when we consider that they are derived from four distinct facets of financial markets: Shiller PE focuses on the earnings statement; Q-ratio focuses on the balance sheet; market cap to GNP focuses on corporate value as a proportion of the size of the economy; and deviation from price trend focuses on a technical price series. Taken together, they capture a wide swath of information about markets.

We analyzed the power of each of these 'valuation' measures to explain inflation-adjusted stock returns including reinvested dividends over subsequent multi-year periods. Our analysis provides compelling evidence that future returns will be lower when starting valuations are high, and that returns will be higher in periods where starting valuations are low.

This last point may seem obvious, but I want to emphasize a critical point about traditional wealth management of which most investors are not aware:

Many traditional investment advisors do not account for whether markets are cheap or expensive when determining investors' long-term asset allocation. In our experience, an investor who visited a traditional Investment Advisor at the peak of the technology bubble in early 2000 would, in practice, have been advised to allocate the same proportion of his wealth to stocks as an investor who visited an Advisor near the bottom of the markets in early 2009. This despite the fact that the first investor would have had a valuation-based expected return on his stock portfolio from January 2000 of negative 2% per year, while the second investor would expect inflation-adjusted compound annual returns of 6.5%. For an investor with $1,000,000 to invest, this would represent a difference of more than $1.26 million in cumulative wealth over a decade.

Said differently, traditional wealth advice is rooted in the assumption that the best estimate of future returns is the average long-term return to stocks. No matter where markets are on the continuum from very cheap to very expensive, traditional Advisors will make recommendations on the assumption that investors should expect 6.5% inflation adjusted returns on stocks over all investment horizons.

John Hussman at Hussman funds is careful to qualify the value of this analysis: "Rich valuation is strongly associated with weak subsequent returns, but only reliably so over periods of 7-10 years. In contrast, the present syndrome of overvalued, overbought, overbullish, rising-yield conditions is typically associated with abrupt and often steep losses, but is more commonly resolved over a period of months rather than years." (Hussman, Feb 2013).

Thus, we are not making a forecast of market returns over the next several months; in fact, markets could go substantially higher from here. However, over the next 10 to 15 years, markets are very likely to revert to average valuations, which are much lower than current levels. This study will demonstrate that investors should expect 6.5% returns to stocks only during those very rare occasions when the stock market passes through 'fair value' on its way to becoming very cheap, or very expensive. At all other periods, there is a better estimate of future returns than the long-term average, and this study endeavours to quantify that estimate.

Investors should be aware that, relative to meaningful historical precedents, markets are currently expensive and overbought by all three measures, indicating a strong likelihood of low inflation-adjusted returns going forward over periods as long as 20 years.

This forecast is also supported by evidence from an analysis of corporate profit margins. In a recent article, John Hussman published a long-term chart of U.S. corporate profits, which demonstrated the magnitude of upward distortion endemic in current corporate profits, which we have reproduced in Chart 1 below. Companies have clearly been benefitting from a period of extraordinary profitability.

Source: John Hussman, 2013

The profit margin picture is critically important. Jeremy Grantham recently stated, "Profit margins are probably the most mean-reverting series in finance, and if profit margins do not mean-revert, then something has gone badly wrong with capitalism. If high profits do not attract competition, there is something wrong with the system and it is not functioning properly." On this basis, we can expect profit margins to begin to revert to more normalized ratios over coming months. If so, stocks may face a future where multiples to corporate earnings are contracting at the same time that the growth in earnings is also contracting. This double feedback mechanism may partially explain why our statistical model predicts such low real returns in coming years. Caveat Emptor.

Modeling Across Many Horizons

Many studies have been published on the Shiller PE, and how well (or not) it estimates future returns. Almost all of these studies apply a rolling 10-year window to earnings as advocated by Dr. Shiller. But is there something magical about a 10-year earnings smoothing factor? Further, is there anything magical about a 10-year forecast horizon?

Kitces (2008, PDF format) demonstrated that "the safe withdrawal rate for a 30-year retirement period has shown a 0.91 correlation to the annualized real return of the portfolio over the first 15 years of the time period". So there is clearly merit in studying a 15-year forecast horizon as well. Further, the tables below will demonstrate that statistical models have the greatest explanatory power at the 15-year horizon.

This study will attempt to address the question of 'perfect forecast horizon', perfect valuation factor, and 'perfect earnings smoothing factor', by analyzing the explanatory power of earnings, the Q-Ratio, and regressed historical stock returns, over return horizons from 1 to 30 years. We will also put all of the factors together to construct an optimized model.

Table 1. below provides a snapshot of some of the results from our analysis. The table shows estimated future returns based on a coherent aggregation of several factor models over some important investment horizons.

Table 1. Factor Based Return Forecasts Over Important Investment Horizons

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

You can see from the table that, according to a model that incorporates valuation estimates from 4 distinct domains, and which explains over 80% of historical returns since 1871, stocks are likely to deliver 1% or less in real total returns over the next 5 to 20 years. Yikes.

Process

The purpose of our analysis was to examine several methods of capturing market valuation to determine which methods were more or less efficacious. Furthermore, we were interested in how to best integrate our valuation metrics into a coherent statistical framework that would provide us with the best estimate of future returns.

Our approach relies on a common statistical technique called linear regression, which takes as inputs the valuation metrics we calculate from a variety of sources, and determines how sensitive actual future returns are to contemporaneous observations of each metric. Linear regression creates a linear function, which by definition can be described by a slope value and an intercept value, which we provide below for each metric and each forecast horizon. A further advantage of linear regression is that we can measure how confident we can be in the estimate provided by the analysis. The quantity we use to measure confidence in the estimates is called the R-Squared.

The following matrices show the R-Squared ratio, regression slope, regression intercept, and current forecast returns based on a regression analysis for each valuation factor. The matrices are heat-mapped so that larger values are reddish, and small or negative values are blue-ish. Click on each image for a large version.

Matrix 1. Explanatory power of valuation/future returns relationships

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

Matrix 1. contains a few important observations. Notably, over periods of 10-20 years, the Q ratio, very long-term smoothed PE ratios, and market capitalization / GNP ratios are equally explanatory, with R-Squared ratios around 55%. The best estimate (perhaps tautologically given the derivation) is derived from the price residuals, which simply quantify how extended prices are above or below their long-term trend.

The worst estimates are those derived from trailing 12-month PE ratios (PE1 in Matrix 1 above). Many analysts quote 'Trailing 12-Months' or TTM PE ratios for the market as a tool to assess whether markets are cheap or expensive. If you hear an analyst quoting the market's PE ratio, odds are they are referring to this TTM number. Our analysis slightly modifies this measure by averaging the PE over the prior 12 months rather than using trailing cumulative earnings through the current month, but this change does not substantially alter the results.

As it turns out, TTM (or PE1) Price/Earnings ratios offer the least information about subsequent returns relative to all of the other metrics in our sample. As a result, investors should be extremely skeptical of conclusions about market return prospects presented by analysts who justify their forecasts based on trailing 12-month ratios.

Forecasting Expected Returns

We expect you to be skeptical of our unconventional assertions, so below we provide the precise calculations we used to determine our estimates. The following matrices provide the slope and intercept coefficients for each regression. We have provided these in order to illustrate how we calculated the values for the final matrix below of predicted future returns to stocks.

Matrix 2. Slope of regression line for each valuation factor/time horizon pair.

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

Matrix 3. Intercept of regression line for each valuation factor/time horizon pair.

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

Matrix 4. shows forecast future real returns over each time horizon, as calculated from the slopes and intercepts above, by using the most recent values for each valuation metric (through February 2013).

For statistical reasons which are beyond the scope of this study, when we solve for future returns based on current monthly data, we utilize the rank in the equation for each metric, not the nominal value.

For example, the 15-year return forecast based on the current Q-Ratio can be calculated by multiplying the current ordinal rank of the Q-Ratio (1171) by the slope from Matrix 2. at the intersection of 'Q-Ratio' and '15-Year Rtns' (-0.000086098), and then adding the intercept at the same intersection (0.119607) from Matrix 3. The result is 0.0188, or 1.88%, as you can see in Matrix 4. below at the same intersection (Q-Ratio | 15-Year Rtns).

Matrix 4. Modeled forecast future returns using current valuations.

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

Finally, at the bottom of the above matrix we show the forecast returns over each future horizon based on our best-fit multiple regression from the factors above. From the matrix, note that the best forecast for future real equity returns integrating all available valuation metrics is 1% or less per year over horizons covering the next 5 to 20 years. We also provided the R-squared for each multiple regression underneath each forecast; you can see that at the 15-year forecast horizon, our regression explains 80% of total returns to stocks.

Chart 2. below demonstrates how closely the model tracks actual future 15-year returns. The red line tracks the model's forecast annualized real total returns over subsequent 15-year periods using our best fit multiple regression model . The blue line shows the actual annualized real total returns over the same 15-year horizon.

Chart 2. 15-Year Forecast Returns vs. 15-Year Actual Future Returns

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see that 15-year "Regression Forecast" returns are -0.43% per year using market valuations as of February 28, 2013.

Putting the Predictions to the Test

A model is not very interesting or useful unless it actually does a good job of predicting the future. To that end, we tested the model's predictive capacity at some key turning points in markets over the past century or more to see how well it predicted future inflation-adjusted returns.

Table 2. Comparing Long-term average forecasts with model forecasts

Source: Shiller (2013), DShort.com (2013), Chris Turner (2013), World Exchange Forum (2013), Federal Reserve (2013), Butler|Philbrick|Gordillo & Associates (2013)

You can see we tested against periods during the Great Depression, the 1970s inflationary bear market, the 1982 bottom, and the middle of the 1990s technology bubble in 1995. The table also shows expected 15-year returns given market valuations at the 2009 bottom, and current levels. These are shaded green because we do not have 15-year future returns from these periods yet.

Observe that, at the very bottom of the bear market in 2009, real total return forecasts never edged higher than 7%, which is only slightly above the long-term average return. This suggests that prices just approached fair value at the market's bottom; they were nowhere near the level of cheapness that markets achieved at bottoms in 1932 or 1982. As of the end of February 2013, annualized future returns over the next 15 years are expected to be less than 0 percent.

We compared the forecasts from our model with what would be expected from using just the long-term average real returns of 6.5% as a constant forecast, and demonstrated that always using the long-term average return as the future return estimate resulted in 350% more error than estimations from our multi-factor regression model over 15-year forecast horizons (1.22% annualized return error from our model vs 5.55% using the long-term average). Clearly the model offers substantially more insight into future return expectations than simple long-term averages, especially near valuation extremes.

Conclusions

The 'Regression Forecast' return predictions along the bottom of Matrix 4. are robust predictions for future stock returns, as they account for over 100 different cuts of the data, using 4 distinct valuation techniques, and utilize the most explanatory statistical relationships. The models explain up to 82% of future returns based on R-Squared, and are statistically significant at p~0. Despite the model's robustness over longer horizons, it is critical to note that even this model has very little explanatory power over horizons less than 6 or 7 years, so the model should not be used as a short-term market-timing tool.

Returns in the reddish row labeled "PE1" in Matrix 4 were forecast using just the most recent 12 months of earnings data, and correlate strongly with common "Trailing 12-Month" PE ratios cited in the media. Matrix 1. demonstrates that this trailing 12 month measure is not worth very much as a measure for forecasting future returns over any horizon. However, the more constructive results from this metric probably helps to explain the general consensus among sell-side market strategists that markets will do just fine over coming years.

Just remember that these analysts have no proven ability whatsoever to predict market returns (see here, here, and here). This reality probably has less to do with the analytical ability of most analysts, and more to do with the fact that most clients would choose to avoid investing in stocks altogether if they were told to expect negative real returns over the long-term from high valuations.

Investors would do much better to heed the results of robust statistical analyses of actual market history, and play to the relative odds. This analysis suggests that markets are currently expensive, and asserts a very high probability of low returns to stocks (and possibly other asset classes) in the future. Remember, any returns earned above the average are necessarily earned at someone else's expense, so it will likely be necessary to do something radically different than everyone else to capture excess returns going forward.

Those investors who are determined to achieve long-term financial objectives should be heavily motivated to seek alternatives to traditional investment options given the grim prospects outlined above. Such investors may find solace in some of the approaches related to 'tactical alpha' that we have described in a variety of prior articles.

Asset Allocation and Safe Withdrawal Rates: A Whitepaper

2013-03-08T10:15:00.000-08:00

Balanced Portfolios: Keeping it Real

2013-02-20T10:32:00.000-08:00

It's important for clients to understand what they're getting themselves into with a typical balanced portfolio.

The following charts show the distribution of real historical returns over 1, 5, and 10 year horizons for a portfolio consisting of 60% stocks and 40% bonds.

Some facts clients might not be aware of:

A balanced portfolio can drop as much as 35% in any given year
Balanced portfolios have delivered negative real returns over 10 year periods 15% of the time
Over all rolling 5 year periods, a balanced portfolio has yielded real returns ranging from -10% through +22% annualized

Chart 1. Probability of negative real returns to a 60/40 U.S. stock/bond portfolio over 1, 5 and 10 year horizons

Source: Shiller, Federal Reserve

Chart 2. Range of real returns to a U.S. 60/40 stock/bond portfolio over 1, 5, and 10 year horizons

Source: Shiller, Federal Reserve

Chart 3. Frequency distribution of real returns to U.S. 60/40 stock/bond portfolio over rolling 12 month periods

Source: Shiller, Federal Reserve

Chart 4. Frequency distribution of real returns to U.S. 60/40 stock/bond portfolio over rolling 5 year (60 month) periods

Source: Shiller, Federal Reserve

Chart 5. Frequency distribution of real returns to U.S. 60/40 stock/bond portfolio over rolling 10 year (120 month) periods.

Source: Shiller, Federal Reserve

Predicting Markets, or Marketing Predictions

2013-01-31T17:20:00.000-08:00

Mark Twain suggested that it is better to remain quiet and be thought a fool, than to open your mouth and remove all doubt.

Would that the 'gurus' who populate the investment and economics landscape would heed Twain's advice. Of course, that will never happen.

We know from studies of expert judgement that gurus who make nuanced predictions and hedge their bets attract much less attention than experts who spin dramatic predictions with unswerving confidence. As a result, firms are predisposed to encourage gurus to voice strong opinions and divergent views that stand out from the crowd. Unfortunately, the qualities that make some gurus more marketable than others are likely to render them less accurate: balanced experts tend to be more accurate than loud ideologues, and their opinions tend to be less damaging when they go wrong.

And even the best experts get it wrong a lot. In fact, they get it wrong more than they get it right. How do we know?

The best and most comprehensive study of expert judgment was performed by Philip Tetlock. In 1985 Tetlock, fascinated by his previous experience serving on political intelligence committees in the early 1980s, set out to discover just how accurate expert forecasters were in their predictions of future events. Over a span of almost 20 years, he interviewed 284 experts about their level of confidence that a certain outcome would come to pass. Forecasts were solicited across a wide variety of domains, including economics, politics, climate, military strategy, financial markets, legal opinions, and other complex domains with uncertain outcomes. In all, Tetlock accumulated an astounding 82,000 forecasts.

This represents an incredible body of evidence about expert judgment, and Tetlock's analysis rendered several astounding conclusions:

Expert forecasts were less well calibrated than one would expect from random guesses
Aggregated forecasts were better than any individual forecasts, but were still worse than random guesses
Experts who appeared in the media most regularly were the least accurate
Experts with the most extreme views were also the least accurate
Experts exhibited higher forecast calibration outside of their field of expertise
Among all 284 experts, not one demonstrated forecast accuracy beyond random guesses

In short, experts would have delivered better forecasts by flipping coins. But there was a silver lining.

Tetlock also tracked some simple, rules based statistical models alongside the experts to see if these models would be competitive in terms of forecast calibration. He found that many simple models performed with substantially better calibration than the experts, and delivered accuracy well beyond random chance. Chock another one up for the quants.

You might be wondering whether there are any similar types of studies conducted specifically in the area of financial markets. You're in luck, as there are have been several.

CXO Advisory has been tracking and publishing gurus' forecasts of market direction since 1998. Recently, CXO published a review of all 6,459 forecasts from all of the market 'gurus' that they tracked from 1998 - 2012. Specifically, the gurus were graded on their ability to call the direction of the market, but were not penalized for missing the magnitude of the move.

Over 14 years, CXO concluded that the average guru's accuracy in calling the direction of the market has been about 47%, or slightly worse than a coin toss. The following chart shows how the accuracy of forecasts has stabilized over time around the 47% mark as the sample size expanded over time. In other words, the experts were less reliable than flipping coins.

Source: CXO Advisory

The evidence does not end there. The following charts, sourced from James Montier's incredibly useful book, Behavioural Investing (2007), show aggregate forecasts from Wall Street's most famous oracles through time, next to the actual trajectory of the forecast variable.

Chart 1. Consensus bond yields forecasts 1 year out vs. actual

Chart 2. Consensus S&P500 level 1 year forecasts vs. actual

Chart 3. Consensus S&P500 aggregate earnings 1 year forecasts vs. actual

In all cases the analysts appear to do a noteworthy job of describing what just happened, but appear to have no vision whatsoever about what is about to happen next. This applies to interest rates, the level of stock indices, and aggregate earnings.

Source: Despair.com

Do any experts get it right? What about the experts at the Federal Reserve who are in charge of setting interest rates? Can they predict the magnitude or direction of interest rates just six months hence?

A working paper entitled "History of the Forecasters: An Assessment of the Semi-Annual U.S. Treasury Bond Yield Forecast Survey" (Brooks & Gray, 2003) studied the ability of Federal Reserve economists, including Alan Greenspan, from 1982 - 2002 to discover whether the group of experts that sets interest rates is able to effectively forecast their trajectory through time.

Chart 3.

Source: (Brooks & Gray, 2003)

Again we see a strong talent for describing what has just happened, but no talent whatsoever for predicting what will happen next. Just how poor was the forecasting ability of Fed economists, including sitting Fed Chairman Alan Greenspan, over the 20 year survey?

Chart 4.

Source: (Brooks & Gray, 2003)

The scatter plot above shows how Fed forecasts of interest rates just six months out are negatively correlated with actual outcomes. The r-squared of the regression is 7%, which is not statistically significant, so don't bet the farm against the Fed either. The point is, they can't forecast any better than anyone else.

There is ample evidence that strategists and gurus are unlikely to add much value to the investing process - at least where the goal is to grow your portfolio. Our next article will address another ubiquitous observation in wealth management - overconfidence - and discuss solutions for disillusioned investors looking for a new direction with better odds of success.

Track Records are Rubbish (or Why Managers are Factors in Drag)

2013-01-07T11:13:00.000-08:00

As usual, you are the butt of the joke.

Everywhere you turn, you are bombarded with 1, 3, and 5 year track records for investment products. The investment management industry knows that you are influenced by percent symbols preceded by large numbers, so they market products with the best 1, 3 and 5 year track records, prominently featuring them in newspaper and TV advertisements, knowing that you will be unable to resist the urge to chase into those funds to avoid missing another year of riches.

Source: fanpop.com

Unfortunately, as you probably surmised, this almost never works out. The products with the best track records over the past few years are not the products that deliver the best track records in subsequent years. In fact, there is strong evidence that chasing managers with strong 3 and 5 year track records is actually harmful to your portfolio health. This article will explore the evidence against using a 3 to 5 year track record to make investment decisions, and point to some alternative solutions.

3 Year Track Records Are for Suckers

The most commonly cited study of actual retail investor behaviour is the Dalbar Quantitative Analysis of Investor Behaviour which summarizes findings about mutual fund investor behaviour over the past 20 years. We plucked two important, and we think related, facts from the piece and summarized them in charts 1 and 2 below. Chart 1. shows the average holding period for each class of mutual fund (stocks, bonds and balanced funds), and Chart 2. shows the realized returns to actual investors on their stock and bond mutual fund holdings, over the period 1991 - 2011.

Chart 1. Stock and bond investors hold funds for 3 years; balanced investors give it one more year

Source: Dalbar, 2012

Chart 2. Actual results to mutual fund investors vs. stock and bond benchmarks - 1991 to 2011

Source: Dalbar

From Chart 1. we can see that, on average, retail investors go chasing into new 'hot funds' about every 3 years or so; balanced investors seem to hang on a little longer, for reasons we explored in this article. Chart 2. highlights the insanity of this approach. Equity investors earned 4% per year less than the large cap stock benchmark over the same period, while bond investors fared even worse. Sure, about half of the decay can be attributed to fees and taxes, and a portion to bad market timing (strangely we didn't receive any calls from investors in a panic to buy in early 2009), but a measurable portion of the lag is due to misguided product selection on the basis of three year track records.

Chart 3., from the annual SPIVA report on active manager performance (2011 version) demonstrates the tendency for managers who demonstrate top quartile performance over a 5 year period to fall out of the top quartile over the next 5 years. One might randomly expect 25% of the managers who rank in the top quartile in the first 5 years to again rank in the top quartile during the second period. In fact, just 6% of these managers actually persist in the top quartile, implying a very substantial reversion to the mean effect.

Chart 3. Mutual fund manager performance persistence over 5 year periods

Source: SPIVA (2012)

Chart 4. shows that institutions act largely on the same schedule as retail investors, with manager termination decisions based largely on 3 to 5 year trailing results. This is not surprising because institutions are run by humans too.

Chart 4. Average evaluation period for manager termination by pension funds

Source: Employee Benefit Research Institute

Chart 5. clearly illustrates the impact of this phenomenon in the pension space. The grey bars represent the average annualized performance of terminated managers in the three years prior to, and three years subsequent to, their termination. The white bars represent the performance of replacement managers in the same years. Clearly institutions are hiring managers with exceptional historical track records over trailing 3 year periods, and firing managers with poor track records. The joke is on the institutions, however, since on average the fired managers go on to outperform the hired managers over the subsequent 1, 2, and 3 year periods!

Chart 5. Excess returns to terminated and newly hired managers in the 3 years prior to, and subsequent to, termination

What an incredibly frustrating reality for retail and institutional investors alike. How can it be that managers with the best track records over as long as 5 years don't work out to be great investments in subsequent years? Does a track record mean anything? For the most part, we don't think so.

Manager Skill, or Factors in Drag?

It is important to remember that most investment managers are human beings. (I say 'most' because a minuscule but growing portion of managers are actually computers). As such, most managers are really just overconfident, incoherent collections of habits, assumptions, ideologies, and cognitive and emotional biases emanating from the most dangerous black-box of all - the human mind. Sometimes these habits, assumptions and biases are aligned with the market, and the manager does well. Sometimes the manager is 'out of sync', and he does poorly.

In reality, it is better to think of managers as inconsistent conduits to somewhat persistent factors that manifest in markets from time to time to drive outperformance from a certain investment approach. In the equity space, academics suggest that 4 factors explain the majority of long-term stockpicking performance. One might infer that the success or failure of most managers over any period of 3 to 5 years largely depends on whether the manager's biases were aligned with one of the following factors that happened to also be working over the same period.

Market factor: this is commonly referred to as beta, and refers to the fact that most stocks tend to move in the same direction as the index
Small-cap factor: it has long been recognized that small-cap stocks outperform large-cap stocks over the long-term
Value factor: cheap stocks tend to outperform expensive stocks over the long term
Momentum factor: stocks that have gone up over the past 1 to 12 months tend to outperform over the long term

Recently, academics and practitioners have reluctantly added a low volatility (or low beta) factor to explain the observed outperformance of low volatility stock portfolios, and we will include this factor in our analyses below.

Chart 6. offers graphical evidence of the value and momentum effect within large-capitalization stocks. Specifically, the chart demonstrates how a strategy of rotating into the strongest stocks every month, and a strategy of rotating into the cheapest stocks every year, have outperformed a strategy of holding the broad stock market index since 1927.

Chart 6. U.S. large capitalization stock market value and momentum factor tilt portfolios

Source: Ken French database

It is our assertion that clients should be much less concerned with the track records of individual managers, and much more concerned with the performance of a manager's style factor. If you can identify what factors (or what mix of factors) is most likely to generate the strongest risk-adjusted returns over your rebalance horizon, this information is of much greater value than identifying which managers might outperform their style benchmarks.

This assertion is strongly confirmed by results from Financial Product Differentiation Over the State Space in the Mutual Fund Industry by Li and Qiu (2010), who showed that 95.7% of cross sectional mutual fund performance is explained by the traditional four Carhart factors: market beta, small-cap, value, and momentum.

If 96% of mutual fund performance is explained by style factors, and most managers underperform the market and their style benchmarks, then investors should concentrate on allocating to factors, not managers. In the real world, when the value factor is outperforming, value biased managers will be high-fiving each other at the water cooler and celebrating their unique and robust stock-picking talent. Growth (or anti-value) managers, meanwhile, will be crying in their beer and lamenting the 'broken' market that isn't cooperating with their investment bias. Chart 7. clearly illustrates this effect, as value managers outperformed for the first four years of the last decade, gaining 26% vs. their growth oriented peers by late 2006.

Chart 7. Value vs. Growth: Luck or Skill?

Source: Stockcharts.com

However, just as value managers were buying their Porsches and brownstones in 2006, their performance streak ended. Over the next 6 years, value managers endured a steady diet of crow while their growth brethren feasted on rich returns. Chart 8. illustrates the same phenomenon for managers with small vs. large-cap biases over a 20 year horizon, but the same effect plays out in all factors: dividend stocks, momentum stocks, low volatility stocks, etc.

Chart 8. Small cap vs. Large Cap: Luck or Skill?

Source: Stockcharts.com

If style factors explain 96% of equity manager performance, and a single factor can deliver 25% - 50% or more of outperformance over a four year period, you can see that the decision to allocate to either value or growth, small-cap or large-cap (insert any factor here) completely dominates the decision about which specific value, growth, small-cap or big-cap manager to use.

Surely Buffet is a Special Case, Right? Wrong.

Interestingly, a group at Yale investigated the full trading history of Warren Buffet's investment vehicle, Berkshire Hathaway to discover whether and which systematic factor exposures can effectively explain the seeming miraculous long-term outperformance Buffett has delivered over the years. The authors regressed the monthly returns to Buffet's portfolio (assembled through 13F filings) against the same 5 factors plus another factor, 'Quality', as defined in Asness, Frazzini, and Pedersen (2012b). They discovered that Buffet's strategy was essentially to purchase low beta, high quality stocks (using the long held academic definitions), and lever his portfolio by 60%. The authors regressed Buffet's returns against their 6 factors and then simulated the growth of the equivalent factor portfolio (green line) over Buffet's full investment horizon and compared it to Buffet's actual performance (blue line). The results are in chart 9. below.

Chart 9.

Regarding the ability of factors to explain away Buffet's magical performance streak, the Yale authors suggest:

We see that Berkshire loads significantly on the [low beta] and [quality] factors, reflecting that Buffett likes to buy safe, high-quality stocks. Controlling for these factors drives the alpha of Berkshire’s public stock portfolio down to a statistically insignificant annualized 0.1%, meaning that these factors almost completely explain the performance of Buffett’s public portfolio.

Style Boxes Are Silly

The small-cap and value factors form an integral framework for many institutions, as they are the two dimensions used in a traditional 'style box' model. Investors who are guided by this model seek to gain exposure to each 'style box' by seeking out top managers in each style.

Figure 1. Morningstar's Style Box

Source: Morningstar

In reality, this is just a misguided method of factor investing; misguided because investors just end up with what is essentially a 'market' portfolio in the end, as they own both small and big stocks, and value and growth stocks. Further, 'large cap' and 'growth' are anti-factors, which means they have tended to deliver returns below the market portfolio over the long-term. For this reason (and others that are more nuanced), the style box model should be abandoned in favour of a model that embraces true systematic factor tilts against an efficient 'market portfolio'.

Should We Buy Strong Factors?

We've learned that we should be thinking about allocating to factors instead of managers because managers are just inconsistent factors in drag with a strong propensity to underperform. But how should we think about allocating to factors?

We tested a strategy of rotating into the strongest and weakest factors quarterly based on trailing 1, 3, and 5 year performance to see if any of these approaches work any better than holding an equal-weight portfolio of factor tilts, rebalanced quarterly.

Table 1. Summary of factor rotation strategies

Source: Ken French database, Standard & Poor's, Yahoo finance

We've highlighted the worst performing strategies in red. You can see that a strategy of allocating to the factor that performed the best over the past 3 and 5 year periods delivered the worst absolute and risk-adjusted performance over our sample period (1995 - 2012). In fact, the best approaches would have been to allocate to factors that delivered the worst performance over either the past 1 or 5 years, or to allocate equally to the best and worst factors over the prior 1 year period. A strategy of allocating equally to all factors and rebalancing quarterly delivered similar risk-adjusted returns, but lower absolute returns.

From the table above, we would conclude that there is a weak mean-reversion effect with equity market factors over 1 year and 5 years, and an even weaker momentum effect over a 1 year horizon. Clearly the worst strategies are the ones that are embraced by most investors: buying the strongest performing approach over the past 3 to 5 year period.

Future Directions

From a statistical standpoint, factors don't appear to exhibit either a meaningful momentum or mean reversion signal, so investors really don't have much hope of excess returns from chasing into managers with great track records or backing up the truck on managers with awful track records.

However, both of these dynamics really come down to estimating which factor(s) will deliver the highest returns. If we take the perspective that simple performance offers no meaningful information about future returns, then we are left with optimization alternatives related to relative volatility, such as risk parity, or the covariance matrix, such as minimum variance. We explore these approaches at length in our paper, 'Portfolio Optimization with Factor Tilts', but here is a sneak peak.

Chart 10. 5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1%), Max 100% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Chart 11. 5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1% daily), Max 200% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Mutual fund companies and institutional consultants will continue to feed your biases by advertising their best track records, but you don't have to fall for it. With a little research - and an open mind - you can uncover novel methods based on academically validated principles with a proven history of delivering market-beating returns with lower risk.

In our opinion, the most interesting and prospective extension of the concepts discussed above are in the form of Tactical Alpha rather than traditional security selection. This type of approach deals with the allocation of factors across multiple asset classes (see here from AQR[registration required] and here for our own paper), which allows for many more sources of return and diversification, which gets us much closer to investment Nirvana.

The Full Montier: Absolute vs. Relative Value

2013-01-03T07:31:00.000-08:00

James Montier, one of our favourite thinkers and fellow evangelist for behavioural economics and evidence based investing, published a great report last year entitled, "I Want to Break Free, or, Strategic Asset Allocation ≠ Static Asset Allocation". The piece is a tour de force against the ubiquitous concept of "Strategic Asset Allocation" (SAA) which argues that investors should set an asset allocation at the start of their investment horizon that theoretically balances individual risk tolerance against long-term average market risks, and then regularly rebalance back to this target allocation.

As we have argued many times in this blog, traditional SAA is hamstrung because there is no mechanism to alter the asset allocation given changes in relative expected returns and risks from each asset class over time. Inconceivably, adherents to this approach would have advocated exactly the same mix of stocks and bonds in December 1999, when stocks were as overvalued as they had ever been in history, as they would have advocated in 1982 when stocks were dirt cheap. We have argued, and Montier apparently concurs, that investors should be constantly aware of whether prospective returns to stocks are high or low, and alter asset allocations accordingly through time.

Montier is a die-hard value investor, so he views prospective returns through this lens. He asserts that investors should only invest in markets when they offer the prospect of reasonable future real returns on the basis of reasonable valuations, and they should avoid markets when they offer low returns. While this seems eminently reasonable, in practice this logic can be very difficult for investors to adhere to because markets can continue to get more and more expensive (or cheaper) for many years, and investors often find it difficult to stand on the sidelines and watch the market shoot into the stratosphere. For example, markets entered a period of extreme valuation by many measures in 1994 and continued to push higher for 6 more years before finally succumbing to valuation levels that were, by some measures, more than twice as high as any other period in history.

For this reason, most wealth managers, institutions, and advisors practice Strategic Asset Allocation, which keeps investors fully invested in their target mix of stocks and bonds at all times. Where active bets are taken in pursuit of better performance, they take the form of relative value approaches where individual securities are selected for portfolios because they have lower valuations than their peers. This approach is starkly different than the absolute value approach described in the previous paragraph because with the absolute value approach, an investor will hold cash when no investments offer strong absolute returns, whereas relative value investors will always be fully invested, even when all investments are expensive and offer low returns.

Absolute Value: A Few Tests

We thought it would be fun to test an absolute value approach per Montier's prescription using our favorite long-term stock-market data source, Shiller's database. The following charts illustrate how an absolute return investor might have fared had he chosen to move out of stocks and into cash where the real absolute valuation of the stock market ended the prior month below a certain threshold. For ease, we chose the cyclically adjusted earnings yield as the valuation metric, which is just the reciprocal of the Shiller PE. We then adjusted the yield value for the realized year-over-year inflation rate to find the real earnings yield. Finally, we used an 'expanding window' approach to find the percentile rank of the real earnings yield to eliminate as much lookahead bias as possible.

Note that because we are using real earnings yield rather than nominal earnings yield, markets can get cheap or expensive in three ways:

changes in inflation
changes in earnings
changes in price

As a result, while markets would appear to be quite expensive today based on nominal earnings yield, which is in the top quintile of all values over the past 140 years, the real earnings yield is less extreme because yoy inflation is so low. Should inflation pick up, the real earnings yield will decline, all else equal, which would alter the current state of our model (in stocks or in cash).

Chart 1. Valuation based asset allocation: own S&P500 when valuation < long-term average, otherwise hold cash

Source: Shiller (2012), Federal Reserve

Using the expanding window approach, an investor would have spent about 80% of months in cash over the past 80 years or so, implying a fairly consistent expansion in PE ratios over time (we identify periods where market valuations are above our threshold with grey areas on the chart). Even so, by investing in markets only when they are truly cheap (> median real earnings yield) and holding cash otherwise, investors would have generated about 70% of the total return to stocks with less than half the volatility and 73% lower drawdowns since 1934. The reduction in drawdowns is especially important in the context of Montier's definition of risk: the permanent impairment of capital.

We know from history however that when markets move from being inexpensive up through fair value, they usually move well into the range of 'overvalued' before peaking. If that's the case, investors might choose to hold onto stocks until they move further into the expensive range. Chart 2. shows the performance of a strategy that holds stocks unless they are in the top quintile of valuations (bottom quintile of real earnings yields), and holds cash otherwise.

Chart 2. Valuation based asset allocation: own S&P500 when valuation < 80th percentile, otherwise hold cash

Source: Shiller (2012), Federal Reserve

By tolerating higher, but not extreme, valuations investors would have achieved higher returns than the markets overall (11.4% vs. 10.4%) with 26% less volatility and 40% lower drawdowns. As a result, the Sharpe ratio of this approach was 0.8 vs. 0.51 for buy & hold.

A more coherent approach to this framework might eliminate the absolute threshold entirely in favour of a scaled approach. For example, an investor might hold stocks in proportion to the percentile rank of the real earnings yield, and hold the balance in cash. For example when the real earnings yield is at the 80th percentile, the investor would hold 80% stocks and the balance of 20% in cash. Conversely, when stock earnings yields are at the 20th percentile, he would own 20% stocks and 80% cash. Again, this measure is based on valuations at the prior month's close, and using an expanding window to avoid lookahead bias. Chart 3. shows the results of this approach.

Chart 3. Valuation based asset allocation: own S&P500 in proportion to the percentile value of real earnings yield (hold balance in cash)

Source: Shiller (2012), Federal Reserve

This coherent approach avoids having to choose a cutoff threshold, which makes it more robust. Further, the Sharpe ratio is almost as high as for the model with an 80th percentile threshold, though in this case it is because of very low average volatility (5.1% vs. 9.6%), as the returns are considerably lower.

Lastly, we wondered how the same approach would have worked if instead of allocating to cash, we allocated to Treasuries. Chart 4. gives us the answer.

Chart 4. Valuation based asset allocation: own S&P500 in proportion to percentile value of real earnings yield (hold balance in Treasuries).

Source: Shiller (2012), Federal Reserve

Future Directions

James Montier is incensed by the ubiquitous calibration of strategic asset allocation with 'static' asset allocation because static allocation makes no accommodation for the fact that market valuations and commensurate expected returns fluctuate dramatically over time. Does it make sense for investors to be mostly indifferent to expected returns in setting their asset allocation targets?

In keeping with Montier's absolute value philosophy, we investigated several dynamic allocation strategies based on reducing or eliminating exposure to markets as they get more or less expensive, using the real earnings yield as our yardstick. In every case we tested the absolute value based approach delivered a higher Sharpe ratio, and a much higher ratio of returns to our approximation of Montier's measure of risk - maximum drawdowns.

The primary challenge with these approaches is that they require adherents to exit markets just as the party gets going into major peaks. Major market peaks manifest in the midst of extreme optimism and enthusiasm about the future which sweeps every last investor dollar into stocks over several euphoric years. It takes extreme fortitude to stand aside in cash during these long periods of parabolic market gains, and we know from the published studies in behavioural finance that most investors will buckle and go all-in just before the market peaks and rolls over.

Investment managers that adhere to this type of approach will suffer enormous career risks during these periods, and lose a large portion of their assets under management. Montier's current firm, GMO, admits to losing over 40% (!!) of total client assets in the several years leading up to the 2000 market peak, and John Hussman has experienced similar investor attrition over the last few years as his valuation models have kept him largely on the sidelines during the market's current bull market run. To paraphrase Keynes 'The markets can stay irrational longer than you can keep clients.'

We believe that successful investment management involves two key elements:

Systematically apply an evidence based approach to investments that maximizes return with minimal risk
All else equal, and with a clear understanding of investors' behavioural flaws, apply a strategy with the highest probability that investors will stick with it over time

avoid large drawdowns to reduce emotional decision making based on fear
participate in major bull markets to reduce emotional decision making based on greed

There are several approaches that embrace these two broad qualities, but our preference is toward strategies that leverage momentum and volatility management. These techniques are practiced with demonstrable results by the best trend following managers, but we'd like to think our Adaptive Asset Allocation program represents another attractive alternative.

Don't Take Our Word For It

2012-12-19T13:35:00.000-08:00

"It is difficult to get a man to understand something, when his salary depends upon his not understanding it!" Upton Sinclair

Long-time readers will know that we periodically publish a statistical forecast for U.S. stock market returns over horizons from 5 to 30 years, which we generate from a variety of long-term valuation metrics. We were motivated to conduct this analysis because we observed an enormous amount of misunderstanding and misinformation in estimates quoted in various media sources, which largely serve to protect the interests of equity managers and investment firms whose livelihood relies on equity enthusiasm.

A handful of trustworthy buy-side firms consistently publish similar forecasts based on their own analyses, and there has been a flurry of reports lately, so we thought we would summarize the findings of others who have investigated this topic so that readers don't have to just take our word for it.

Chart 1. below summarizes the forecasts of several firms or independent analysts based on papers published in the last month or so. Since few investors invest purely in stocks, we used large cap stock market forecasts as well as the current yield on the Barclays U.S. Aggregate Bond Index, and the most recent inflation expectations reading from the Cleveland Fed's model to create a real forecast for a U.S. 60/40 balanced portfolio. AQR actually published a balanced fund forecast independent of its stock market forecast, so we used their estimate directly.

Chart 1. Forecast total real returns to a U.S. 60/40 balanced portfolio over the next 7-10 years, annualized

Sorry folks, but good stock picking won't meaningfully alter this conclusion. But don't lose hope - we may have an answer.

The following reports were sources for Chart 1, and we would encourage you to read them all.

GMO forecast

AQR forecast

Hussman forecast

Gray forecast

Pimco forecast

BPG forecast

Tactical Alpha: The Case for Active Asset Allocation

2012-12-03T20:01:00.003-08:00

Patients with certain brain injuries often do not recognize their own limbs on one side of their body; they often wake up alarmed at the presence of an arm or leg in the bed next to them on one side of their body, which they do not recognize as their own. The name of this condition is hemispatial neglect, and it pertains to a person's awareness about one half of their field of view. Sufferers also often ignore words on one side of a page, eat the food only on one side of their plate, or render incomplete drawings of objects or faces.

The human brain is an incredible puzzle, but conditions like this may offer clues to the mystery of why investors systematically ignore over half of the opportunity to earn excess returns in markets. Despite countless studies showcasing the absence of persistent alpha in the security selection domain, and the overwhelming improbability of identifying alpha generators in advance, the vast majority of active investors continue to flock to traditional active management in pursuit of elusive excess returns.

Meanwhile, most investors remain inconceivably blind to the opportunity to generate excess returns through the other half of the active investment space - active asset allocation - despite a growing body of research suggesting this approach may be a source of substantial untapped 'tactical alpha'.

Many investors perceive that the opportunity to generate incremental excess returns is much higher in the security selection space than the asset allocation space because there are vastly more securities (i.e. stocks and bonds) than there are asset classes (i.e. stock markets and bond markets). This perception influences the relative priority placed on the pursuit of alpha from active security selection, relative to active asset allocation. This article will address this imbalance and provide compelling evidence that equal priority (at least) should be placed on generating excess returns from asset allocation, even at the expense of sacrificing active security selection.

For most institutions, the asset allocation decision and the security selection decision embody a tradeoff. This is due to the structural frictions embedded in the use of external managers employed in an attempt to 'beat the benchmark' through active security selection in a specific market.

Unfortunately, institutional investors' ability to move dynamically in and out of asset classes is constrained by the allocation and redemption policies of these traditional investment managers, such that agile rotation among and between markets and asset classes is difficult on shorter term horizons of, say, less than one year. For this reason, institutions that embrace the ability of managers to deliver alpha through security selection will necessarily sacrifice their ability to extract value from a more dynamic asset allocation process.

Market inefficiencies exist for a variety of reasons, such as asymmetric information, tax frictions, and emotional biases, but perhaps the most economically significant inefficiencies stem from structural constraints imposed on a large segment of investors. We view the structural bias in favour of security selection alpha vs. tactical alpha as an important example of this type of constraint. As a result, we assert that tactical alpha - active asset allocation - represents one of the most economically important sources of excess returns available to investors in public markets.

The next sections will review salient research contributions in the field of performance attribution related to active asset allocation versus active security selection. Our objective is to demonstrate the importance of active asset allocation as a source of potential excess returns, and persuade progressive investors to allocate more capital and resources to this objective, even if that means scaling back their commitment to the pursuit of traditional sources of alpha.

We will also add to the existing research with a novel examination of the unconstrained potential to extract excess returns from asset allocation vs. security selection using a normative quantitative approach.

Shoulders of Giants

Most studies in this area focus on analysis of pension funds and mutual funds, and explore the degree to which total portfolio return is explained by deviations from an institutions' policy asset class weights. Portfolio returns are the aggregation of the returns to the policy portfolio and 'active returns', which in most studies is defined as the residual not accounted for by the policy portfolio.

For example, Brinson regressed monthly portfolio total returns for pension funds against the monthly returns to each funds' policy portfolio, and determined that the policy portfolio explains 90% of the monthly variability in total returns. While this analysis is helpful, as it illustrates the impact of asset allocation on long-term portfolio performance, it does not allow us to determine the underlying factors that drive the unexplained 10% of returns. Further, it was highlighted by future studies, including the Kaplan study we describe below, that in fact the majority of monthly pension fund performance can be explained by the fund's decision to invest in capital markets at all, vs. holding cash.

Kaplan and Ibbotson added a second dimension to the analysis by exploring the degree to which fund policy weights explained the cross-sectional differences in total returns across a basket of funds over a ten year investment period. The purpose of the cross sectional analysis was to analyze the degree to which differences in policy weights explained the difference in the total return between funds. They discovered that asset allocation policy explained 40% of the difference in the total return across funds over the full period, and asserted that the residual difference was some combination of, "asset class timing, style within asset classes, security selection, and fees", and that for pension funds it was also attributable to manager selection.

Many people thought that the Brinson studies analyzed the proportion of fund total performance that was attributable to each funds' policy portfolio weights, rather than analyzing the proportion of fund variance. Kaplan and Ibbotson answered this question too, using the original Brinson data as well as the data from their own later studies. Table 1 summarizes their results.

Table 1. Percentage of Total Return Level Explained by Policy Return

Source: Kaplan and Ibbotson (2000)

The average across all studies is 104%. Some readers may find this measure confusing. How can asset allocation explain greater than 100% of total returns?

Remember that the total return to the funds in the studies was equal to the sum of the total return to the funds' policy portfolio using asset class benchmarks, plus the active return, minus trading frictions. So the results of this study demonstrate that, over the periods studied in the analyses, the average institutional investor lost 4% of total return to fees, ineffective active management, or poor manager selection. Given the asset allocation constraints on most institutions, the vast majority of this return decay was a result of poor security selection.

This begs the questions:

Why do investors continue to seek excess returns from active security selection?
Is there another source of active returns

Free from Constraints

Unfortunately, neither the Brinson nor the Kaplan/Ibbotson studies explored the degree to which the variability of returns was due to active asset allocation bets versus active security selection bets. Fortunately, Assoé, L'Ehr and Plant [ALP] (2006) performed an analysis, modeled after Kritzman and Page (2003), that applied a creative approach to answer this exact question. ALP used a normative framework rather than an empirical framework like that embraced by Brinson, Ibbotson and Kaplan, in which the potential returns in each quarterly period from 1985 - 2005 were explored for a large set of constrained, randomly generated asset class portfolios and security portfolios.

In the ALP analysis, benchmark weights were assigned for a theoretical fund that included cash (5%), bonds (30%), stocks (40%), real estate (10%), private equity (10%), and commodities (5%). At the start of each annual period, 100 draws were made from the asset pool according to the above proportions, with each draw representing 1% of the final portfolio for that year. The returns to the random portfolio are then computed for each quarter of the subsequent year, after which a new random portfolio is constructed in the same way for each year from 1985 through 2005. Then this process is repeated 10,000 times, with each repetition representing one sample portfolio.

The purpose of this procedure is to generate a large sample of possible portfolios generated exclusively from small changes to the asset allocation around prescribed weights. To this end the dispersion of portfolio returns is due exclusively to changes in the asset allocation, as opposed to the other variables cited in the Kaplan and Ibbotson study.

A similar procedure is used to generate stock portfolios from a long-term S&P 500 stock dataset. In this case stock portfolios are created at the start of each year by randomly selecting 100 stocks, where any given stocks' probability of inclusion at each random draw is equal to the stocks' current weight in the index. This procedure is also repeated 10,000 times over the entire 20 year investment period.

Chart 1. describes the dispersion between the 95th and 5th percentile portfolios in each quarter over the investment horizon for the asset allocation portfolios and the stock selection portfolios. Note that the paper asserts that the average annualized dispersion between 95th and 5th percentile portfolios over the entire sample is equivalent for asset allocation and security selection, suggesting that in aggregate asset allocation and security selection provide equal opportunities to add value in an active portfolio management process.

Chart 1. Relative importance of asset allocation and security selection: difference between the 5th and 95th percentile quarterly performance

Source: Assoé, L'Ehr and Plant (2006)

ALP suggest that the results above reveal 3 important takeaways from the analysis. Directly from the paper:

the relative importance of asset allocation and security selection is time-dependent;
the asset allocation driven dispersion is more volatile than the security selection induced dispersion
the security selection activity generates as much dispersion in active return as asset allocation so that it cannot be unequivocally declared that one activity is structurally more or less important than the other

We would add a few other observations from this analysis. First, the paper deliberately constrains the allocations to the six asset classes by weighting them in the asset 'pool' according to a typical institutional weighting scheme. While this assumption is consistent with the decision-making latitude of traditional institutions, which are dominated by traditional consulting relationships, it does not allow the analysis to account for the full opportunity set offered by an unconstrained asset allocation decision, such as the opportunity set available to CTAs or unconstrained asset allocators seeking tactical alpha.

Second, the equity weights are constrained by weighting them in the equity 'pool' according to the market cap weighting in the S&P500. True active managers, especially outside the traditional mutual fund space, would take considerably more latitude in selecting stocks, and even traditional managers are beginning to accept the large amount of research demonstrating the long-term superiority of an equal weight basket over the typical market capitalization weighted approach.

Third - and this is the major focus of the rest of this article - the authors do not seek to explore the cause of the time-varying nature of the relative value of asset allocation vs. security selection. From Chart 1 we can see that at times the asset allocation contribution dominates the contribution of security selection, while at other times the reverse is true. What are the driving forces behind these time-varying shifts?

Asset Allocation or Security Selection: An Answer

Initially, our curiosity was peaked by This field has been plowed thoroughly over the years, first by Brinson et al., and later by Ibbotson and Kaplan, among others, but these pioneers left several important unanswered questions that the Staub and Singer article addressed.

This question is addressed by Staub and Singer in a paper entitled, 'Asset Allocation vs. Security Selection: Their Relative Importance', published in the CFA Journal (2011). The following is from the abstract:

Various researchers have investigated the importance of asset allocation versus security selection. Although we think this question is conceptually weak—because asset allocation and security selection have different missions—we address it to ensure appropriate quantitative treatment. We focus on feasibility rather than on what managers actually do. Hence, our approach is free of benchmark thinking and makes no assumptions regarding portfolio positions or potential constraints.

We have emphasized the final sentence because it addresses the issues we raised above regarding the constraints applied in the ALP paper.

At core, Staub and Singer assert that the only information required to determine the contribution of any asset class to standardized portfolio returns is the correlation matrix. This is because the magnitude of contribution is purely a function of leverage; an asset with a low ambient volatility can be scaled up and down at will. As such, the authors examine a correlation matrix composed of the following levels of grouping:

The investment decision: invest in risky assets vs. holding cash
Asset classes
Geographic markets within each asset class
Securities within each geographic market

Note that the decision to invest in risk assets vs. cash invokes the basket of risky assets, which in turn consists of different geographic markets within each asset class. Finally, each market contains individual securities. In this way, each layer of portfolio decision has a cascading impact on more granular sets of assets down the chain.

Further, the authors assume the following:

There are 20 independent stock markets and 20 independent bond markets
Each independent market is composed of 100 securities

Broadly, this decision tree describes the opportunity set for most large institutions, at least among the portion of their portfolios that is allocated to traditional asset classes (stocks and bonds).

Finally, the paper establishes stable correlation estimates between each security category and market, which quantify the impact of decisions in one layer on the constituents of other layers of the investment process.

• stocks in a national market have a correlation of 0.50,

• bonds in a national market have a correlation of 0.80,

• stocks of different national markets have a correlation of 0.40,

• bonds of different national markets have a correlation of 0.60,

• stocks and bonds of the same national market have a correlation of 0.30, and

• stocks and bonds of different national markets have a correlation of 0.20.

With these assumptions in place, the authors use a powerful statistical technique (Principal Component Analysis) to identify the explanatory power of each dimension of standardized portfolio returns, with the following results:

Chart 2. Cumulative eigenvalues for 'layers' of investment decisions

Source: Staub and Singer, 2011

You can see that, with the authors' correlation assumptions, 65% of potential portfolio standardized returns are explained in aggregate by the investment vs. cash decision; the asset allocation decision; and the market selection decision. The remaining 35% is derived from individual security selection decisions.

The Impact of Changing Correlations

The Staub and Singer paper offers a clue about what drives the time varying nature of the relative importance of asset allocation and security selection observed in the ALP paper: the relative correlation between assets, markets, and securities. But of course correlations are not static, as implied in Staub and Singer.

Our contribution to this discussion then, is an analysis of how changes in the correlations between asset classes (stock and bond markets), and between individual securities, affects their relative contribution to portfolio returns.

To perform this analysis, we used exactly the same procedure as laid out in Staub and Singer, except that we repeated the analysis for a variety of different estimates of correlation. We focused specifically on how the standardized portfolio return attribution changed as we changed the correlation between stock and bond markets, and varied the correlation between individual stocks, on a domestic market.

In contrast with ALP, and consistent with Staub and Singer, we applied no constraints to the analysis. An unconstrained analysis more effectively reveals the true opportunity set available to managers who pursue tactical alpha as well as traditional alpha.

We varied the correlation between domestic stocks and bonds from -1 to 1 to reflect the fact that stocks and bonds are sometimes highly correlated, sometimes highly negatively correlated, and sometimes exhibit no correlation at all, as evidenced by Chart 3. In contrast, domestic stocks do not in practice ever exhibit average correlations less than 0 (see Chart 4.), so we varied this coefficient between 0 and 1.

Chart 3. 60-day rolling correlation between stocks and bonds

Source: Yahoo finance

Chart 4. Implied correlation between S&P 500 stocks

Source: CBOE

Matrix 1. below reproduces the Straub and Singer analysis for each stock/bond and stock/stock correlation combination along the spectrum for each described above. For clarity, the number in each cell equates to the total amount of standardized portfolio variance that is cumulatively attributable to the invest/cash, asset class, and market choice opportunities. The balance (1 - the percentage in the cell) is attributable to the security selection opportunity.

Matrix 1. Sensitivity of potential standardized return attribution from active asset allocation vs. active security selection to changes in correlation estimates

Source: Butler|Philbrick|Gordillo & Associates, JP Belanger (Quantum Financier)

We highlighted two values in circles: the green circle highlights the value that corresponds with current measures for stock/bond and stock/stock correlations per Charts 3. and 4. Note that at current estimates for intra- and inter-market correlations, about 73% of potential portfolio variance is explained by asset allocation. The red circle corresponds to the long-term average measures for the same correlations over the 2004-2012 period, again per Charts 3 and 4., suggesting that on average asset allocation accounts for 69% of potential alpha, while security selection offers just 31%.

From Charts 3. and 4. above, and corresponding cells in Matrix 1. below, it would therefore appear that we are currently entrenched in a period where the asset allocation decision is of measurably greater importance than it has proven to be historically.

Future Directions

As discussed in the opening paragraph of this article, the question of whether to seek value from active asset allocation or traditional security selection is not a trivial one. This is because the decision to seek value through security selection is usually carried out through allocation to external managers with specialization in certain markets or assets. In order to carry out their active investment management process, these managers require that capital be committed for meaningful periods.

Unfortunately, this runs counter to the need for agility in asset allocation required to derive value from tactical asset allocation efforts.

This survey of asset allocation / security selection studies, and our group's own contribution to this important domain, serves to illustrate the relative importance of asset allocation in the pursuit of incremental risk-adjusted returns. Further, most institutions face structural, inertial and regulatory impediments to the implementation of meaningful asset allocation program. This means that there is a very large and economically significant opportunity for open-minded institutions that are willing to deviate from the status quo.

Investors who are interested in exploring active asset allocation strategies are invited to explore the following articles and papers:

Adaptive Asset Allocation: A Primer - Butler, Philbrick, Gordillo & Varadi
Using Factor Momentum to Optimize GTAA Portfolios - QUSMA
Relative Strength Strategies for Investing - Faber
Applying Value and Momentum Across Asset Classes in a Quant TAA Framework - Wang
Value and Momentum Everywhere – Asness, Moskowitz, & Pedersen
Modern Tactical Asset Allocation – de Silva
A Factor Approach to Asset Allocation – de Silva
Global Tactical Asset Allocation: Exploiting the opportunity of relative movements across asset classes and financial markets – Potjer & Gould
Global Tactical Cross-Asset Allocation: Applying Value and Momentum Across Asset Classes - Blitz & Van Vliet
Advanced Theory and Methodology of TAA – Lee

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Links to other websites or references to products, services or publications other than those of Macquarie Private Wealth Inc.(MPW) on this website do not imply the endorsement or approval of such websites’ products, services or publications by MPW. MPW makes no representations or warranties with respect to, and is not responsible or liable for, these websites’ products, services or publications. Macquarie Private Wealth Inc. is a member of Canadian Investor Protection Fund and IIROC.

Equity Portfolio Optimization with Factor Tilts

2012-11-20T08:47:00.000-08:00

Abstract

A variety of techniques are applied to improve upon passive capitalization weighted equity market portfolios via intelligent integration of the four equity market factors introduced by Fama, French and Carhart. In consideration of structural and regulatory constraints imposed upon most investment practitioners, long-only factor tilt portfolios are substituted for the traditional long-short factors, which facilitates simple implementation of techniques using liquid Exchange Traded Funds. Factor tilt portfolios are assembled using equal weight, equal volatility weight, risk parity and minimum variance optimizations, and simple filters are introduced to reduce turnover and commensurate trading frictions. Finally, a simple but prospective balanced portfolio framework is proposed.

Introduction

There has been a cluster of papers recently about factor allocations as an addition to the traditional asset allocation framework. We believe the market cap, small cap, and value equity factors described by Fama and French (1992), as well as the momentum factor identified by Jagadeesh and Titman (1993) and eventually specified by Carhart (1997), represent mildly interesting diversifiers for portfolios in certain contexts. However, many institutions are increasingly interested in how to intelligently allocate to these factors to improve the risk-adjusted performance of their equity portfolios. This led us to explore optimal allocation methods.

Sharpe introduced the first equity factor, sometimes called ‘market beta’, in 1964 when he described the Capital Asset Pricing Model (CAPM). The CAPM model was meant to explain the degree to which market returns to stocks were a function of non-diversifiable risk; stocks with higher non-diversifiable risk were theoretically presumed to possess a possess a higher required rate of return in order to compensate for the extra risk of owning them. Fama and French extended the model in 1992 to describe the excess returns observed in small capitalization stocks, and ‘value’ stocks, the latter which was defined by stocks’ price to book ratio.

In Fama’s and French’s initial tests it was observed that stocks with low market capitalizations delivered higher returns than their large capitalization counterparts. It was also observed that stocks with high book values relative to their market values offered higher returns than stocks with low book to market ratios. Further, these performance anomalies could not be completely explained by higher market betas associated with the factor portfolios.

In 1993 Jagadeesh and Titman published research on the momentum factor, which they defined as a stocks’ 12 month historical return, with a lag of one month. They found that stocks that delivered high returns over the past 12 months (with a 1 month lag) tended to outperform over the next month; this worked in reverse as well, such that stocks with poor performance in the recent past tended to underperform over the next month.

While the low volatility anomaly was noted in the literature as far back as 1977 (Miller, 1977), Miller first published exclusively on the low volatility anomaly in 2001. Additionally, Eric Falkenstein submitted his dissertation on the phenomenon in 1994, but it seems the academic community was not ready to accept a theoretical framework that effectively repudiated the CAPM at the time. As a result, his findings were never published. However, the seminal work on this factor seems to belong to Ang, Hodrick, Xing and Zhang (2006) with their examination of U.S. stock markets, while Baker and Haugen (2012) confirmed Ang et al.’s results in all major international equity markets earlier this year.

Robeco provided a superb summary of the observed magnitude of the above anomalies in a 2011 paper, Strategic Allocation to Premiums in the Equity Market, from which we copied the table below.

Source: Robeco

These are not inconsiderable premiums considering that they represent simple, persistent, systematic techniques that anyone can apply. This is especially true now that there are liquid ETFs that effectively capture these factors that anyone can use in portfolios:

• Small-cap stocks: IWM (cap weighted) and EWRS (equal weight)

• Value stocks: IVE (S&P 500), IWD (Russell 1000), PRF (FTSE RAFI)

• Momentum stocks: PDP (all-cap), HMTM (large-cap), SMTM (small-cap)

• Low Volatility: SPLV (volatility weighted), LVOL (volatility weighted)

In contrast to most academic factor investigations, this paper will focus on the same long-only versions of the factors described in the Robeco paper, as most practitioners encounter structural or regulatory barriers to shorting. Further, we would argue that short factors should be disaggregated from long factors, as long and short factors often 'work' at different times, and long-only factors display more persistence in practice.

This article will explore factors in a variety of asset allocation frameworks; we will introduce the factors individually and then see if we can create a better passive 'equity' basket, and extend this concept to create a better 'balanced' portfolio.

Factor Charts

To get us started, we have published below the charts and summary statistics for each of the major long-only factor tilts listed above. For all factors except the low volatility factor we sourced the data from Ken French's database. We used the S&P Low Volatility Index Total Return series for the low volatility anomaly. As the Low Vol data only goes back to 1991, the charts go back to 1992 in order to provide a year of 'priming' for the asset allocation overlays that we will introduce in later posts.

Large Cap Stocks

Source: Ken French database, 2012

Small Cap

Source: Ken French database, 2012

Large Cap Value

Source: Ken French database, 2012

Large Cap Momentum

Source: Ken French database, 2012

Large Cap Low Volatility

Source: Standard and Poor’s, 2012

Equal Weight

The obvious next step in our exploration is to determine how well the factors work together in a portfolio. To answer, we first ran an equal weight factor tilt portfolio, rebalanced quarterly with data back to 1992:

Five Equity Factors, Equal Weight, Rabalanced Quarterly

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Equal allocations to long-only factor tilts improve what is essentially a long-only beta portfolio (the Fama French Large Cap portfolio) by about 2.25% in terms of CAGR, and offer slight improvements to volatility, drawdowns, and the frequency of positive periods. Of course, these improvements come at the expense of extra trading.

Equal Volatility Weighting

We have explored volatility management techniques at length in many prior articles (see here, here, here, here, and here for a few examples). Equal volatility weighted portfolios are constructed to target an equal volatility contribution by all assets in the portfolio, such that the portfolio is always fully invested. This requires that volatility be estimated for each asset going into every rebalance period; we use the 60-day observed historical volatility for all estimates in this article to be consistent with our other articles, though there is no particular significance behind using this lookback horizon.

Five Equity Factors, Equal Volatility Weight, Rebalanced Quarterly

Source: Ken French database, Standard & Poor’s, Yahoo Finance

This technique doesn't offer much improvement over simple equal weighting, in all likelihood because the factor tilts are all so highly correlated during periods of market distress.

Position Size Volatility Limits

In this variation on the theme of volatility management, factors are granted equal volatility weighting in the portfolio up to a fixed volatility contribution limit, in this case 1% daily. When any asset exhibits volatility in excess of its 1% limit, exposure to that asset is scaled back in favour of cash in order to maintain our prescribed volatility limit. In this way, total portfolio exposure is less than 100% during periods where individual positions are highly volatile.

5 Equity Factors, Equal Volatility Budgets (1% daily), Rebalanced Quarterly

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Setting position level volatility limits does improve risk-adjusted performance (see Sharpe ratio), in this case exclusively due to lower realized average portfolio volatility. More notably, drawdown is reduced by 40% because allocations are scaled back during the high volatility periods that are generally characterized by large drawdowns.

This technique does improve measurably with more active rebalancing, as evidenced by the results below based on a monthly rebalance schedule:

5 Equity Factors, Equal Weight Volatility Budgets (1% daily), Rebalanced Monthly

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Observe: A realized Sharpe over 0.6 with no tactical overlay at all.

While some might object to the large number of trades, in this case the number of trades is deceiving because most trades are small and nuanced in reaction to small changes in volatility. Further, by setting range-based rebalancing targets of 25% (that is, when any allocation target changes by 25% or more relative to its current allocation in the portfolio, the whole portfolio is rebalanced to new target weights), we can reduce turnover by 70% with no loss in performance.

5 Equity Factors, Equal Weight Volatility Budgets (1% daily), Rebalanced Monthly, 25% Filter

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Risk Parity

The risk parity concept merges precepts from equal volatility weighting at the individual asset level, and fixed volatility budgeting at the portfolio level, with the idea that lower volatility assets can be levered up to provide a similar return contribution to the portfolio as more risky assets while better balancing risk across the portfolio.

Risk parity requires a volatility budget to be set at the portfolio level; in this case, we maintain the same 1% daily target for portfolio volatility using 60 day realized volatility as the estimate for each asset, as well as for the portfolio in aggregate.

Note from the chart below that it is not possible to reach our volatility target without the use of leverage; the realized volatility of the un-levered version is just 13%.

5 Equity Factors, Risk Parity (1% daily), Rebalanced Monthly, 25% Filter

Source: Ken French database, Standard & Poor’s, Yahoo Finance

It is a simple thing to use traditional margin to reach our volatility target with up to 100% leverage (or a maximum portfolio exposure of 200%) when required during periods of low aggregate portfolio volatility.

Obviously this less constrained version provides better performance, adding 2% to annualized returns, with commensurately higher volatility but, perhaps surprisingly, almost no incremental boost in drawdown. The following simulation also includes a cost of margin equal to .5% above the t-bill rate, which is excruciatingly onerous, but we like to be conservative.

5 Equity Factors, Risk Parity (1% daily), Rebalanced Monthly, 25% Filter, Max 200% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Minimum Variance

Minimum variance algorithms strive to create optimal portfolios using the equations described by Modern Portfolio Theory, but with the objective of minimizing total portfolio variance rather than maximizing portfolio Sharpe. In contrast with standard mean-variance optimization therefore, minimum variance optimization does not require or use any return estimates, focusing instead exclusively on volatility and the covariance matrix.

The average correlation between momentum and value tilts over the past 20 years is 0.85; between value and low volatility, it is 0.82; and between momentum and low volatility it is 0.75. As a result, there is an opportunity to leverage the diversification between factors explicitly, a process for which minimum variance optimization is well suited.

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter

Source: Ken French database, Standard & Poor’s, Yahoo Finance

As with virtually all optimization procedures we have analyzed over the years, the minimum variance optimization is improved by overlaying a portfolio level volatility target. In this case we will use the same 1% daily target as in our risk parity example above.

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1%), Max 100% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

This seems to be quite a powerful combination. We have achieved a Sharpe ratio of 0.84 with a pure beta portfolio. Returns increase by almost 4% per year and drawdowns are reduced by 45% while volatility drops by 40%.

Adventurous beta seekers might wish to lever up the minimum variance portfolio at opportune times in order to actually achieve the target 1% daily volatility. If we set a maximum leverage factor of 100%, we achieve the following profile:

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1% daily), Max 200% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

A Better Balanced Fund

As a parting gift, we ran the minimum variance portfolio as the equity portion of a risk parity version of a traditional balanced portfolio, with a target volatility of 7% annualized (equal to the realized volatility of the 10 year Treasury over the same period), rebalanced quarterly.

5 Equity Factors (Minimum Variance) and 10-Year Treasuries, Risk Parity (7% annualized), Max 100% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Notice that, due to the lower volatility of the minimum variance factor tilt equity portfolio, and a low structural correlation between the factor portfolio and Treasuries, the realized volatility of this balanced fund is just 5.4% despite our 7% target. Of equal importance, the maximum drawdown for this portfolio is just 11.65% over the past 20 years!

Many prospectus mutual funds can carry up to 125% exposure under their mandates. If we raise the maximum exposure to accommodate this limit, we can get closer to our 7% target, with commensurately juicier returns.

5 Equity Factors (Minimum Variance) and 10-Year Treasuries, Risk Parity (7% annualized), Max 125% Exposure

Source: Ken French database, Standard & Poor’s, Yahoo Finance

Conclusion

Long-only factor tilt portfolios are very accessible by average investors using highly liquid Exchange Traded Funds. Equity factors appear to provide some diversification benefits in a portfolio context, and algorithms that explicitly account for portfolio level volatility and factor covariance can provide a very substantial boost to absolute returns while reducing portfolio risk.

Indeed, investors might wish to explore these techniques as interesting complements to existing equity allocations, especially in the context of a diversified balanced portfolio.

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Global CAPE Model Optimization

2012-10-18T10:32:00.002-07:00

Check out our new whitepaper, published in collaboration with Mebane Faber, and based on his recently published 'Global Value: Building Trading Models with the 10-Year CAPE':

Download it here.

Histogram of Rolling 20-Year Real Total Returns to U.S. Stocks

2012-10-18T10:23:00.001-07:00

The Permanent Portfolio Turns Japanese

2012-09-27T07:40:00.000-07:00

Our last few articles (here and here) dealt with the Permanent Portfolio, a widely embraced static asset allocation concept proposed by Harry Browne in 1982. To review, the simple Permanent Portfolio consists of equal weight allocations to cash (T-bills), Treasuries, stocks and gold to ward against the four major financial states of the world:

We can hear the chorus of protests about how cash is not a hedge against inflation. Tell it to the judge - by which we mean the only judge that counts - the evidence.

The following chart, taken from Ang's recent chapter on forecasting stock market returns, illustrates the correlation between inflation and the returns to cash and stocks over horizons from 1 month to 10 years. Note from the chart that equity returns in excess of cash (T-bill) yields are negatively correlated with inflation for at least 10 years after an inflation shock, while cash returns adapt quickly to changes in inflation.

Chart 1. Correlation of excess returns to cash and stocks with changes in inflation.

Source: Ang (2012)

The U.S. market has experienced at least three of the four states above since 1970. The 1970s was clearly a period of inflationary stagnation (stagflation), where commodities, gold and extremely short-duration bonds were the only sources of positive returns. This was followed by an intense and prolonged period of disinflationary growth from 1982 through 2000 which saw U.S. stocks compound at rates above 15% annualized for almost two decades. Long duration Treasury bonds also performed very well in this period as rates dropped from 15% in 1981 to 5% in 2001.

After 2000, aggressive central bank priming succeeded in creating a period of inflationary growth which ended in the Great Financial Crisis of 2008. This period was dominated by commodities, gold, and the markets of those emerging economies that benefited from high commodity prices.

We have no confidence whatsoever in defining the state of current markets, though we suspect we may experience a period of deflationary stagnation in the intermediate term before all is said and done.

Periods of deflationary stagnation are (so far) quite uncommon in the modern era, and especially among developed economies for which we have accurate and granular data. The one prominent standout is, of course, Japan which began its period of deflationary stagnation in 1990 after the coincident bursting of the Japanese banking, stock and property bubble.

Japan as a Deflationary Case Study

Deflation is a period of falling prices, and Japan offers plenty of examples of this phenomenon over the last 20 years or more. As seen in Chart 2 below, commercial real estate prices experienced the most profound bubble, rising by almost 4x from 1985 through 1990, but residential real estate also tripled in price over the same period. Over the subsequent 22 years, commercial property collapsed to half the value it went for in 1985, and residential real estate currently goes for about the same price it went for almost 30 years ago.

Chart 2. Japanese Real Estate Prices, 1985 - 2010

Source: japaninvestor.net

The story of the Japanese stock market is now very well known. Japanese stocks (Nikkei) dropped almost 80% from 1990 through their interim bottom in 2003, and then dropped further to their bottom in early 2009. Total returns to Japanese stocks over the period were -5.29% annualized, for a total return of -71% through June 29, 2012.

Chart 3. Nikkei total return, 1990 - 2012

Source: Data from Bloomberg

Despite the best efforts of the Bank of Japan to debase their currency (and re-inflate asset prices) through extensive quantitative easing over the past 20+ years, the Yen has appreciated strongly, moving from almost 160 yen to 1 U.S. dollar in 1990 to under 80 currently (i.e. one dollar can purchase half as many yen today as in 1990, so the yen has doubled in value vs. the dollar).

Chart 4. Number of Japanese yen to 1 U.S. dollar

Source: FRED database

The strength of the yen has complicated efforts to diversify into alternative global asset classes, which are mostly denominated in dollars. The following chart (Chart 5.) of gold in yen highlights this challenge for Japanese investors. While gold's strength since 2000 has swamped yen strength, investors endured a 57% drawdown over the first 10 years, and did not break even on their investment until 2005!

Chart 5. Gold priced in Japanese Yen

Source: Data from Bloomberg

The Permanent Portfolio Turns Japanese

Intuitively, given the poor performance of Japanese stocks; extremely low short term interest rates over much of the last 15 years, and; yen strength eating into dollar denominated assets like gold, the Japanese Permanent Portfolio was not nearly as fruitful as the U.S. version.

Note: The daily total return data for Japanese asset classes that we use in this analysis deviate somewhat from other similar studies of the Japanese Permanent Portfolio that we've seen. While we have done our best to source and, in the case of interest rate indices, transform the data appropriately, the absolute performance numbers of the strategy are, in our opinion, less important. Rather, we are much more interested in validating (or not) the risk management techniques we proposed in our earlier Permanent Portfolio Shakedown Part II, in the context of a Japan's very different market environment.

Chart 6. Simple Permanent Portfolio Japan

Source: Bloomberg

Clearly the Japanese Permanent Portfolio (PP) delivered much better total returns over the past 20 years than the Japanese stock market on its own, and indeed performed better than the traditional Japanese 50/50 stock bond portfolio that we explored in great detail in Rebalancing Japan.

Volatility Management

In examining the impact of volatility management on the Japanese Permanent Portfolio, we will follow the same investigative trajectory that we followed in our original Permanent Portfolio Shakedown Part II for the next series of case studies. Note that, while the original Japanese PP exhibited an average volatility of about 8% annualized, we will stick with 7% portfolio volatility targets in order to be consistent with the original U.S. based articles.

As a reminder, we target portfolio volatility by measuring the volatility of the portfolio at each rebalance period, and adjust total portfolio exposure lower if observed volatility is too high by substituting t-bills. The first case maintains equal portfolio exposure to all four assets, but reduces pro-rata exposure in response to expanding portfolio volatility.

Chart 7. Simple Permanent Portfolio Japan, 7% target volatility, rebalanced monthly, 1992 - 2012

Source: Bloomberg

In our experience, the primary utility of managing portfolio volatility to a target is a reduction in drawdowns and increase in Sharpe ratio, with a very small sacrifice to absolute returns. The Japanese PP outcome is consistent with this observation, as Sharpe ratio increases slightly while drawdown drops substantially to 13% from 22%.

Risk Parity

The next step is to migrate to an equal volatility allocation instead of the equal capital allocation example in Chart 7.

Adherents to the risk parity philosophy aim to create portfolios where each asset class contributes an equal amount of volatility to the portfolio rather than an equal amount of capital. Chart 5. approximates a risk parity approach using stocks, gold and Treasuries, with a 7% risk target. The T-bill allocation is dynamic where cash expands and contracts in the portfolio in order to keep the portfolio volatility close to our 7% target.

Chart 8. Simple Permanent Portfolio Japan, Risk Parity, 7% target volatility, 1992 - 2012

Source: Bloomberg

The Risk Parity overlay delivers a substantial uptick in performance and portfolio stability, as evidenced by the more consistently upward sloping equity line. Absolute portfolio performance increases substantially, as does the Sharpe ratio, which is double the Sharpe of the original portfolio. Higher returns are accompanied by a lower drawdown as well, under 12%. Risk Parity also improves the percentage of positive rolling 12-month periods, which we take very seriously as a measure of consistency.

The large improvement from Risk Parity is clearly the result of the fact that risk parity approaches tend to greatly overweight bond positions, given the low volatility of bonds relative to stocks and gold. Japanese bonds were the best performing of the four asset classes over the period.

Tactical Approaches

To repeat from our original article:

The potential problem, as we see it, with any static asset allocation, including the permanent portfolio's permanent equal weight allocations to stocks, bonds, gold and cash, is that sometimes everything is expensive all at once, and returns to all asset classes have the potential to be low or negative in tandem. The current environment may represent one of these periods, where certainly bonds and cash are more expensive than they have ever been, with yields on Treasuries lower than at any other time in the last 220 years (source: Bank of America). Cash yields essentially zero. We think stocks are expensive as well (see here andhere), and gold is at best a wildcard, having rallied by 500% or more from its lows in 2001.

If we are right, and the permanent portfolio is vulnerable to synchronized losses, then it makes sense to explore some tactical or dynamic overlays to help avoid investing in asset classes in sustained downtrends.

Mebane Faber is credited with bringing moving averages to the masses with his Quantitative Approach to Tactical Asset Allocation whitepaper in 2005. In it, he describes an approach that applies a 10-month moving average to basket of 5 asset classes: stocks, Treasuries, commodities, REITs and international stocks. While there is nothing magical about the 10-month moving average, this approach is ubiquitously cited elsewhere, and in our testing we observed no material difference with other moving averages. The following simulations apply monthly rebalancing.

Chart 9. Simple Permanent Portfolio Japan, 10-Month MA, 1992 - 2012

Source: Bloomberg

The 10-month moving average overlay does improve absoute returns and volatility, but at the expense of a larger drawdown, which is higher even than the 22% drawdown experienced by the original Japanese PP.

The last approach marries Faber's tactical overlay with a portfolio risk target of 7%. This approach delivered the best risk-adjusted performance for the U.S. model, so we were quite interested in how it would work in Japan.

Chart 10. Simple Permanent Portfolio Japan, 10-Month MA, 7% Target Volatility, 1992 - 2012

Source: Bloomberg

The target volatility technique performs similar magic in Japan as it did for the U.S. PP, though the absolute numbers are still not nearly as good. Returns of 5% annualized are 40% higher than the original Japanese PP portfolio, and risk-adjusted returns are more than double, with a Sharpe of 0.77 compared with the original portfolio's .37. Drawdown drops to a tolerable 13.7% from 22%.

Conclusion

The Japanese experience has clearly been very different from the U.S. experience over the past 20 years, as Japan has endured a persistent period of deflationary stagnation while the U.S. has so far experienced growth of both the deflationary and inflationary variety. This has had a profound impact on Japanese stocks and bonds, as well as the yen, which in turn impacted returns to Japanese investors from foreign assets like gold.

That said, the traditionally implemented Permanent Portfolio would have served Japanese investors much better than stocks on their own, or even a balanced stock/bond portfolio over the past 20 years, with double the Sharpe ratio, higher returns, and much lower drawdowns.

Consistent with our findings in the U.S., techniques that manage the volatility of the individual portfolio holdings and/or target a total portfolio volatility delivered similar or better returns, and for the most part much lower drawdowns. The Risk Parity and Tactical approach with target volatility delivered the highest, most consistent returns with the lowest drawdowns.

Overall, passive Japanese investors were better served by the Permanent Portfolio than other traditional asset allocation models over the past 20 years, but even the best tactical and risk management overlays could only produce returns of about 5% per year. U.S. and other international investors might wish to consider this potential outcome in the context of retirement or institutional funding needs.

Permanent Portfolio Shakedown Part II

2012-08-27T08:11:00.001-07:00

In Part I of the Permanent Portfolio Shakedown we investigated the history of the approach, tracing it back to Harry Browne in 1982. The company he helped to found, The Permanent Portfolio Family of Funds, has been running their version of the strategy in a mutual fund for almost 30 years, with fairly impressive results.

Harry's thoughts about the portfolio are worth repeating in this second instalment:

Established in 1982, in an era of stagnant economic growth and rampant inflation, Permanent Portfolio seeks to provide a sound structure and disciplined approach to asset allocation. The Fund was born in an environment where investors didn’t know where to turn. Regardless of what an investor did, they were losing money. Harry Browne, one of the founders of the fund stated, “It’s easy to think you know what the future holds, but the future invariably contradicts our expectations. Over and over again we are proven wrong when we bet too much on our expectations. Uncertainty is a fact of life.” No one can accurately predict the future.

[The] Permanent Portfolio recognizes this limitation and seeks to invest a fixed “Target Percentage” of its assets to six carefully chosen, diverse and “non-correlated” investment categories. Such diversification in a single mutual fund seeks to mitigate risk regardless of the economic climate. [Emphasis ours]

Harry's critical revelation was that no amount of knowledge about markets or economies will enable an investor to accurately see into the future, so investors should balance portfolios between diversified asset classes to 'mitigate risk regardless of the economic climate'. This is consistent with the broad intention of Ray Dalio's 'All Weather' portfolio and the 'Risk Parity' paradigm he spawned, with important differences that we will address later in this article.

Later in his career, Harry suggested that a permanent portfolio could be constructed very simply with equal allocations to stocks, Treasuries, t-bills and gold. We explored this simple mix in Part 1 to discover how well this portfolio has done since 1970 relative to other common allocation strategies, such as 60/40, and discovered that the 'Simple Permanent Portfolio' approach has delivered relatively impressive results over the past 40 years.

Simple vs. Complex Permanent Portfolio

The Permanent Portfolio Family of Funds has been running their Permanent Portfolio mutual fund since 1983, so we wanted to explore the performance of the actual fund versus the simple version since the fund's inception. The Permanent Portfolio Family of Funds only provides annual returns to the mutual fund since inception, so the chart reflects annual returns to both approaches.

Chart 1. Permanent Portfolio mutual fund (PRPFX) vs. Simple Permanent Portfolio

Source: Permanent Portfolio Family of Funds, Ken French, Shiller, FRED

You will note visually that the simple portfolio tracks the mutual fund quite well, and indeed the correlation between them is 0.70 over the period, which suggests that the simple portfolio explains about 50% of the returns to the mutual fund over the period. PRPFX had a miserable year in 1984, losing about 13% that year while the simple portfolio held in with a return that year of about 4%, but PRPFX made up for it from 2002 - 2007 with substantially higher returns than the simple portfolio, perhaps because of its exposure to real estate.

The annualized returns to the fund are 6.8% vs. 7.8% for the simple version, but this difference would be accounted for by the fund's 0.76% MER and the fees one would incur to purchase the indices in the simple portfolio in ETF form. After accounting for this, the returns are effectively the same. The volatility of the simple portfolio is lower however, at least using annual return data. PRPFX has a realized annual volatility of 8.3 vs. 5.3 for the simple version, which means the return/risk ratio is lower for the mutual fund: 0.82 vs. 1.45.

The rest of this article will utilize daily long-term data for each of the four asset classes in the simple version of the approach going back to 1970. The simple permanent portfolio delivered the following return and risk profile going back to 1970 (a review from Part 1). You will note annualized returns of 8.55%, a return/volatility ratio of 1.25, and a maximum drawdown of about 18%, with 93% of rolling 12-month periods delivering positive nominal returns (right bottom corner of data table). We will benchmark all subsequent tests against this basic profile.

Chart 2. Simple Permanent Portfolio, rebalanced quarterly, 1970 - 2012

Source: Ken French, Shiller, FRED

Volatility Management

The Permanent Portfolio approach has a faithful following, and for good reason, but we are going to risk introducing a few simple overlays to the basic approach in an effort to improve risk adjusted returns.

The most obvious first step, at least for us, is to introduce a volatility management overlay to maintain a consistent risk profile in all market environments. In our experience, we have yet to examine a portfolio management approach where the return/risk profile is not improved by intelligent volatility management.

The long-term ex-post observed volatility of the basic simple permanent portfolio is 7%, so we will use this target to actively manage the portfolio volatility using the exact same 25% capital allocation to each of the four asset classes. As a reminder, we target portfolio volatility by measuring the volatility of the portfolio at each rebalance period and adjusting total portfolio exposure lower if observed volatility is too high by adding cash.

Chart 3. Simple Permanent Portfolio, 7% target volatility, rebalanced quarterly, 1970 - 2012

Source: Ken French, Shiller, FRED

The volatility targeting approach seems to add some value, raising returns from 8.55% to 8.8% annualized, and reducing the maximum drawdown to 12.4% from 18%, or about one third. This seems like a simple, coherent, and intuitive improvement that is worthwhile implementing.

Risk Parity

Risk Parity proponents will protest that the current incarnation of the simple approach has a massively skewed risk profile. Chart 4. shows the return and risk contributions for each of the 4 asset classes in the basic equal weight approach - you may have to click on the image for a readable version. IRX is the t-bill (cash) index.

Chart 4. Marginal Return and Risk contributions 1970 - 2012

Source: Ken French, Shiller, FRED

You can see that stocks and gold (VTILT and GLDLT respectively) contribute about 5x - 8x as much marginal volatility to the portfolio as Treasuries (IEFLT), though they only contribute about 25% more returns.

The marginal risk contribution accounts for the risk each asset contributes to the portfolio after accounting for the asset's diversification potential. While Treasuries are structurally less volatile than stocks or gold over the long-term, they also provide stronger diversification than either stocks or bonds within the portfolio. As a result, Treasuries 'hit above their weight class' in the portfolio in terms of the diversification they provide relative to the risk they introduce. This explains why the marginal risk contribution of stocks and gold is greater than either's proportional volatility, while the risk contribution of bonds is lower than bond's proportional volatility.

Adherents to the risk parity philosophy aim to create portfolios where each asset class contributes an equal amount of volatility to the portfolio rather than an equal amount of capital. Chart 5. approximates a risk parity approach using stocks, gold and Treasuries, with a 7% risk target. The cash allocation is dynamic where cash expands and contracts in the portfolio in order to keep the portfolio volatility close to our 7% target.

Chart 5. Simple Permanent Portfolio, Risk Parity, 7% target volatility 1970 - 2012

Source: Ken French, Shiller, FRED

The 7% target volatility risk parity version above delivers similar returns to the traditional simple approach, with 13% lower volatility and 35% lower drawdown. However, the ex-post allocation to cash at a 7% volatility target is just 8%. In order to have a 25% average allocation to cash over the period, in keeping with the traditional simple approach, we need to apply a 5% risk target instead.

Chart 6. Simple Permanent Portfolio, Risk Parity, 5% target volatility, 1970 - 2012

Source: Ken French, Shiller, FRED

The realized ex-post volatility of the 5% target volatility risk parity permanent portfolio is just 4.84%, and the largest drawdown was just 8.4%, for which investors would have been compensated with a 7.89% annualized return. Pretty amazing for a portfolio with half the volatility and just 25% of the drawdown of a typical bond portfolio!

A Tactical Permanent Portfolio

We'll really be treading on thin ice with the die-hard permanent portfolio crowd with these next simulations, but I hope they will forgive our impiety in our perpetual pursuit of a 'better way'.

The potential problem, as we see it, with any static asset allocation, including the permanent portfolio's permanent equal weight allocations to stocks, bonds, gold and cash, is that sometimes everything is expensive all at once, and returns to all asset classes have the potential to be low or negative in tandem. The current environment may represent one of these periods, where certainly bonds and cash are more expensive than they have ever been, with yields on Treasuries lower than at any other time in the last 220 years (source: Bank of America). Cash yields essentially zero. We think stocks are expensive as well (see here and here), and gold is at best a wildcard, having rallied by 500% or more from its lows in 2001.

If we are right, and the permanent portfolio is vulnerable to synchronized losses, then it makes sense to explore some tactical or dynamic overlays to help avoid investing in asset classes in sustained downtrends.

Mebane Faber is credited with bringing moving averages to the masses with his Quantitative Approach to Tactical Asset Allocation whitepaper in 2005. In it, he describes an approach that applies a 10-month moving average to basket of 5 asset classes: stocks, Treasuries, commodities, REITs and international stocks. While there is nothing magical about the 10-month moving average, this approach is ubiquitously cited elsewhere, and in our testing we observed no material difference with other moving averages. The following simulations apply monthly rebalancing.

Chart 7. Simple Permanent Portfolio, 10-Month MA, 1970 - 2012

Source: Faber, Ken French, Shiller, FRED

Chart 7. delivers a pretty compelling equity line. You will note that returns rise above 10% annualized over the period while volatility and drawdowns remain similar to the original simple approach. The majority of losses to this approach occurred during the tumultuous 1970s and 1980, with the largest drawdown occurring in March of 1980 as gold and stocks collapsed at the same time while both were far above their respective 10-month moving averages.

We stated above that risk adjusted returns are almost always improved by managing portfolio level volatility, so below we tested the Faber 10-month moving average approach but also applied a 7% target volatility overlay. Chart 8 shows the results of this combination.

Chart 8. Simple Permanent Portfolio, 10-Month MA, 1970 - 2012

Source: Faber, Ken French, Shiller, FRED

Now we are really cooking! While the absolute performance of the approach drops by about 0.4 percentage points per year, the risk profile drops dramatically; volatility drops to 5.5% annualized and the maximum drawdown drops to 9% from 19%. Even better, investors would have realized positive results over 98% of rolling 12-month periods!

Conclusions

Permanent Portfolio adherents are right to be proud of the performance of their approach over the past 40 years. Of all the static asset allocation approaches we have tested, the PP ranks near the top of the list in terms of risk-adjusted returns. Further, the philosophy behind its construction is consistent with the goal of resilience in the face of any economic environment.

Even PP zealots would be silly not to consider some of the simple volatility-based overlays that we presented however. Simple volatility management techniques are philosophically and empirically coherent, and deliver similar results with much smaller drawdowns.

While risk management is important, it does not address the most important challenge to the traditional portfolio: what happens next. That is, how will the traditional model behave going forward in the current environment, where all assets have been artificially inflated at once via coordinated global central bank intervention. Will the portfolio prove resilient to a period of sustained global deflation with Treasury yields already at record lows?

Tactical overlays to the traditional approach may help address this problem by systematically exiting asset classes that are exhibiting strong and/or sustained negative price trends.

The simple Faber moving average approach on its own does not seem to deliver much value above the profile of the traditional PP approach. However, combining a tactical moving average approach with simple volatility management delivers similar high returns, but without the major drawdown characteristics of the simple MA approach.

Further, this approach delivered positive returns over 98% of periods since 1970.

Permanent Portfolio Shakedown Part 1

2012-08-20T08:42:00.000-07:00

The Permanent Portfolio is an asset allocation concept first introduced by Harry Browne in 1982. The Permanent Portfolio Family of Funds website has this to say about the strategy, which they have been running in mutual fund format for about 20 years.

Established in 1982, in an era of stagnant economic growth and rampant inflation, Permanent Portfolio seeks to provide a sound structure and disciplined approach to asset allocation. The Fund was born in an environment where investors didn’t know where to turn. Regardless of what an investor did, they were losing money. Harry Browne, one of the founders of the fund stated, “It’s easy to think you know what the future holds, but the future invariably contradicts our expectations. Over and over again we are proven wrong when we bet too much on our expectations. Uncertainty is a fact of life.” No one can accurately predict the future.

[The] Permanent Portfolio recognizes this limitation and seeks to invest a fixed “Target Percentage” of its assets to six carefully chosen, diverse and “non-correlated” investment categories. Such diversification in a single mutual fund seeks to mitigate risk regardless of the economic climate. [Emphasis ours]

The Permanent Portfolio mutual fund purports to invest in 6 major asset classes according to the fixed prescribed weights in Chart 1, but the asset classes in Chart 1 leave a lot of 'wiggle room', so we performed a factor analysis to determine asset class exposures over the past 3 years (Chart 2).

Chart 1. PRPFX weights from the fact sheet.

Source: Permanent Portfolio Family of Funds

The factor analysis below is the product of a multiple regression analysis whereby the daily performance of the Permanent Portfolio mutual fund is regressed on a basket of global risk factors. The factors in Chart 2. were statistically significant in explaining the performance of the portfolio over the past 3 years; non-significant factors were rejected.

Chart 2.

Source: Yahoo finance

You can see that the performance of the Permanent Portfolio can largely be attributed to high-grade U.S. bonds (AGG), U.S. stocks (VTI), and Gold (GLD) over the past three years, with each contributing about 20% to performance. All 8 factors together explain over 90% of portfolio returns for the period (see R-Squared = 0.92885).

On several occasions, Mr. Brown indicated that a simple equal allocation to stocks, gold, Treasuries, and T-bills would probably achieve the same goals as the more complex portfolio used in his mutual fund. Empirically, these four assets have worked very well together in portfolios for at least one reason: the long-term ex-post pair-wise correlations between the assets is essentially zero over the past 40 years, which means they offer superb long-term diversification potential.

A High Hurdle

Before we investigate the performance of the Permanent Portfolio, let's set the stage by taking a look at the performance of some more conventional approaches using daily total return data back to 1970. All multi-asset portfolios are rebalanced quarterly.

Chart 3. U.S. Total Stock Market

Source: Ken French

Chart 4. 60/40 Stocks/Treasuries

Source: Ken French, Shiller

Equities and the 60/40 portfolio have delivered essentially the same 9.6% total returns since 1970, (an astonishing blow to CAPM), but the 60/40 portfolio delivered its returns with almost 40% less volatility (10% vs. 17%) and drawdown (30% vs. 53%).

Chart 5. Permanent Portfolio (Equal Weight stocks, gold, Treasuries, and cash), 1970 - 2012

Source: Ken French, Shiller, CRB

The Permanent Portfolio provided returns of 8.55% per year over the same period, which is over 1% per year lower than either stocks or the 60/40 portfolio. However, because of the low correlations between the assets, this portfolio had substantially lower risk than 60/40. Ex-post volatility averaged less than 7% versus 10.4% for 60/40, and the maximum drawdown was reduced by almost half (18% vs. 30%)

The plain-vanilla version of this strategy is quite compelling on its own, and tough to beat. Unfortunately, the approach faces the same challenge as other static allocation approaches in the current environment: record low interest rates and expensive stocks and commodities, which suggests that returns to this approach may not be as strong over the next several years.

In Part 2 of this series we are going to explore some simple techniques that might further improve the performance of this approach, including volatility management, risk parity, moving averages and finally Adaptive Asset Allocation.

Focus On What You Can Control

2012-08-10T10:17:00.000-07:00

Andrew Ang has published online draft versions of some sections from his forthcoming book, Asset Management, and from what I've read so far it promises to be a treasure trove, at least for the narrow sliver of investment managers that care about evidence over theory.

His chapter on 'Equities Market Level' is especially interesting to us, as it explores two areas of research that we have also explored at length in many articles on this blog: statistical forecasting of long-term stock market returns, and; the observation and management of portfolio volatility.

The chapter is 50 pages long, and well worth reading (here), but for brevity I want to highlight a few critically important findings:

1. Volatility is very forecastable, and it is therefore possible to effectively manage risk in portfolios.

In fact, using standard volatility forecasting methods, the correlation between the volatility estimate at the beginning of any month, and the realized volatility over the subsequent month, is 63%, which suggests more than 12x greater forecast-ability for volatility relative to returns.
Long-time readers will recall that we have posted many articles that deal with this topic, and we would encourage new readers to examine some of this research.

Ang used an intuitive (but somewhat complicated) method to test the performance of a strategy which actively manages the volatility of a portfolio of U.S. stocks through time based on the VIX implied volatility index, so that when the VIX is high, the portfolio holds a higher cash (t-bill) position in order to maintain the expected volatility of the portfolio in the face of large changes in the volatility distribution through time.
From Ang:

If volatility is so predictable, then volatility trading should lead to terrific investment gains. It does. Despite my pessimism on predicting expected returns of the previous section, I am far more enthusiastic on strategies predicting volatilities.

...[The chart below] shows that the cumulated returns (left-hand axis) of [a] volatility timing strategy largely avoided the drawdowns of the static strategy during the early 2000s and the 2008 financial crisis. During these periods VIX (right-hand axis) was high and the volatility timing strategy shifted into T-bills. It thus avoided the low returns occurring when volatility spiked.

The mean of the static 60%-40% strategy in [the chart below] is 7.9% and its reward-to-risk ratio is 0.82. In contrast, the volatility timing strategy has a mean of 10.1% and a reward-to-risk ratio of 1.95. Volatility strategies have good performance.

Source: Ang (2012)

2. It is really difficult to forecast equity returns over time horizons that are meaningful for most investors.

While equity returns over the very long term are about 9% nominal and 6.6% real, the range of possible equity returns is very wide over shorter time frames out to 20 years or more. The following chart from our AAA whitepaper shows the distribution of rolling 20-year real returns to stocks using Professor Shiller's database, which has stock and bond return information back to 1871.

Source: Shiller (2012)

The following table from Ang quantifies the degree to which a wide variety of valuation, economic and trend-based factors explain equity returns over periods from 1 quarter to 5 years. Ang confirms our discovery that the Shiller PE is a robust explanatory variable for stock returns, with statistical significance at all horizons studied.

The only other statistically significant factor tested by Ang was the Consumption-Wealth ratio, though the author correctly highlights the 'look-ahead' bias embedded in this measure, which means it can not be used effectively for contemporaneous forecasting.

Source: Ang (2012)

Ang provides a superb summary of the implications of this analysis on forecasting stock returns for investors, and I feel it's worth re-publishing here in its entirety.

Note that the first point pertains directly to our Estimating Future Returns report, as Ang highlights the spurious confidence implied by R-squared values in studies with long-term overlapping periods. We would definitely agree with Ang's caution, but we would also point out that estimates generated by our model are still likely to prove to be much more accurate than simple long-term average estimates in forecasting stock market returns going forward.

There are time-varying risk premiums, but they are difficult to estimate. If you attempt to take advantage of them, do the following:

Use good statistical techniques. Overstating statistical significance, for example by using the wrong t-statistics and thereby making predictability look “too good,” will hurt you when you implement investment strategies. One manifestation of spuriously high R2 in fitted in samples is that the performance deteriorates markedly going out of sample. Consistent with the spurious high R2 s, Welch and Goyal (2008) find that the historical average of excess stock returns forecasts better than almost all predictive variables. Use smart econometric techniques that combine a lot of information, but be careful about data mining, and take into account the possibility of shifts in regime

Use economic models. Notice that the best predictors in Table 7 were valuation ratios. Prediction of equity risk premiums is the same as prediction of economic value. If you can impose economic structure, do it. Campbell and Thompson (2008), among others, find that imposing economic intuition and constraints from economic models help.

Be humble. If you’re trying to time the market, then have humility. Predicting returns is hard to do. Since it is difficult to statistically detect predictability, it will also be easy to delude yourself in thinking you are the greatest manager in the world because of a lucky streak (this is self-attribution bias) and this overconfidence will really hurt when the luck runs out. You will also need the right governance structure to withstand painful periods that may extend for years. Note there are very few who have skill, especially among those who think they have skill.

3. Cash (t-bills) represent a much better hedge against inflation than stocks.
This revelation will probably come as a major shock to equity investors who believe that their equity portfolio represents their best shot at hedging against an inflationary shock from misguided central bank intervention.

The following chart from Ang clearly illustrates this point. Ang performed a robust pearson correlation analysis between, stock, bond and cash returns and inflation. Stocks exhibit negative correlation vs. inflation in absolute terms over periods less than 3 years; that is, when inflation increases, stocks react negatively in the short term. After 3 years, stocks are relatively agnostic to changes in inflation, as inflation estimates change in response to changes in inflation regime.

On the other hand, t-bill yields adapt fairly quickly to changes in inflation, with correlations rising toward 0.5 after about a 3 year horizon, where they find a plateau. Conversely, when stock returns are adjusted for t-bill yields to represent excess returns, they exhibit a negative correlation vis-a-vis inflation for the entire horizon out to 10 years in the range of -0.1 to -0.2.

The incontrovertible message from this analysis is that investors should hold a healthy slug of cash in portfolios to hedge against inflation - in diametric opposition to prevailing investment dogma.

Source: Ang (2012)

Takeaways

There a few big ideas here.

First: focus on what you can control, and budget for what you can't.

You can’t control the long-term returns to markets, and the evidence above strongly suggests that you can’t even make a very good forecast about what to expect. You can observe, measure, and to a very large degree control the volatility of your portfolio, however. And it happens that by controlling for volatility in the right way, you will have a high probability of achieving higher absolute returns.

Even if controlling for volatility doesn’t deliver higher returns over your investment horizon, it will definitely achieve two important goals:

1. You will enjoy a more stable investment experience with less anxiety, and therefore be much less likely to make highly detrimental behavioural errors under situations of extreme pressure
2. You will improve the sustainability of your retirement plan because you will substantially narrow the range of potential negative market outcomes. For more on this, we strongly encourage you to read this important article.

The other important takeaway is that investment dogma is often (dare I say, mostly?) wrong, and that it is important to verify the empirical validity of many basic investment concepts before putting real money to work.

For example, the volatility management tests revealed what we have known for some while: higher returns do not necessarily require higher risk. In fact, smart low risk strategies often outperform high-risk strategies in both absolute and risk-adjusted terms.

Further, evidence from the above examination of correlations between stocks, t-bills and inflation directly contradicts one of the most popular myths in finance: that is, that stocks will protect your portfolio in the event of an inflationary shock, while cash will become worthless. Certainly, cash under the mattress is much more vulnerable to inflation, but cash held in cash-like instruments like high quality government Treasury bills actually offer better protection than stocks, which are likely to lose value after adjusting for inflation.

Estimating Future Stock Market Returns: August 2012 Update

2012-08-08T08:29:00.000-07:00

"Mankind are so much the same, in all times and places, that history informs us of nothing new or strange in this particular. Its chief use is only to discover the constant and universal principles of human nature." - David Hume

Long-time readers will know that we do not make predictions in the normal sense. That is, we endorse the decisive evidence that markets and economies are complex, dynamic systems which are not reducible to normal cause-effect analysis. However, we are willing to acknowledge the likelihood that the future is likely to rhyme with the past. Thus, we apply simple statistical models to discover mean estimates of what the future may hold over meaningful investment horizons (10+ years), while acknowledging the wide range of possibilities that exist around these averages.

There are several reasons why it may be useful to have a more robust estimate of future expected returns on stocks:

People who are approaching retirement need to estimate probable returns in order to budget how much they need to save.

A retiree's level of sustainable income is largely dictated by expected returns over the early years of retirement.

Investors of all types must make an informed decision about how best to allocate their capital among various investment opportunities.

This study contributes substantially to research on smoothed earnings and Shiller PE by adding three new valuation indicators: the Q-Ratio, total market capitalization to GNP, and deviations from the long-term price trends. The Q-Ratio measures how expensive stocks are relative to the replacement value of corporate assets. Market capitalization to GNP accounts for the aggregate value of U.S. publicly traded business as a porportion of the size of the economy. In 2001, Warren Buffett wrote an article in Fortunewhere he states, "The ratio has certain limitations in telling you what you need to know. Still, it is probably the best single measure of where valuations stand at any given moment." Lastly, deviations from the long-term trend of the S&P inflation adjusted price series indicate how 'stretched' values are above or below their long-term averages.

This last point may seem obvious, but I want to emphasize a critical point about traditional wealth management of which most investors are not aware:

Traditional investment planning does not account for whether markets are cheap or expensive. An investor who visited a traditional Investment Advisor at the peak of the technology bubble in early 2000 would, in practice, be advised to allocate the same proportion of his wealth to stocks as an investor who visited an Advisor near the bottom of the markets in early 2009. This despite the fact that the first investor would have had a valuation-based expected return on his stock portfolio from January 2000 of negative 2% per year, while the second investor would expect inflation-adjusted compound annual returns of 6.5%. For an investor with $1,000,000 to invest, this would represent a difference of more than $1.26 million in cumulative wealth over a decade.

John Hussman at Hussman funds is careful to qualify the value of this analysis: "Rich valuation is strongly associated with weak subsequent returns, but only reliably so over periods of 7-10 years. In contrast, the present syndrome of overvalued, overbought, overbullish, rising-yield conditions is typically associated with abrupt and often steep losses, but is more commonly resolved over a period of months rather than years." (Hussman, Feb 14, 2011). Thus, we are not making a forecast of market returns over the next several months; in fact, markets could go substantially higher from here. However, over the next 10 to 15 years, markets are very likely to revert to average valuations, which are much lower than current levels. This study will demonstrate that investors should expect 6.5% returns to stocks only during those very rare occasions when the stock market passes through 'fair value' on its way to becoming very cheap, or very expensive. At all other periods, there is a better estimate of future returns than the long-term average, and this study will quantify that estimate.

This prediction is also supported by evidence from an analysis of corporate profit margins. In his recent book, Vitaly Katsenelson provided in Chart 1 of long-term profit margins to U.S. companies. Companies have clearly been benefitting from a period of extraordinary profitability.

Source: Vitaly Katsenelson (2011) The profit margin picture is critically important. Jeremy Grantham recently stated, "Profit margins are probably the most mean-reverting series in finance, and if profit margins do not mean-revert, then something has gone badly wrong with capitalism. If high profits do not attract competition, there is something wrong with the system and it is not functioning properly." On this basis, we can expect profit margins to begin to revert to more normalized ratios over coming months. If so, stocks may face a future where multiples to corporate earnings are contracting at the same time that the growth in earnings is also contracting. This double feedback mechanism may partially explain why our statistical model predicts such low real returns in coming years. Caveat Emptor.

Modeling Across Many Horizons

Table 1. below provides a snapshot of some of the results from our analysis. The table shows estimated future returns based on several factor models over some important investment horizons. The "Best Fit Multiple Regression" is by far the most accurate model, but other results are provided for context.

Table 1. Factor Based Return Forecasts Over Important Investment Horizons

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see from the table that every single valuation factor model generates results which suggest a very low future return environment for stocks. Further, the 'Best Fit Multiple Regression', which has historically provided a surprising degree of forecast accuracy, confirms this outlook with a high degree of confidence (see explanation below). Those who are not interested in our process can skip to the bottom sections, 'Putting the Predictions to the Test', and 'Conclusion'.

Process

The following matrices show the R-Squared ratio, regression slope, regression intercept, and current predicted forecast returns for each valuation factor. The matrices are heat-mapped so that larger values are reddish, and small or negative values are blue-ish. Click on each image for a large version.

Matrix 1. Explanatory power of valuation/future returns relationships

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Many analysts quote 'Trailing 12-Months' or TTM PE ratios for the market as a tool to assess whether markets are cheap or expensive. If you hear an analyst quoting the market's PE ratio, odds are they are referring to this TTM number. Our analysis slightly modifies this measure by averaging the PE over the prior 12 months rather than using trailing cumulative earnings through the current month, but this change does not substantially alter the results. As it turns out, TTM average earnings have very mild explanatory value over periods greater than 8 years. However, the explanatory power of TTM earnings is substantially less reliable than all other factors studied in this analysis, so investors may wish to pay little heed to this indicator of whether stocks are cheap or expensive.

Forecasting Expected Returns

The next matrices provide the slope and intercept coefficients for each regression. We have provided these in order to illustrate how we calculated the values for the final matrix below of predicted future returns to stocks.

Matrix 2. Slope of regression line for each valuation factor/time horizon pair.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Matrix 3. Intercept of regression line for each valuation factor/time horizon pair.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Our final matrix below shows predicted future real returns over each time horizon, as calculated from the slopes and intercepts above, by using the most recent values for each of the 13 earnings series, the Q-Ratio, and the return series as inputs. For statistical reasons which are beyond the scope of this study, we have substituted the ordinal rank for the nominal value for each factor in running our analysis. Therefore, when we solve for future returns based on current monthly data, we apply the monthly rank in the equations.

For example, the 15-year return prediction based on the current Q-Ratio can be calculated by multiplying the current ordinal rank of the Q-Ratio (969) by the slope from Matrix 2. at the intersection of 'Q-Ratio' and '15-Year Rtns' (-0.0000894), and then adding the intercept at the same intersection (0.1202323) from Matrix 3. The result is 0.0336, or 3.36%, as you can see in Matrix 4. below at the same intersection (Q-Ratio : 15-Year Rtns).

Matrix 4. Modeled forecast future returns using current valuations.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Finally, at the bottom of the above matrix we show the forecast returns over each future horizon based on our best-fit multiple regression from the factors above. We began testing the multiple regression against the Q-ratio, the 15-year Shiller PE, the price regression, and the market cap to GNP as a 4 factor model. However, we discovered that the 15-year PE provided more noise than signal to the regression (that is, these factors were not statistically significant and reduced the F-score), so we narrowed the regression to include just the Q ratio, market cap/GNP, and the real price series over each forecast horizon.

We provided the R-squared for each multiple regression at the bottom of each forecast horizon column in Matrix 4.; you can see that at the 15-year forecast horizon, our regression explains 82% of total returns to stocks. Further, the regression is very highly statistically significant, with a p value of effectively zero.

Chart 2. below demonstrates how closely the model tracks actual future 15-year returns. The red line tracks the model's forecast annualized real total returns over subsequent 15-year periods using the Q ratio and deviation from price regression as inputs at each period. The blue line shows the actual annualized real total returns over the same 15-year horizon.

Chart 2. 15-Year Forecast Returns vs. 15-Year Actual Future Returns

Click for a larger image

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see that 15-year "Regression Forecast" returns are 0.69% per year and 10-year returns are forecast to be 2.49% per year using market valuations as of July 30, 2012.

Putting the Predictions to the Test

Table 2. Comparing Long-term average forecasts with model forecasts

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see we tested against periods during the Great Depression, the 1970s inflationary bear market, the 1982 bottom, and the middle of the 1990s technology bubble in 1995. The table also shows expected 15-year returns given market valuations at the 2009 bottom, and current levels. These are shaded green because we do not have 15-year future returns from these periods yet. Note real total return forecasts of 5.92% annualized from the bottom of the market in February 2009. This suggests that prices just approached fair value at the market's bottom, but they were nowhere near the level of cheapness that markets achieved at bottoms in 1932 or 1982. As of the end of July 2012, annualized future returns over the next 15 years are expected to be less than 1 percent.

We compared the forecasts from our model with what would be expected from using just the long-term average real returns of 6.5% as a constant forecast, and demonstrated that estimates form long-term average returns yield over 433% more error than estimations from our model over these 15-year forecast horizons (1.28% annualized return error from our model vs 5.55% using the long-term average). Clearly the model offers substantially more insight into future return expectations than simple long-term averages, especially near valuation extremes.

Conclusions

The 'Regression Forecast' return predictions along the bottom of Matrix 4. are robust predictions for future stock returns, as they account for over 100 different cuts of the data, using 3 distinct valuation techniques, and utilize the most explanatory statistical relationships. The models explain up to 82% of future returns based on R-Squared, and are statistically significant at p~0. It is worth noting, however, that even this model has very little explanatory power over horizons less than 6 or 7 years, so almost anything is possible in the short-term.

Returns in the reddish row labeled "PE1" in Matrix 4 were forecast using just the most recent 12 months of earnings data, and correlate strongly with common "Trailing 12-Month" PE ratios cited in the media. Note that our Matrix 1. proves that this trailing 12 month measure is not worth very much as a measure for forecasting future returns over any horizon. However, the more constructive results from this metric probably helps to explain the general consensus among sell-side market strategists that markets will do just fine over coming years. Just remember that these analysts have no proven ability whatsoever in predicting market returns (see here, here, and here). Further, it can be argued that their firms have a substantial incentive to keep their clients invested in stocks.

You're Looking at the Wrong Number

2012-07-27T03:00:00.000-07:00

In a prior post entitled 'Retirement's Volatility Bogeyman' we introduced the critical concept that volatility is the unsung villain of retirement sustainability. This article will reiterate the concepts we presented in the prior article, and demonstrate how an investor can tolerate lower returns so long as volatility is actively managed in the context of a more traditional balanced portfolio.

As a reminder, every non-pensioned person nearing or in retirement should become intimately acquainted with the following two terms:

Safe Withdrawal Rate (SWR): the percent of your retirement portfolio that you can safely withdraw each year for income, assuming the income is adjusted upward each year to account for inflation.

Retirement Sustainability Quotient (RSQ): the probability that your retirement portfolio will sustain you through death given certain assumptions about lifespan, inflation, returns, volatility and income withdrawal rate. You should target an RSQ of 85%, which means you are 85% confident that your plan will sustain you through retirement.

Portfolio Volatility Determines RSQ and SWR

The chart below shows how higher portfolio volatility results in lower SWRs, holding everything else constant:

All portfolios deliver 7% average returns.

Future inflation will be 2.5%.

Median remaining lifespan is 20 years (about right for a 65 year old woman).

We want to target an 85% Retirement Sustainability Quotient (RSQ).

Note how SWR declines as portfolio volatility rises.

Source: Butler|Philbrick|Gordillo & Associates, 2012

The green bar marks the volatility of a 50/50 stock/U.S. Treasury balanced portfolio over the long-term, while the red bar marks the long-term volatility of a diversified stock index. Note the SWR of the stock/bond portfolio is 6% versus 3.4% for the stock portfolio, highlighting the steep tax that volatility levies on retirement income.

Steady Eddy and Risky Ricky

This is actually quite intuitive when you think about it. Imagine a scenario where two retired persons, Steady Eddy and Risky Ricky by name, draw the same average annual income of $100,000 from their respective retirement portfolios. Both draw an income that is a percentage of the assets in their retirement portfolio at the end of the prior year.

Steady Eddy's portfolio is invested in a balanced strategy with a volatility of 9.5%, while Risky Ricky is entirely in stocks with a volatility of 16.5%. Both portfolios earn the same return (as they have done for the past 15, 20 and 25 years, though we will address this in greater detail below).

Due to the lower volatility of Steady Eddy's portfolio, his income is less volatile: 95% of the time his income is between $82,000 and $117,000. In contrast, Risky Ricky's portfolio swings wildly from year to year, and therefore so does his income: 95% of the time his income is between $67,000 and $133,000. Of course, both of their incomes average out to the same $100,000 per year over time.

All other things equal, which person would you expect to be more conservative in the amount of income they spend each year? Obviously, if your income were subject to a large amount of variability each year then you would tend to be more conservative in your spending; perhaps you would squirrel away some income each year in case next year's income comes in on the low end of the range.

This relates directly to the impact of volatility on SWRs in the chart above. Volatility introduces uncertainty which is amplified by the fact that money is being extracted from the portfolio each and every year regardless of portfolio growth or losses.

How Much Gain Will Neutralize the Pain?

Of course, this effect can be moderated by increasing average portfolio returns, which would then increase average available income. The question becomes, how much extra return is required to justify higher levels of portfolio volatility?

The chart below defines this relationship quantitatively by illustrating the average return that a portfolio must deliver to neutralize an increase in portfolio volatility. In this case we hold the following assumptions constant:

Withdrawal rate is 5% of portfolio value, adjusted each year for inflation.

Inflation is 2.5%.

Retirement Sustainability Quotient target is 85%.

Median remaining lifespan is 20 years.

Source: Butler|Philbrick|Gordillo & Associates, 2012

Again, the green bar represents the balanced stock/Treasury bond portfolio discussed above, and the red bar represents an all-stock portfolio. From the chart, you can see that the balanced portfolio needs to deliver 6.8% returns to achieve an 85% RSQ with a 5% withdrawal rate. The higher volatility stock portfolio, on the other hand, requires a 9.2% returns to achieve the same outcomes.

In theory, higher returns in your retirement portfolio should equate to higher sustainable retirement income. In reality, higher returns at the expense of higher volatility actually reduces your retirement sustainability.

Focus on What You Can Control

It is impossible to control the intermediate- to long-term returns to asset classes, but we can control the assets we hold in portfolios, and the allocation between them. To a large extent, we can also control the volatility of our portfolio, if not total portfolio risk.

First, let's focus on a typical 60/40 stock/bond portfolio, which is the template for many retirement accounts. Not incidentally, this is also the flagship allocation for most small and medium sized foundations and endowments.

For our study, we focus on returns to Treasuries rather than corporate bonds because we couldn't find good daily data for corporate bonds, and because Treasuries alone provide true diversification against financial shocks, which means they perform as bonds should when it really counts.

Chart. A 60/40 portfolio 1963 - 2012

Source: Ken French, FRED

The simple 60/40 portfolio exhibited pretty good performance over the almost 50 year period from 1963, delivering 8.82% annualized returns with a volatility of 9.91%. Unfortunately, the strategy lost 31% of its value in 1973/1974, and 26% in 2008/2009, which would have been very difficult to stomach.

Next, we investigated a 60/40 strategy with two simple twists: we applied a 60/40 risk weighting instead of the typical capital weighting, and we applied a target volatility of 6% at the portfolio level to maintain a stable risk experience.

Chart. A 60/40 volatility weighted portfolio with 6% ex-ante target volatility, 1963-2012

Source: Ken French, FRED

We observe a drop in returns from 8.8% per year to 7.8%, which is not insignificant. However, the risk character changes much more dramatically. Ex-post observed volatility drops from 9.91% to 5.33%, a reduction of 46%, and drawdowns are also much more muted, dropping by almost 50% from over 30% to 16.5%.

Let's examine the impact of this simple risk management overlay on the Safe Withdrawal Rate that each strategy will support.

Chart. Safe Withdrawal Rate for Traditional 60/40 portfolio vs. 60/40 risk weighted portfolio with 6% volatility target

Source: Ken French, FRED, QWeMA

Astute observers will notice that despite the higher average returns to the traditional 60/40 portfolio, the risk managed portfolio will support a higher SWR: 6.8% vs. 6.6%. This offers an excellent example of the impact of volatility on the SWR. An investor can tolerate lower returns so long as volatility is actively managed.

Further, from a behavioural and experiential standpoint, the risk managed portfolio provides a much more stable experience that investors are more likely to stick with. This last point is absolutely critical, as the chart below from Dalbar shows that the inability of traditional balanced investors to stick with their strategy over the long-term caused these investors to trail a 60/40 balanced index strategy by 5.94% per year over the 20 years through the end of 2011.

Chart. Realized investor returns vs. indexes

Source: Dalbar, Ken French, FRED
Balanced portfolio is rebalanced monthly

Dividend Delusions

2012-07-23T18:42:00.001-07:00

Just a short post to highlight the frothy premiums currently being bestowed upon the 'slow and steady' blue-chip dividend stocks at the moment. As central banks have successfully reduced yields on government and high grade corporate bonds to levels that will not sustain institutional funding or retirement income goals, investors of all stripes have flocked to dividend funds in their chase for yield.

Unfortunately, in the stampede for yield, investors in dividend stocks are overlooking the single most critical fact: valuations for the 'bluest of blue chip' dividend stocks, as measured by the Dow Jones Select Dividend Index, are now higher in aggregate than valuations for the broader market.

This must represent a profound source of consternation for traditional value investors, who must be enormously frustrated that their value bias can no longer be reconciled with a dividend focus.

Chart 1. Price to Book Discount of Dow Jones Select Dividend Index vs. Russell 1000

Source: Bloomberg

Chart 2. Price to Earnings Discount of Dow Jones Select Dividend Index vs. Russell 1000

Source: Bloomberg

You can see that based on both PE ratio and PB ratio that dividend stocks are valued at or near a premium to the broader stock market. Further, looking back to 2003 (the inception of the dividend index), dividend stocks have rarely been more expensive relative to the broader market.

Readers of this blog won't be surprised to learn that we would advocate for investors to replace their thirst for yield with a thirst for low volatility. The following charts make the case.

Chart 3. Low volatility stocks outperform the market in absolute and relative terms

Source: Deutsche Bank

Chart 4. Low volatility stocks are substantially cheaper than dividend stocks

Source: Yahoo finance

Chart 5. When yields are adjusted for risk, rational investors would be agnostic about investing in low volatility versus high dividend stocks, but would prefer either to the market index

Source: Yahoo finance

Chart 6. Last but not least, low volatility stocks in aggregate are under-owned - in stark contrast to the extremely over-owned dividend sectors.

Source: Deutsche Bank

Adaptive Asset Allocation for a Regime Agnostic 'Balanced Fund'

2012-06-15T05:50:00.000-07:00

Risk Parity: Past its Prime
This is a follow-on to our research on Adaptive Asset Allocation

Our last article described an Adaptive Risk Parity (ARP) framework for a stock/bond balanced allocation, and discussed the advantages and risks relative to traditional 60/40 approach. While ARP makes intuitive, logical and empirical sense as an allocation framework, there are long-term risks to this approach related to asset class regimes.

Stocks, bonds and other asset classes generally move through long periods of high total return followed by long-periods of low total return. While there is more contention about where we are in the long-term stock cycle, there can be little debate about whether we are closer to the end or the beginning of the long-term interest rate cycle.

The chart below from Mebane Faber's great new(ish) series on Risk Parity demonstrates the long-term efficacy of a static version of the approach for a portfolio of stocks and bonds using long-term relative stock and bond volatility for allocations, and targeting the same long-term volatility as the 60/40 portfolio (10.44%). Notice that to achieve the same level of risk as a 60/40 portfolio, the risk parity portfolio must be levered by 160%.

Chart 1. Long-term risk parity with S&P 500 and 10-Year Treasuries, 1972 - 2012

Source: Mabane Faber, 2012

While the performance of the static risk parity approach is better over the full period, Faber points out that the relative out-performance is sensitive to the start and end dates of the observation period. If we go back in time to mid 2000 and observe the relative performance over the first 28 years, we may have drawn a different conclusion.

Chart 2. Long-term risk parity with S&P 500 and 10-Year Treasuries, 1972 - 2000

Source: Mabane Faber, 2012

So what happened during the last decade to create such a massive disparity in returns? The next chart offers a clue: it plots the progression of interest rates since 2000.

Chart 3. 10-Year Treasury yield, 2000 - 2012

Source: FRED database

Clearly this has been an exceptional period for interest rates, as they have dropped by over 70% over the past 12 years, delivering almost 7.6% in total returns per year, compared with 0.80% per year for stocks.

The question is, with interest rates at or very near historic lows, and the relative return differential between risk parity and more traditional approaches at an all-time high, should we expect this approach to continue to dominate other approaches going forward? Or should we acknowledge that the best days for risk parity are probably behind us - and adapt?

Adaptive Asset Allocation (AAA)

In this article we will apply the integrated AAA approach described in our whitepaper to a more traditional stock and bond portfolio to create a resilient 'balanced fund' that is immune to the interest rate bias that represents the Achilles Heel of risk parity.

AAA uses estimates of returns, volatility and correlation for assets in a portfolio based on recently observed measures of these parameters, rather than long-term averages. These estimates are then integrated using a robust mean-variance optimization algorithm analogous to the equations described under the banner of Modern Portfolio Theory.

Estimates for returns and correlations are drawn from time series for each asset over a 6-month look-back horizon, while volatility is measured over a shorter 60 day horizon. Further, portfolio level volatility at each rebalance period is managed to a 10% target. Depending on the measured volatility of the assets, and the correlation between them, at each rebalance period, cash or leverage may be required to reach the volatility target. No yield on cash or cost of leverage is included for this illustration.

Chart 4. Adaptive Asset Allocation balanced portfolio, rebalanced monthly, 1995 - May 31, 2012
Max 200% exposure

Source: Data from Yahoo Finance

For those with no tolerance for leverage or margin, here is a version of the AAA approach with a maximum 100% portfolio exposure.

Chart 5. Adaptive Asset Allocation balanced portfolio, rebalanced monthly, 1995 - May 31, 2012

Max 100% exposure

Source: Data from Yahoo Finance

You can see that the Adaptive Asset Allocation framework described in our whitepaper applies quite well to a typical balanced portfolio of stocks and bonds. To illustrate the adaptive nature of the program, the diagram below illustrates how the portfolio adapts its allocations over time based on changing momentum, volatility and correlation dynamics.

You can see that the starting allocation for June would have been 53.72% in stocks and 46.28% in bonds.

Chart 6. Adaptive Asset Allocation balanced portfolio, historical allocations, Aug 31, 2011 - May 31, 1012. Max 100% exposure.

Source: Data from Yahoo Finance

Notice how during late 2011's extreme market behaviour, the AAA balanced portfolio dramatically reduced exposure to both stocks and bonds, lowering equity allocation to 11% and Treasury allocations to 39% at the end of September, with the balance in a 50% cash allocation. This was necessary to maintain the target 10% portfolio volatility during a period where the observed volatility was much too high.

Also notice that, for the most part, the allocations do not stray too far from the Investment Policy Statement (IPS) guidelines for a typical balanced investor. Where deviations do occur, they are usually biased toward too much cash, and rarely last more than a month or two except during extreme situations like 2008.

Fortunately, many IPSs have enough flexibility in their guidelines to to allow for deviations from stated benchmarks over periods up to 3 months, and longer deviations are allowed with appropriate client consultation.

As a result, while portfolio flexibility is an important and central element of the AAA framework, the examples above demonstrate that it is constrained enough to make it a compelling and comprehensive alternative for traditional balanced clients.

Conclusion

The November article 'Rebalancing Resurrected' introduced the concept of weighting portfolio allocations based on relative volatility rather than as a set portion of capital. It was shown that relative volatility sizing delivered a substantial improvement to risk-adjusted returns without sacrificing absolute returns.

The prior article on Adaptive Risk Parity was a natural extension to a volatility sizing approach because it applies the same math to allocate between the assets based on volatility, but then overlays a risk budget at the portfolio level. The ARP approach further improved risk adjusted performance with consistent absolute performance.

Further, by allowing the portfolio to take on a limited amount of leverage at times of low asset level volatility and/or very low asset correlations in order to achieve the target risk budget, the ARP portfolio delivered a 27% improvement in absolute returns with the same level of portfolio volatility as the traditional balanced portfolio.

Finally, in acknowledgment of the primary flaw in the usual risk parity approach - the structural overweight to fixed income - we applied an Adaptive Asset Allocation framework that applied better estimates of return, volatility and correlation to create rolling optimal portfolios. This framework delivered performance consistent with the ARP approach, but because it is guided by asset class momentum as well as relative volatility and correlations, it is robust to structural shifts in interest rate regimes.

Investors are looking for robust, adaptive investment solutions to manage indelible liabilities like funding objectives or retirements. Traditional SAA and endowment model 60/40 portfolios are vulnerable to long-term shifts in return, volatility and correlation regimes across asset classes. This risk is especially acute with interest rates at historic lows.

The Adaptive Asset Allocation framework offers a working solution for investors that provides strong returns with managed risk, a combination that substantially and positively skews the probability of success for investors, regardless of market outcomes.

Adaptive Risk Parity for a Better 'Balanced Fund'

2012-06-06T05:11:00.002-07:00

Rebalancing Revisited

Back in November of 2011 we published our first article introducing the concept of volatility sizing for asset allocation within a stock and bond portfolio as an alternative to traditional static capital weightings, such as 60/40. The volatility sizing technique produced an 18% improvement in risk-adjusted performance, including a 30% reduction in peak-to-trough drawdown.

More recently, we integrated volatility related ideas from the original article along with concepts related to momentum, correlation, and the architecture of Modern Portfolio Theory, to introduce a novel Adaptive Asset Allocation framework (expanded whitepaper here) for a broad basket of global asset classes.

In this article we revert our focus back to stocks and bonds. Specifically, we will demonstrate how to create a more optimal 'balanced fund' using ETFs tracking the S&P 500 and long-term Treasuries by applying a strategy we call Active Risk Parity (ARP). This approach borrows heavily from the literature related to standard risk parity, but overlays active volatility management both at the individual asset class level, and the portfolio level, to achieve a 27% improvement in absolute returns, and a 29% improvement in risk-adjusted performance, relative to a traditional balanced portfolio.

Recall that the difference between the previously described volatility weighted approach and a typical balanced approach, is that rather than allocating equal portions of capital to assets in a portfolio, the volatility weighted portfolio allocates equal portions of risk, as measured by recently observed volatility.

To illustrate this concept consider the following chart, which captures the relative contribution of portfolio volatility from stocks versus bonds in a typical 60/40 balanced portfolio.

Chart 1. Marginal risk contribution: 60/40 portfolio of U.S. stocks vs. Treasuries, 1995 - 2012

Source: Data from Yahoo Finance

The blue area reflects the proportion of portfolio volatility attributable to the 60% stock allocation, while the red area indicates the proportion contributed by the 40% Treasury allocation. Note that while the capital is allocated 60/40 to stocks and bonds respectively, the risk is actually allocated about 80/20. This reality is lost on most investors, including most investment managers, despite the hard lessons learned during recent bear market periods.

The volatility weighting framework allocates capital to assets at each rebalance period such that each asset class contributes an equal amount of risk to the portfolio rather than a set proportion of capital. In our November article we compared the performance of a traditional 50/50 capital allocated approach to the performance of a volatility weighted approach using data for stocks and Treasuries going back to 1995. The following charts update the performance of these two mandates through the close of trading on May 31, 2012.

Chart 2. Equal weight portfolio of stocks and bonds, rebalanced quarterly, Jan 1995 - May 2012

Source: Data from Yahoo Finance

Chart 3. Equal volatility weighted portfolio of stocks and bonds, rebalanced quarterly, Jan 1995 - May 2012

Source: Data from Yahoo Finance

The relative volatility weighted portfolio delivers better risk adjusted, and absolute, performance than the traditional 50/50 portfolio. Further, in two other prior articles we demonstrated that this approach to asset allocation is equally robust for Canadian and Japanese balanced portfolios as well.

Given that asset allocation is improved by focusing on proportional risk rather than proportional capital, we are ready to explore a more robust application of this concept.

Active Risk Parity

The volatility weighting approach described above ensures that the volatility contributions of stocks and bonds are equal in a fully invested portfolio. While this approach promises a much more stable return distribution than the traditional 50/50 capital allocation framework, it is still vulnerable to short- and intermediate-term changes in asset correlations which impacts total risk at the portfolio level.

Recall that portfolio volatility is impacted by the volatilities of the individual assets AND the correlation between those assets. For example, if we assume two assets have the same volatility, then the following chart quantifies the change in portfolio level volatility as a function of the change in correlation between the assets based on Markowitz' famous equation.

In contrast, in a Risk Parity framework once the assets have been risk-weighted within the portfolio, the portfolio itself is then levered or de-levered to achieve a desired target for portfolio volatility. The math for volatility targeting is simply:

target volatility

observed volatility

For example, a Risk Parity investor targeting a 10% risk budget for a portfolio with observed volatility of 8% would allocate 10% / 8% = 125% to the portfolio, which would require 25% leverage.

Typically, Risk Parity suffers from the same issues as Strategic Asset Allocation related to the fact that the guiding assumptions for the volatility and correlation inputs to the portfolio optimization are derived from long-term average values. We have published several research pieces (here) discussing the dangers of using long-term average values for portfolio inputs, so we will avoid that error here. Rather, we will use 60 day rolling measures of volatility and correlation for allocation decisions at each rebalance period.

For the purpose of this article we have coined a new term, Active Risk Parity (ARP), which captures the risk parity concept but applies better portfolio optimization estimates based on near-term observed values. The following ARP performance chart uses a 60 day trailing observation period to allocate at each rebalance period, and to also target a 10% portfolio volatility, rebalanced quarterly. In an effort to keep leverage to manageable levels, maximum portfolio exposure has been limited to 200%, which is practical for typical margin accounts. Note that we have assumed no yield on cash nor costs associated with the use of leverage for this illustration.

Chart 4. Active Risk Parity balanced portfolio, rebalanced quarterly, 1995 - May 31, 2012
Max 200% exposure

Source: Data from Yahoo Finance

For investors with no tolerance for margin or leverage, the following chart updates the ARP portfolio assuming a maximum of 100% exposure.

Chart 5. Active Risk Parity balanced portfolio, rebalanced quarterly, 1995 - May 31, 2012

Max 100% exposure

Source: Data from Yahoo Finance

Risk Parity, and ARP in particular have significant advantages over a typical asset allocation framework. Obviously, risk adjusted performance is improved substantially in terms of both average portfolio volatility and drawdowns. In addition, absolute performance is consistent with no leverage, and about 27% higher with leverage, at a similar average level of volatility.

Some Challenges

However, Risk Parity skeptics have long complained that the success of the approach can largely be attributed to the much higher relative allocation to fixed income over a testing period where interest rates have steadily declined. Bonds are structurally much less volatile than stocks, and so command a much higher allocation in a Risk Parity framework on average relative to a typical balanced approach. Obviously during a period of steadily declining rates a risk parity portfolio will have an advantage.

But what happens to a risk parity approach when, inevitably, rates start to rise again. Should bonds continue to maintain such a perpetually overweighted position in portfolios when long-term Treasuries promise yields of less than 3% for the next 30 years?

We feel this is a valid point. Obviously, return estimates need to be factored into the portfolio optimization somehow. However, we don't accept that this argument suggests that investors should move away from risk parity back toward the traditional Strategic Asset Allocation approach.

The next article will apply our Adaptive Asset Allocation framework to improve on the ARP approach by introducing a return estimate. This will short-circuit the fixed income conundrum so that balanced investors have a chance to capture a larger proportion of returns to stocks as rates normalize.

Adaptive Asset Allocation: A True Revolution in Portfolio Management

2012-05-10T15:09:00.000-07:00

Modern Portfolio Theory (MTP) has been derided by practitioners, academics, and the media over the past ten years because the dominant application of the theory, Strategic Asset Allocation, has delivered poor performance and high volatility since the millennial technology crash.

Strategic Asset Allocation probably deserves the negative press it receives, but the mathematical identity described by Markowitz in his 1967 paper is axiomatic in the same way Pythagoras' equations describe the properties of right triangles, or Schrodinger's equations describe the positional probabilities of electrons.

The math is the math.

Bear with me!

Modern Portfolio Theory requires three parameters to create optimal portfolios from two or more assets:

Expected returns
Expected volatility
Expected correlation

Strategic Asset Allocation applies MPT using long-term averages of these parameters to create diversified portfolios that theoretically maximize the excess returns of the portfolio per unit of volatility.

The problem with Strategic Asset Allocation is not the math of MPT - the problem is with the assumption that the best estimates for returns, volatility and correlations are the long-term averages.

Garbage In: Garbage Out (GIGO)

GIGO: Returns

The magnitude of this error in assumptions cannot be overstated because long-term averages hide enormous variability over shorter periods which can be observed and utilized for better portfolio assembly.

Consider the following chart, which shows the range of real returns to U.S. stocks over rolling 20-year periods from 1871 through 2009. While 20 years or so approximates a typical retirement investment horizon, it exceeds, by multiples, the average psychological horizon of most investors which is much closer to 3 or 4 years.

Source: Shiller, Butler|Philbrick|Gordillo & Associates

You will note that, even over horizons as long as 20 years, annualized real returns to stocks range from -0.22% right before the Great Depression crash, to 13.61% during the 20 years ending in March of 2000.

For portfolios created using traditional Strategic Asset Allocation, this amount of variability in returns means the difference between living on food stamps after 10 years of retirement and leaving a deca-million dollar legacy for heirs. In other words, a retirement constructed using long-term average return estimates is analogous to a game of retirement Russian Roulette, where luck alone decides your fate.
Garbage long-term average estimates in: garbage portfolio results out.

GIGO: Volatility

There is a great deal going on under the surface with volatility estimates too. For example, while long-term daily average volatility is around 20% annualized for stocks, and 7% for 10-year Treasury bonds, the following two charts show how realized volatility fluctuates dramatically over time for both stocks and bonds.

S&P 500 60-Day Rolling Standard Deviation (Index points)

10-Year Treasury 60-Day Rolling Standard Deviation (Index points)

Source: Stockcharts.com

Incredibly, you can see that the volatility of a bond portfolio can fluctuate by over 1000% over a 60 day period, and the volatility of a U.S. stock portfolio can fluctuate by almost 1500%.

This has a dramatic impact on the risk profile of a typical balanced portfolio, and therefore on the experience of a typical balanced investor. Most investors believe that if a portfolio is divided 60% into stocks and 40% into bonds, that these asset classes contribute the same proportion of risk to the portfolio.

However, as the next chart shows, for a portfolio consisting of 60% S&P500 and 40% 10-year Treasuries, the stock portion of the portfolio actually contributes over 80% of total portfolio volatility on average, and over 90% of portfolio volatility about 5% of the time. In late 2008 for example, a 60/40 portfolio generally behaved as though it was over 90% stocks!

Garbage long-term average estimates in: garbage portfolio results out.

Source: Yahoo Finance, Butler|Philbrick|Gordillo & Associates Strategies

GIGO: Correlation

By now it probably comes as no surprise that the correlation between asset classes fluctuates substantially over time as well. While the long-term correlation between U.S. stocks and Treasuries, and U.S. stocks and gold, are low or even negative over the long-term, the actual realized correlation between these assets oscillates between strong and weak over time.

Source: Stockcharts.com

From the charts, notice that the long-term average 60-day rolling correlation between stocks and Treasuries over the 12-year period shown is -0.42, and the correlation between stocks and gold is +0.22.

However, the stock/Treasury correlation varies between -0.82 and +0.27 over the period, and the stock/gold correlation varies between -0.84 and +0.91. You could fly a 747 through those ranges, and the current correlation has an enormous impact on portfolio volatility.

Source: Butler|Philbrick|Gordillo & Associates

In fact, as you can see from the chart above, the volatility of a 50/50 stock/bond portfolio increases by 100% as correlation increases from -0.8 to +0.2, holding all else constant.
Garbage long-term average estimates in: garbage portfolio results out.
Return, volatility and diversification estimates vary widely from their long-term averages over the short and intermediate terms. Managers who do not monitor and adjust portfolios to these changes risk substantial deviation from stated portfolio objectives, and are almost certain to deliver a sub-optimal experience for investors.

The Objective of Portfolio Optimization

One of the most important axioms in finance is that the best estimate of tomorrow's value is today's value. Our prior articles in this series clearly demonstrate this important concept for returns, volatility and correlation.

Which begs the question: If we can measure the value of these variables over the recent past, and they are better estimates over the near-term than long-term average values, why don't we use current observed values for portfolio optimization instead? Why would we choose to hold a static asset allocation in portfolios when it is possible to adapt over time based on observed current conditions?

It is worth noting that the overall objective of asset allocation is to deliver the highest returns per unit of volatility. In finance, this is called the 'Sharpe ratio'*.

You may wonder why we don't we just focus on returns. Well, one reason is that higher risk portfolios are much more difficult to stick with. While we may know logically that stocks deliver reasonable long-term returns, we may find it difficult to ride out sustained losses of 50%, 60% or greater on the way to our promised long-term growth. Under such circumstances most of us will cry 'Uncle' at the wrong time and permanently harvest a large loss.

That's why in our examples below we also highlight a measure called 'maximum drawdown', which describes the maximum peak-to-trough daily loss of each portfolio over the period under investigation. Between volatility and maximum drawdown we capture a substantial portion of meaningful risk.

For those in or near retirement, when evaluating the tests below remember that higher returns alone will not improve retirement income or sustainability. For retirees drawing income, or those within 5 years of retiring, the most important measure of portfolio performance is the returns/volatility ratio: the higher this ratio, the higher the sustainable retirement income from a portfolio.

Introducing Adaptive Asset Allocation

To illustrate the revolutionary advantage that accrues from using recent observed portfolio parameters to regularly adapt portfolios to changing market conditions, consider a portfolio consisting of 10 major global asset classes:

U.S. stocks
European stocks
Japanese stocks
Emerging market stocks
U.S. REITs
International REITs
U.S. intermediate Treasuries
U.S. long-term Treasuries
Commodities
Gold

Going back to 1995, if we held this basket of assets in equal weight, and rebalanced monthly, we would have experienced the following portfolio growth profile [Example 1].

Example 1: 10 Assets, Equal Weight Rebalanced Monthly

Source: Yahoo finance, Butler|Philbrick|Gordillo & Associates

We saw above in GIGO: Volatility above how volatile assets like stocks dominate the total risk of a typical portfolio, and the chart above provides further proof. But what happens if we observe the actual volatility of each asset in the portfolio over the past 60 days, and adjust the allocations at each monthly rebalance period so that each asset contributes the same 1% daily volatility to the portfolio, to a maximum of 100% exposure [Example 2]?

Example 2: 10 Assets, Volatility Weighted Rebalanced Monthly

Source: Yahoo finance, Butler|Philbrick|Gordillo & Associates

By simply sizing each asset in the portfolio so that it contributes the same 1% daily volatility based on observed volatility over the prior 60 days, the return delivered per unit of risk (Sharpe) almost doubles from 0.66 to 1.23 versus the equal-weight portfolio, and the maximum drawdown is cut in half from 44% to under 20%.

This is a dramatic reduction in risk without sacrificing any returns. Aside from the reduced emotional burden this approach provides, it also very substantially boosts safe withdrawal rates for retirement or endowment portfolios, but that's a tale for another post.

Now let's re-introduce momentum as a better return estimate. We demonstrated how assets that have risen the most over the prior 6 to 12 months tend to continue to outperform over subsequent weeks. Momentum is therefore just a better way of estimating performance over the near-term future. So let's consider a new portfolio assembled monthly from the top 5 assets out of the 10 asset basket above, based on their performance over the past 6 months. This will be our pure Momentum Portfolio [Example 3].
Example 3: 10 Assets, Top 5 Equal Weight By 6-Month Momentum, Rebalanced Monthly

Source: Yahoo finance, Butler|Philbrick|Gordillo & Associates

You can see that by holding the top 5 assets each month based exclusively on their 6-month momentum, we again nearly double the Sharpe ratio, but we also substantially increase annualized returns - from 8.36% for the equal weight to 14.30% for our Momentum Portfolio. The average volatility for the momentum portfolio is slightly lower than the equal weight portfolio at 11.6% versus 12.7% annualized, and the drawdown is 40% smaller.

Our next step is to combine estimates of return based on momentum with estimates of volatility based on recent observed volatility. The following chart shows the performance of an approach that assembles the top 5 assets by 6-month momentum, and then applies the same volatility sizing overlay as we used in Example 2, so that each of the top 5 assets contributes the same 1% of daily risk to the portfolio, again to a maximum of 100% exposure [Example 4].

Example 4: 10 Assets, Top 5 By 6-Month Momentum, Volatility Weighted, Rebalanced Monthly

Source: Yahoo finance, Butler|Philbrick|Gordillo & Associates

This technique lowers returns slightly from 14.3% to 13.7%, but the Sharpe ratio increases from 1.23 to 1.51, and the maximum drawdown drops to 16% from 26%.

The next and final step is to integrate momentum, volatility and correlation using our improved return (momentum), volatility and correlation estimates to achieve true Adaptive Asset Allocation (AAA).

A novel approach to this might be to create portfolios at each monthly rebalance based on the Top 5 assets by 6-month momentum, but allocate among the assets according to a minimum variance algorithm rather than by volatility sizing each asset individually.

The minimum variance algorithm takes into account the volatility and correlations between the Top 5 assets to create the momentum portfolio with the lowest expected portfolio level volatility. If we rebalance the portfolio monthly with this approach we achieve the following performance [Example 5.].

Example 5: 10 Assets, Top 5 By 6-Month Momentum, Minimum Variance, Rebalanced Monthly

Source: Yahoo Finance, Butler|Philbrick|Gordillo & Associates

You can see that by integrating our last factor, correlation, we are able to achieve higher returns of 15.4% versus 13.7%, and with a substantially higher Sharpe ratio of 1.71 versus 1.51, while preserving the maximum drawdown profile under 16%.

The Next Generation of Portfolio Management

While there are much better algorithms to integrate momentum, volatility and correlation, the examples above show a clear evolution of techniques that demonstrate how to integrate the three primary variables used for portfolio construction under a true Adaptive Asset Allocation framework.

Portfolios assembled using classic Strategic Asset Allocation are vulnerable to the 'flaw of averages' where long-term average values hide enormous variability over time. Quantitative Tactical Asset Allocation suffers from considerably lower returns over time, and is vulnerable to changing market character. For example, QTAA has suffered recently because the dispersion of returns around monthly moving averages has increased by multiples over the past few years.

In contrast, Adaptive Asset Allocation is robust to changes in market character because proper application uses a variety of standard parameter lookbacks for estimation. Further, volatility and correlation management, as well as more regular rebalance frequency, provides substantial tailwinds for portfolios. Lastly, AAA portfolios are always optimally diversified, which makes them robust to market shocks which wreak havoc on more concentrated tactical portfolios.

The portfolio management industry is undergoing a revolution analogous to the shift that occurred after Markowitz introduced his Modern Portfolio Theory in 1967. Managers who embrace the new methods will increasingly dominate traditional managers; those who fail to adapt will, inevitably, face extinction.

*[Geek note: Technically, the Sharpe ratio is calculated using returns in excess of the cash yield, though we use a simple return/risk ratio in this article.]

Intuition is for Suckers

2012-05-09T11:31:00.000-07:00

There has been a great deal of press on Aswath Damodaran’s paper ”Value Investing: Investing for Grown Ups?” in which Damodaran asked, “If value investing works, why do value investors underperform?

This 77 page report offers plenty of grist for the mill, but one study really stood out because it highlights the problem with the first order thinking that most investors, including some of the highest profile managers, use in their security selection process.

It is a commonly held belief that so-called 'blue chip' or 'high quality' stocks will outperform over the long-term. High quality is often defined as a function of balance sheet strength, earnings consistency, capital efficiency and margins, with companies who rank highly in these areas generally favored over companies who rate lowly. This obviously makes intuitive sense.

Interestingly however, and as so often happens in markets, the obvious and intuitive assumption turns out to be dead wrong. The following table, taken from Damodaran's paper, shows the average financial characteristics of two portfolios formed from screens of high quality stocks or 'Excellent Companies' versus low quality or 'Unexcellent Companies'. Clearly the financial characteristics of the Excellent Companies portfolio would appear substantially more attractive and, in theory, would warrant higher returns.

Source: Clayman, Damodaran, 2012

This wouldn't be a very interesting post if the results worked out as expected, and in fact they don't. You can see from the chart below that the un-excellent companies substantially outperformed the excellent companies over the investigated period.

So what happened? You mean we can't count on strong investment performance from the companies with superior financial characteristics?

This is a good example of first order thinking. According to the report, most people examine company fundamentals and, if they are strong, assume that an investment in that company will work out well over time. Unfortunately, if everyone else is looking for companies using similar criteria, then those companies will experience a larger demand for shares. The larger demand will have already pushed the price of these stocks higher to reflect the strong fundamentals, and investors who pay higher prices for a value stock will necessarily receive lower returns over the long term.

In contrast, 'un-excellent' companies are in very low demand, which means their stocks will be relatively cheaper. In fact, the price of low quality value stocks is cheaper than would otherwise be warranted by fundamentals, because people assume that these low quality stocks will generate lower returns. As a result of their unexpectedly low prices, a diversified portfolio of these companies actually ends up delivering better long-term returns.

What can we say? No one said it was easy to make money in markets. If it were, then typical investors would be beating the market rather than lagging the markets by 3 to 5% per year, per the chart below. One of the reasons behind this disparity is that it is difficult to act against your intuition, and your intuition is often wrong because of myriad emotional and cognitive biases.

In other words, our wetware isn't equipped to make profitable choices in complex domains like the markets.

Source: Dalbar, 2012

Another important example of the fallibility of our wetware relates to the common myth that you must take higher risk to achieve higher returns. The following chart compares the returns of two portfolios: the red line reflects the performance of a portfolio formed from the most volatile U.S. stocks each quarter back to 1987, while the grey line shows the performance of the least volatile stocks.

Against all intuition, lower risk stocks outperform higher risk stocks, and by a substantial margin. Lower risk = higher return? Who'd a thunk?

While it's interesting to learn that lower risk equals higher returns in stocks, you may also be surprised to learn that stocks deliver their best performance during periods of low stock market volatility, and deliver their worst results during periods of high volatility. The chart below shines a spotlight on this effect.

Source: Yahoo Finance, DarwinFunds.ca

The chart highlights that the compound returns from stocks during periods of highest volatility delivered negative returns, while the returns during periods of lowest volatility delivered spectacular returns.

This is highly relevant because, while it is more difficult to forecast returns, it is much easier to forecast volatility. The following chart shows the near linear correlation between a monthly forecast based on a weighted average of recent monthly market volatility, and the actual market volatility realized over the subsequent month.

Source: Falkenblog

Given that we can effectively forecast volatility, and periods of high volatility generally correlate with periods of lower returns, imagine what we can achieve by lowering exposure when forecast volatility is above a certain threshold, and increasing exposure when forecast volatility is below the threshold.

To see how we integrate this technique and other concepts into our portfolio management approach, please visit us online at DarwinFunds.ca.