The post Tactical Alpha in Theory and Practice (Part II): Principal Component Analysis appeared first on GestaltU.

]]>Principal Component Analysis (PCA) is a technique for extracting the endogenous, or latent, dynamics that exist in a system. For our purpose, we will be performing PCA on investment universes to determine the independent drivers of portfolio variance. These latent drivers – or factors – are not readily identifiable like, for example, the Fama-French factors (Fama and French, 1993), but are rather embedded in the universe itself. As a result, this method contrasts with typical regression techniques, such as Returns Based Style Analysis or Fama-French factor regressions, which impose external factor structure on a universe of assets to explain portfolio variance.

Principal Component Analysis may be performed on a correlation matrix or a covariance matrix. The covariance matrix contains information about assets’ risk, and the direction of this risk, while the correlation matrix contains only information about the direction of risk. For this series of articles, we will focus primarily on the correlation matrix. That’s because in the context of portfolios, correlation is the only truly independent variable, which can not be altered by the portfolio manager. In contrast, a portfolio manager has the ability to scale the risk of an asset up or down by introducing cash or leverage. Please see the appendix at the bottom of this article to learn why this is so.

Principal Component Analysis involves transforming the original correlation matrix to derive factor loadings and eigenvalues. The loadings are in the form of a matrix with the same dimensions as the original correlation matrix. For example, if there were 30 rows and 30 columns in the original correlation matrix, the loadings matrix will also have 30 rows and 30 columns. Each column of the loadings matrix represents a latent factor that explains a portion of the movement of the underlying portfolio. Each row of the loadings matrix corresponds to an asset contained in the original investment universe. Where an asset intersects a column we observe the sensitivity – or ‘loading’ – of that asset on a particular factor. By design, each factor is independent of the other factors, which means they have zero correlation with each other.

When PCA is applied to portfolio analysis, columns in the loadings matrix are referred to as ‘principal portfolios’ because they are composed of long or short positions in the constituent assets. In this way, the factor loadings can be interpreted as asset ‘weights’ in that factor’s ‘principal portfolio’. The returns from these principal portfolios can be observed by applying the weight vector to the asset returns, and, because they are independent, the returns to each principal portfolio will have a correlation of exactly 0 to one another. We can ‘project’ the returns for principal portfolios back through time just as we can for any other type of portfolio.

Each principal portfolio has a corresponding eigenvalue, which describes the proportion of total portfolio standardized variance attributable to that factor. When the correlation matrix is used in the analysis, the sum of standardized variances is equal to the number of variables or assets in the universe under analysis; when the covariance matrix is used the eigenvalues sum to the total portfolio variance. Figure 1. plots the eigenvalues, or standardized variances, derived from a PCA of the correlation matrix formed from the 30 stocks in the Dow Jones over the 252 days from October 1, 2014 through September 30, 2015. Figure 2. shows the principal portfolios of constituent stocks, which load positively or negatively on each factor.

Figure 1. Standardized variance from Principal Component Analysis of Dow Jones Industrial Average, Oct 2014 – Sep 2015

Data source: CSI

Figure 2. Factor loadings for first 15 principal components of Dow Jones Industrial Average, Oct 2014 – Sep 2015

Data source: CSI

In examining the standardized variances in Figure 1, we note that the first factor (Component 1) exerts a disproportionate impact on the Dow Jones 30 stock portfolio. In fact, it is responsible for about the variance of the next most explanatory factor, and for about 45% of total portfolio variance. Generally, in the case of an equity-dominated universe, the factor that captures the most portfolio variance is considered to be market ‘beta’, and quantifies the degree to which the movement of the average stock is related to the movement of the market as a whole. This is validated by the observation that every stock in the Dow loads in the same direction on Component 1. Other factors might capture certain industry sectors, or sensitivity to interest rates, or arbitrage relationships, though in practice it is often not obvious how to link a latent factor derived through PCA to more traditional grouping structures.

As discussed above, it is useful to think of the factor loadings in each principal component as weights in a ‘principal portfolio’. In fact, when (a transformation of) these weights are applied to the original security returns, we can produce the daily returns for each principal portfolio, just as we would for any other portfolio. If done properly, the variance of the principal portfolio will be in proportion to the standardized variance of that factor. For example, principal component 1 in our analysis of Dow 30 stocks explained about 45% of the standardized variance of the total portfolio, so that when we project the returns for principal portfolio 1 (see Figure 3.), the returns have a variance that is 45% of the variance of the equal weight portfolio of Dow stocks.

Figure 3. Returns to principal portfolio 1. vs. returns from an equally weighted portfolio of Dow 30 stocks, and a DJIA tracking ETF (DIA)

Data source: CSI

Since PCA factor portfolios (i.e. principal components) are definitionally independent sources of risk, we can use them to determine the number of independent bets. However, PCA yields a loadings matrix that contains the same number of factors as there are assets, so we are no further ahead. The goal is to identify how many factors capture a *statistically significant* portion of portfolio variance; only these factors represent true independent bets.

Guttman (1954) and Kaiser (1960, 1970), asserted that in order to be significant, “a factor must account for at least as much variance as an individual variable” (Nunnally and Bernstein, 1994). According to the Kaiser-Guttman method, since the average of all standardized eigenvalues is 1, only factors with standardized eigenvalues greater than 1 can be considered to be significant. Note that in Figure 1 we have added a horizontal line at 1 demarcating the cutoff threshold for significance. From visual inspection it’s clear that just 3 factors exceed this threshold over the past year, so on this basis we might say that there are just 3 significant independent sources of risk at play in this asset universe over the time period analysed.

Unfortunately, Horn (1965) observed that even randomly generated correlation matrices will present with what appear to be significant factors, according to the Kaiser-Guttman method, purely by chance. As such, they showed that the Kaiser-Guttman method systematically overestimates the number of significant factors, and proposed that factors should only be considered significant if they explain a greater proportion of variance than what might be expected from random chance.

Figure 4. shows the same factor loadings for the Dow 30 as Figure 1., and a red line that describes the average variance for each factor derived from 3000 random correlation matrices of the same dimension as the sample matrix (and formed over a similar time period). Note that Component 1 substantially exceeds the threshold of what would be expected from random matrices. However, factors 2 through 30 fail to exceed the threshold, suggesting that these factors are not statistically significant. It follows that over the past 252 days the Dow Jones index of 30 stocks represents only 1 statistically significant independent bet. In other words, it has been almost impossible to achieve meaningful diversification from assembling active portfolios of Dow stocks.

Figure 4. Standardized variance from Principal Component Analysis of Dow Jones Industrial Average (blue bars), and from random correlation matrixes (red line) from Oct 2014 – Sep 2015.

Data source: CSI

Now that we have a general understanding of how to interpret the results of PCA in the context of portfolio analysis, we can proceed to the core of our investigation. Specifically, in the next few articles we will examine the sources of independent risk in larger, more diverse portfolios of stocks, and determine how much of this risk is captured by a much smaller universe of global asset classes. Perhaps surprisingly, we will show how a relatively small universe of global asset classes contains the majority of independent bets available across global markets. Importantly, we will link this fact back to Grinold’s Fundamental Law of Active Management to show why active asset allocation may dominate active security selection in the pursuit of better investment performance.

Figure 5. uses vector diagrams to illustrate how the directional forces from two assets, when held in a portfolio, combine to influence the overall volatility of the portfolio, as a function of the correlation between the assets. Consider a portfolio with one half unit of asset a, with volatility , and one half unit of asset b, with volatility . The portfolio volatility is the weighted sum of the volatilities of the individual assets *in the direction of the volatility, *and the direction of volatility between assets is captured by correlation.

Figure 5. Portfolio volatility as a sum of vectors

In 1.a we observe how the volatility forces combine in the portfolio when the assets are perfectly correlated (). Note that the two volatility vectors are moving in exactly the same direction, so that the portfolio volatility is simply the weighted sum of the individual volatilities: . In 1.b we observe how the volatility vectors combine when the assets have no correlation (). In this case, the assets move in completely unrelated directions, and the portfolio volatility is represented by the hypotenuse of a right-angled triangle. In fact, we can use the pythagorean theorem to solve for portfolio volatility: , so , which works out to 11.2% (note that other correlations will work as well, but require slightly more complicated trigonometry). Note that, when the volatility forces do not align in exactly the same direction, the volatility of the portfolio is less than the sum of the volatilities of the two constituent assets.

Figure 1.c and 1.d demonstrate how a portfolio manager can scale exposure to assets in order to alter the risk profile of the portfolio. In this case he moves to 1.4 units of asset a and 0.6 units of asset b, and this substantially alters portfolio volatility. However, even as he actively scales exposure to assets, the correlation between the assets remains constant. As such, you can see why, when it comes to analyzing the independent bets in a portfolio, we should not be distracted by relative volatilities. Correlation is the only indelible feature, which is beyond the control of investors.

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]]>The post Experts Aren’t Helpful, and Other Useful Lessons From “DIY Financial Advisor” appeared first on GestaltU.

]]>The book is divided into three distinct themes: the fallibility of experts, the FACTS framework, and the actual *DIY* investment strategies. On the first theme, the book feels downright comforting in its familiarity. Covering increasingly well-traveled grounds, the aptly named “Part 1: Why You Can Beat The Experts” discusses common themes for In-The-Know investors, such as:

- Investors rely far too much on the wrong type of expertise.
- Wall Street’s incentives are a horrifying mess that are rarely in alignment with the client.
- Humans have numerous evolutionarily-ingrained behavioral biases that often undermine long-term success, and even the most deified experts are subject to the same human foibles.
- Narratives are as compelling as they are useless, and can even sometimes spiral out of control to the point of establishing myth as reality.
- And because of all the previous points, simplified models have an astounding track record of outperforming “experts.”

There is no denying these points. Years ago the research community reached a tipping point on these topics; there’s no going back now. Enlightened investors are simply waiting for society to catch up, and *DIY* is doing its part to speed the process along. As it so eloquently states:

Here’s the bottom line: everyone makes mistakes. And because we recognize our frequent irrational urges, we often seek the judgment of an expert, to avoid becoming our own worst enemy. We assume that experts, with years of experience in their particular fields, are better equipped and incentivized to make unbiased decisions. But is this assumption valid? A surprisingly robust, but neglected branch of academic literature, has studied, for more than 60 years, the assumption that experts make unbiased decisions. The evidence tells a decidedly one-sided story: Systematic decision making, through the use of simple quantitative models with limited inputs, outperforms discretionary decisions made by experts. We’ll leave the last word to Paul Meehl, the eminent scholar in the field of psychology, “There is no controversy in social science that shows such a large body of qualitatively diverse studies coming out so uniformly in the same direction as this one [models outperform experts].”

After laying a solid behavioral foundation, *DIY* moves onto the second theme: developing a framework for assessing the efficacy of financial strategies. Especially useful for investors currently using a financial adviser, Chapter 5 covers the FACTS method. From the book:

For every investment strategy that needs to be assessed, the FACTS framework (Fees, Access, Complexity, Taxes, and Search) can be employed to clarify important considerations for the prospective investor. Our experience suggests that the vast majority of taxable family offices and high-net-worth individuals should focus on strategies with lower costs, higher accessibility and liquidity, easily understood investment processes, higher tax-efficiency, and limited due diligence requirements. For example, FACTS would suggest, in general, that investors make more use of managed accounts and low-cost passively managed 1940 Act products (ETFs and mutual funds), and fewer private hedge funds and private equity vehicles. Using the FACTS framework can help assess cost/benefit trade-offs across strategy characteristics, which in turn, improves portfolio results net of taxes, fees, and overall brain damage.

And then finally, having established the fallibility of experts and a useful framework for assessing investment strategies, *DIY* moves into a discussion of actual investment methods. We won’t spend the time here going through the details of the various risk management and investment models because…*buy the book*. But there are a few points that deserve recognition.

First, diversification is still the cornerstone of any risk management strategy, but it must be implemented intelligently to maximize benefits. This includes making sure diversifying strategies are qualified through the FACTS framework. But there is no escaping it: you should still eat the free lunch. Second, the authors believe in factor investing, but only at the highest levels of reliability. Because of this, their specific strategy recommendations rely heavily on value and momentum as tools for filtering and weighting portfolio holdings. Wes and Jack are just as passionate about applying factor investing for Tactical asset allocation, especially for the purpose of risk management. Specifically, they recommend simple momentum and moving average filters to step aside from asset classes when there is a risk that they may be trending lower. These methods have been shown to preserve returns while substantially reducing the risk of large losses during bear markets.

It’s no secret that we advocate for a similarly active approach to asset allocation. However, we would lodge a minor objection with their assertions about “advanced” allocation strategies. Specifically, Jack and Wes question the utility of mean-variance optimization based largely on studies performed by DeMiguel, Garlappy & Uppal (2009), which show that optimization-based portfolios underperform naive (1/n) portfolios when optimized over rolling 36 month estimation windows. (In an Appendix to the original paper the researchers confirm their original conclusions via a “robustness test” using a lookback window of 60 months). Unfortunately, the DeMiguel et. al. analysis represents a misapplication of factor investing: by using a rolling 3-5 year window to estimate means and covariances, DeMiguel treated the value factor as if it were a momentum factor. We will revisit this issue at length in a future article.

But we digress! Truly, our quibbles with *DIY*’s assertions on optimization are small relative to our overwhelming alignment with the book’s major themes. At the end of the day, investors are well-advised to pay attention to the changes that will have the largest and most immediate impact on their outcomes, and *DIY* makes those perfectly clear:

- Don’t believe the hype on experts,
- Assess your options using the FACTS,
- Diversify for risk management, and
- Harvest persistent factors for risk management and performance.

It’s impossible not to endorse such a practical and well-formulated set of principles. Congratulations to the team at Alpha Architect for publishing a book that will find a permanent place on our financial bookshelf.

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]]>The post Tactical Alpha: Theory & Practice (Pt. I) – Fundamental Law of Active Management appeared first on GestaltU.

]]>For the overwhelming majority of investors, portfolios are broadly organized into strategic silos of stocks and bonds, such as the ubiquitous 60/40 balanced portfolio. By design, the strategic proportions of stocks and bonds in the portfolio change very little over time. However, within each silo investors take active risk by choosing to hold individual stocks and bonds in weights that deviate substantially from passive market-cap weights. While some investors make active decisions on their own, many investors delegate their active bets by hiring active stock and bond investment managers via the purchase of funds or Separately Managed Account (SMA) mandates.

This article series will consist of a theoretical discussion of Tactical Alpha followed by a series of novel empirical studies. Below, we explore the concept of Information Ratio from the perspective of Grinold’s Fundamental Law of Active Management, which links investment performance to both manager skill and the breadth of available investment opportunities. Next, we provide a brief introduction to our primary analytical tool, Principal Component Analysis, which we will use to quantify the true breadth of an investment universe, after accounting for relationships (correlations) between assets. Following that, we propose a framework, following Staub & Singer, to explore the proportion of total investment universe breadth attributable to asset allocation versus security selection under various correlation assumptions.

Subsequent articles will introduce empirical studies, with the goal of quantifying the proportion of breadth derived from a universe of 10 global asset classes (and cash), versus the unexplained breadth introduced by adding first S&P 100 stocks, and then S&P 500 stocks. Following Polokow and Gebbie (2008) we investigate the number of statistically significant independent bets that exist in each universe at each point in time via a rolling PCA factor analysis. Later, we perform a rolling Monte Carlo style analysis of relative breadth by generating random portfolios of assets and stocks similar to the method proposed in Nguyen (2004).

Recall that traditional alpha is the residual return from security selection after accounting for a strategy’s beta with a market index or benchmark .

Tactical Alpha is somewhat less tangible because there is no obvious benchmark. In practice, Tactical Alpha is often defined as active excess return relative to a policy portfolio, that is achieved through Tactical Asset Allocation decisions. Tactical Asset Allocation is simply active deviation from benchmark weights in the policy portfolio due to changing estimates for risk premia across asset classes over time.

Given that Tactical Alpha seeks to deliver excess returns by incurring active risk relative to a policy portfolio, we argue that the Information Ratio is the most appropriate tool to measure value added. Of course, is also used extensively to measure the value of traditional sources of active risk in the realm of security selection. This makes the a practical unbiased ratio for a comparison of these two sources of active risk. It should be noted that the IR and the Sharpe Ratio are equivalent when the benchmark is a risk-free asset.

Grinold’s Fundamental Law of Active Management states that a manager’s is a function of both a manager’s skill in selecting attractive investments, and the breadth of independent investments from which he can draw. Breadth is related to the number of independent sources of return available in a manager’s investment universe, and the number of times the manager turns over the portfolio. A manager who executes a strategy on a small but diverse universe with high turnover may benefit from greater breadth than a manager who executes on a large but homogenous universe with low turnover.

Grinold’s Fundamental Law of Active Management defines as:

or

where represents the Information Coefficient, measured as the correlation between forecasts and outcomes for each bet; is the number of independent bets available in the manager’s eligible universe, and; is the number of times each bet is evaluated in the measurement period. Note that, by substitution, is a measure of a manager’s *skill*, while shows how breadth is a function of both the diversity and frequency of portfolio bets . In other words, a manager with less skill, but who makes more independent bets, may deliver better risk-adjusted returns than a manager with more skill, but who takes fewer bets.

Our goal for this article series is to isolate the impact of breadth on strategy Sharpe ratios. As such, we will assume that managers are able to bring equal skill to bear on any investment universe; that is, we will hold manager skill constant throughout. This is intuitive because there is no reason to believe that managers operating in one universe, say stocks or bonds in a specific geographical market, are any more or less skilled than managers operating in a other universes, such as global asset classes, geographic market indexes, or sectors.

In his original paper, The Fundamental Law of Active Management, Grinold equates the number of independent bets with the number of securities in a manager’s investable universe. For example, a large-cap equity manager may be restricted to investing in securities in the S&P 500, so he has 500 securities to choose from each time he makes a `bet’. In contrast, a tactically oriented investor who focuses on asset allocation may choose between, say, 10 major asset classes. By extension from Grinold’s interpretation, and assuming similar skill and turnover for both managers, the tactical manager would be expected to have an of of the of the large cap equity manager. For the purpose of consistent nomenclature, we will call this ratio the Information Ratio Multiple (IRM). Thus, the IRM will quantify the square root of the number of independent bets in an investment universe.

Unfortunately, Grinold’s interpretation makes the strong assumption that the 500 securities in the stock-picker’s universe, and the asset classes which comprise the tactical manager’s universe, represent `independent bets’. However, this interpretation implicitly assumes that the securities in the specified universe are independent – that is, uncorrelated. That’s because if two bets are positively correlated, they are definitionally not independent.

This is easily demonstrated by taking an extreme example of two securities which are 100% correlated. If we apportion weights to the securities in a portfolio so that they contribute equal volatility, the portfolio of two securities would behave precisely as though it held either of the two securities on its own. Obviously in this case, despite there being two securities, there is really just one bet, and a manager with skill would have no opportunity to earn excess returns by choosing between them. On the other hand, if the two securities are completely uncorrelated, the combined portfolio would behave quite differently than either of the securities on its own, and a manager skillful manager would have an opportunity to be rewarded with excess returns.

Of course, stocks in a given market are almost always positively correlated, while correlation between stocks and bonds may be positive or negative at different times. In fact, over the past 20 years, individual stocks in the S&P 500 have tended toward a pairwise correlation of 0.35 with a 95% range of 0.1 to 0.65, while stocks and Treasuries have averaged a correlation of -0.1 with a 95% range of -.65 to +0.6. As we will see, the fact that correlations deviate from Grinold’s assumption has important implications for managers’ potential to generate high risk-adjusted performance in security selection versus asset allocation. Furthermore, if the trend over the past 20 years continues, stock correlations may continue to rise while stock and bond correlations decline, per Figure 1, with important implications for trends in marginal breadth.

Figure 1. Rolling 252 day correlations

*Source: ReSolve Asset Management, CSI, Barclays, S&P*

In the next article, we will introduce our instrument of data torture, Principal Component Analysis, and demonstrate how we can use this tool to quantify the number of statistically significant ‘bets’ in any market. Later, we will use these tools to demonstrate why a small universe of asset classes can offer greater breadth – and commensurately a larger potential opportunity for alpha – than a much larger, but homogeneous, universe of individual stocks.

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]]>The post Apples and Oranges: A Random Portfolio Case Study appeared first on GestaltU.

]]>Harry expressed some disappointment with the performance of Global Tactical Asset Allocation (GTAA) strategies over the past few years relative to some popular tactical U.S. sector rotation funds.

Harry’s definition of GTAA is any strategy that regularly alters its allocation across a wide variety of global equity markets and asset classes, including bonds, REITs, commodities, and cash. In contrast, tactical U.S. sector products attempt to earn active returns by allocating to the most prospective U.S. equity sectors. In addition, many of the sector strategies can hold substantial amounts in cash when few or no sectors are attractive.

Harry’s point, which is fair in many respects, is that the goal of investing in tactical U.S. sector products is the same as the goal of investing in GTAA products – strong risk-adjusted returns with a smooth equity curve and manageable drawdowns. As an investor, he doesn’t care how his wealth is created, only that it has a reasonable upward slope with fairly small wiggles around the upward trend. If U.S. sectors are more likely to do the trick, that’s where he’d like his money to be.

Unfortunately, there is a major flaw in this logic. You see, even awful U.S. sector rotation products would have been expected to beat top tier GTAA strategies over the past few years. To understand why, consider that an active manager’s ability to deliver returns depends on three factors, which vary in importance through time:

- Manager skill – All else equal, a skilled manager will deliver higher risk-adjusted performance over the long-term.
- Number of independent bets – A manager with skill who makes many bets will have better results than another manager with similar skill who makes fewer bets.
- Opportunity set – If two managers are equally skilled, but one manager is choosing among investments that are all booming while the other is choosing between a group of investments that are all busting, the former manager will prevail almost every time (subject to long-only constraint).

Depending on the interplay between these three factors, mediocre managers operating on an especially strong investment universe should quite often be expected to outperform even very skilled managers who are operating on a weaker universe. Worse, the dynamic and unpredictable nature of global markets are such that this situation can persist for much longer than might seem intuitively reasonable. This makes distinguishing manager skill from luck extremely challenging, especially over short horizons like 3 to 5 years.

To truly gain an understanding of the difference between the opportunities presented by two investment universes, it is helpful to invoke the concept of ‘random portfolios’. Random portfolios are created by randomly assigning portfolio weights among eligible assets in a universe at each rebalance date. It is possible to impose constraints on the character of the random portfolios, such as: all weights must be positive; weights must sum to 1; maximum weights in certain assets; minimum, maximum or target number of holdings, etc., in order to model the true opportunity set available to a manager.

In the following analysis, we examine the relative opportunity sets available to GTAA managers vs. U.S. sector managers over time. Our intention is to discover the relative opportunity – in the form of return distributions – available to managers in each universe over rolling annual periods from 1995 – 2015. To do so, we created 10,000 random portfolios each quarter rom a universe of 10 global asset classes, and another 10,000 portfolios from a universe of 10 global sectors plus cash. At each quarterly rebalance date, random portfolios from each universe are formed, and the daily returns for each portfolio are saved over the subsequent quarterly period. Annual returns are then formed from rolling 4 quarterly periods through time.

Figure 1. provides a snapshot of the annual period ending September 2014, where most random sector portfolios performed substantially better than most random asset class portfolios. Note that, during this period the average Sharpe ratio for sector portfolios was over 2, while the average Sharpe ratio for asset class portfolios was about 0.4. In other words, if both U.S. sector focused managers and global asset allocation managers were monkeys picking portfolios at random, we would expect the average risk-adjusted performance of the sector monkeys to deliver over 4x the performance of the asset class monkeys.

The distributions around these means are also important to our analysis. From visual inspection, you can see that the 5th percentile outcome for sector portfolios (left tail of light blue plot) is about the same as the 95th percentile outcome for asset class portfolios (right tail of the dark blue plot) for this period. In other words, even the least skilled sector allocator choosing the best U.S. sectors over this period would be expected to deliver better performance than the most skilled asset allocator choosing the best assets.

Figure 1. Distribution of Sharpe ratios from 10,000 random portfolio simulations on an asset class and a U.S. sector universe, year ending Sep 30, 2014.Data source: CSI

While Figure 1. highlights a period where sector strategies dominate asset allocation strategies, there are other periods where asset allocation strategies prevail over sector strategies. In Figure 2., we show a similar analysis for the 1 year period ending March 31, 2000, when asset allocation dominated sector strategies.

Figure 2. Distribution of Sharpe ratios from 10,000 random portfolio simulations on an asset class and a U.S. sector universe, year ending March 31, 2000.

Data source: CSI

Of course, we don’t expect our asset managers to act like monkeys. Presumably our managers have skill, and will perform better than what might be expected from random guesses. But we are specifically concerned with comparing an asset allocator’s performance with a sector allocator’s performance over a given observation horizon. In which case, we want to know the chance that portfolios selected by a manager in one universe over the past year would outperform portfolios selected by a manager in the other universe over the same period.

In Figure 3. we plot this quantity over time (for those who are curious, the statistic is called Probability of Superiority). Specifically, we plot the probability that a performance outcome drawn from the asset allocation distribution will exceed a performance outcome drawn from the sector distribution over trailing annual periods ending in each quarter from 1995 – 2015.

Figure 3. Probability that GTAA performance will exceed a sector performance.Data source: CSI

An example will illustrate how to interpret Figure 3. The light blue line peaks in early 2000 at a value of 0.83, indicating that over the prior 4 quarters ending March 2000, there was an 83% chance that a portfolio chosen at random from the asset allocation universe would have a higher Sharpe ratio than a portfolio chosen at random from the sector universe. It follows that an asset allocation manager needn’t have been particularly skilled at that time to deliver better returns than a manager who was selecting among U.S. sectors. On the other hand, in the year ending September 2014, there was almost 0% chance that a portfolio chosen at random from the asset allocation universe would have had a higher Sharpe ratio than a randomly selected sector portfolio. As such, it would have been almost impossible for an asset allocator to deliver better performance in that period.

Another way of looking at the problem is from a direct examination of the relative skill that an asset allocator would have to exhibit in each period to deliver better performance than an average sector allocator. In investment management, skill is measured by Information Coefficient (IC), which is the correlation between ex ante investment bets and optimal ex post outcomes. It is a simple matter to calculate the IC that would be required in each period in order for an asset allocator to outperform a sector allocator because of the Fundamental Law of Active Management:

We have already calculated the performance of asset allocation vs. sector allocation in each period, and we know universe breadth averages for both strategies, so it is a simple matter to rearrange the terms of this equation to solve for the IC.

Using this equation, we can find the empirical IC over each rolling annual period. However, it is less obvious how to interpret Information Coefficient. Fortunately, it’s easy to translate IC into “win rate”, which is the percentage of time a manager makes a bet in the right direction. Win rate and IC are functionally equivalent for interpretation because .

Once we have solved for the IC for each strategy in each period, we can find the excess win rate implied for the asset allocation universe vs. the sector universe. This rate tracks the relative skill that would be required for a manager of an asset allocation strategy to deliver better performance than a manager of a sector strategy in each trailing annual period. Figure 4. plots this value through time.

Figure 4. Win Rate that would be required for a GTAA manager’s performance to exceed a sector manager’s performance over trailing 4 quarters.Data source: CSI

From Figure 4. we see that there are periods when even managers with negative skill at choosing asset classes (win rate < 0.5) will deliver better performance than sector allocators, and vice versa. Over the 4 quarters through Q2 2000, even an asset allocator who’s bets were accurate just 35% of the time would have delivered better performance than an average sector manager. In contrast, over the 4 quarters through Q3 2014, an asset allocator would have had to be accurate with over 78% of his bets to beat an average sector manager.

To put these win rates in perspective, Ding (2010) estimated the ICs for the value and momentum factors in U.S. equities to be 0.017 and 0.025 respectively, which translates to win rates of 50.85% and 51.25% respectively. We also calculated the implied win rates for the Global All Asset value and momentum factors from Asness et. al. (2012) to be 51.3% (they are effectively the same). Given that the strongest observed factors are observed to have average win rates of less than 52%, it is effectively impossible for a manager to overcome win rate hurdles of 55%-70%.

So where do things stand at the moment? Over the annual period ending August 31, 2015 it would have been practically impossible for an asset allocator to deliver stronger performance than a U.S. sector manager. In fact, over the past 8 quarters an asset allocator would have required a win rate over 60% in each period to be competitive with U.S. sectors, which is orders of magnitude higher than what we observe from the best long-term factors.

The fact is, there are periods when allocating in a concentrated way to one major asset class will pay off. But most investors’ concentrated allocation to U.S. stocks did not come about because of thoughtful active bets. Rather, investors are concentrated in U.S. stocks by default, because of home country bias. In addition, many U.S. advisors and CIOs are terrified of tracking error vs. U.S. stocks because the Dow and S&P are such strong emotional benchmarks for clients. This amplifies the already powerful home country bias dynamic.

But make no mistake – U.S. equity domination is a transient phenomenon. It is the financial equivalent to the ancient proverb about the tortoise and the hare. At the moment, U.S. stocks have stormed far ahead of the pack. However, U.S. stocks can not continue to outperform all other asset classes without driving an enormous valuation and yield advantage to other markets. Consider the 8 year period from 2001 – 2009, when even poorly executed global asset allocation strategies left U.S. sectors in the dust.

Those investors who default to concentrated U.S. equity portfolios and ‘balanced funds’ face a day of reckoning. Fortunately, investors have attractive choices for diversification. More passively minded investors might consider the Global Market Portfolio, or a global risk parity strategy. Experienced investors might consider more active approaches that take advantage of factor tilts, such as systematic GTAA strategies. There is no guarantee that global diversification will pay off in the next few weeks or even months. But over the long term, thoughtful global strategies have a much higher probability of delivering against investors’ financial goals. And isn’t that really the point of all this?

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]]>The post Empirical Finance: Meeting Fiduciary Standards Through Skepticism, Not Cynicism appeared first on GestaltU.

]]>**A Primer on Empirical Finance**

Academics and quantitatively minded practitioners in finance spend much of their time trying to discover new sources of excess returns in markets. For the purpose of this article, let’s call these sources of excess returns ‘factors’. The most robust studies begin with a logical premise based on a reasonable theory about sources of risk and how investors behave. Typically a theory proposes that investors misbehave in a consistent way, which helps to inform a hypothesis that the researchers can test by examining data. The hypothesis often asserts that the proposed mistakes provide an opportunity for others to earn excess profits, and the researchers believe the data will support this view.

Good science, however, starts by stating a so-called ‘null hypothesis’, which is consistent with the dominant paradigm. In finance, the dominant paradigm is the ‘Efficient Markets Hypothesis’, which generally states that investors do not make mistakes, and that there are no persistent sources of excess returns in markets. As such, researchers who present a theory for why investors do make persistent mistakes, which provide opportunities for excess profits, face a high hurdle if they expect their peers to embrace their theory.

In finance, these hurdles are represented by statistical thresholds. For example, in order for a finance researcher to reasonably argue that the effect he has discovered is ‘significant’, there must be less than a 5% probability that the effect might have been observed purely by chance. If there is greater than 5% likelihood that the observed effect is the result of luck, the researcher cannot reject the null hypothesis that markets are efficient. Only when the observed effect is substantially large, and/or has been observed across a large number of observations, such that there is less than a 5% chance that the results are due to random chance, can the researcher reject the null hypothesis and claim that his theory has merit.

By convention, most finance researchers prefer to think of statistical significance not in terms of probability values explicitly, but rather in terms of ‘t-scores’. Of course, basic statistics equates any t-score with a probability value, so t-scores and probability values are interchangeable in terms of conclusion. Without going too far down the rabbit hole, suffice to say that under standard assumptions if an effect presents with a t-score greater than ~2, there is less than 5% chance that the effect is random; therefore it is considered to be statistically significant. Where a researcher wants to be extra cautious, he may want the effect to be significant at a 1% threshold, which corresponds to a t-score of about 2.6.

**But there are Many Tests**

In their paper, HLZ assert, quite rightly, that as more researchers run experiments to find factors that explain (i.e. forecast) sources of excess returns, there is an increasing probability that researchers will stumble on spurious factors. In other words, if many researchers are running many tests, it is inevitable that some researchers will find effects that appear to be statistically significant, but which have in fact occurred purely by chance. As such, observers of these studies should become more skeptical of statistically significant results over time.

HLZ suggest that, to counter this known issue, thresholds for statistical significance should increase in proportion to the number of tests that have been conducted to date. They propose three adjustments to account for this issue, and demonstrate that, after accounting for these adjustments, the majority of historical ‘discoveries’ in finance, including those that meet traditional tests of significance, are probably due to random chance.

Figure 1. is drawn from HLZ. The red, green and blue lines on the chart show three methods for how the threshold for statistical significance should rise in recognition of an accelerating number of factor tests through time. For example, according to the Bonferroni test (blue line), the t-score that would indicate statistical significance in 1995 was about 3.25, while tests of new factors conducted today should be rejected unless they exceed a t-score of 3.75. While this might seem like a small increase in threshold value, in fact it represents a hurdle that is almost 6x harder to overcome.

Figure 1. Published t-scores and statistical significance of select equity market factors at time of publication adjusted for data-mining bias.

Source: Harvey, Liu and Zhu, 2014

Factors in Figure 1. are highlighted according to their dates of discovery and the statistical significance (t-score) found in the original papers. Note that the market (MRT), value (HML), momentum (MOM), durable capital goods (DCG), and short-run volatility (SRV) factors exceed even the most conservative adjusted thresholds for statistical significance. Importantly, these factors would still be deemed statistically significant even if they had just been discovered recently, because their t-scores are so high. Perhaps surprisingly for some, the small-cap premium (SMB) did not survive these more rigorous tests.

Michael Edesses argues that the thresholds above substantially understate the true number of tests that have been conducted because research that does not reach a significant conclusion is rarely published. This did not go unnoticed by HLZ. In fact they calculate that the number of published factor papers understates the number of actual factor tests by about 71%. However, when they make adjustments based on these more conservative estimates, the 5 factors above remain statistically significant.

**From Skepticism to Cynicism**

HLZ demonstrate a healthy skepticism in acknowledging the prevalence of Type I error in financial research. In contrast, Michael extends HLZ’s conclusions from healthy skepticism to zealous cynicism. Where HLZ propose structured and well established methods to account for data-mining bias in research, Michael wonders, “Is it impossible to raise the bar high enough?”, and answers: yes!

Unfortunately, Michael offers no evidence to support this contention, and no solution in the event that it is true. As such, Michael leaves financial practitioners in the predicament of having to make decisions in markets, but where no research that might inform these decisions can be trusted. This is hardly constructive.

We contend that HLZ provide a rational framework for raising the bar on financial research. By applying their guidelines, investment practitioners have tools at their disposal to differentiate between spurious conclusions and meaningfully prospective methods, and can make appropriate informed decisions in this context.

**Confidence Inspired by More Evidence**

HLZ is not alone in their desire to bring statistical rigour to the financial research process. Many well respected practitioners share HLZ’s concerns and apply similar methods in their own practices.

One way for practitioners to gain greater confidence in prospective factors is through out-of-sample testing. Fortunately, there is an abundance of out-of-sample analysis validating the most robust factors. One obvious out-of-sample test involves testing the factor on a brand new universe. For example, if a method worked on U.S. stocks, it should also work on stocks in other international stock markets. In addition, if a factor was identified in 1993, then tests over the 20 year period from 1994 – 2013 are also considered out-of-sample. One might also ‘perturb’ a factor’s specification to test for robustness, say by changing the definition of ‘value’ from price-t- book value to price-to-cash-flow or price-to-earnings.

In “Finding Smart Beta in the Factor Zoo”, Jason Hsu and Vitali Kalesnik at Research Affiliates performed tests of the value, momentum, low beta, quality and size factors on stocks across U.S. and international markets. For tests on U.S. markets they used data back to 1967, while international tests were run from 1987. Recall that the size, value and momentum factors were first documented in the early 1990s, and the low beta anomaly was first catalogued by Haugen in the mid-1970s. In addition, all factors were first identified using exclusively U.S. stocks. As such, by testing on international markets over the period 1987-2013 their analysis was legitimately ‘out of sample’. That is, they tested on out-of-sample universes, and over a 26 year horizon, where 20 years were out of sample in time. Results in international markets were consistent with the results of the seminal papers.

In addition, Hsu and Kalesnik tested using different definitions of the factors. For example, they tested ‘value’ as defined by dividends-to-price, cash-flow-to-price, and earnings-to-price as well as the original book-to-price metric. They also varied the lookback horizons and skip-months for momentum, and tested both beta and volatility for the low-beta factor, again with different lookback horizons. As you can see from Figure 2., the value, momentum and low beta factors all proved robust to alternative definitions.

Figure 2. Value, low beta and momentum factors prove robust to alternative specifications

Source: Research Affiliates using CRSP/Compustat data

Clearly Jason Hsu at Research Affiliates takes seriously the concerns raised by HLZ, and has taken steps to increase empirical rigour of their solutions. But they are not alone.

The principals at AQR, principally Cliff Asness and colleagues, performed their own analysis of the value and momentum factors across both a universe of global stocks and a universe of global asset class indexes. Their tests span the period 1972-2011, so about 40% of their analysis period is out of sample in time. Of course, about half of their global stock universe, and the entire global asset class universe, is also out of sample for the entire period. Their results are summarized in Figure 3. below.

Figure 3. Statistical significance of value and momentum factors across global stocks and asset classes, 1972-2011

Source: Asness, Moskowitz and Pedersen, “Value and Momentum Everywhere”

Highlighted in green, note the statistical significance of risk-adjusted excess returns from the value and momentum factors in global stocks (top) and global asset classes (bottom). This analysis validates the persistence of the value and momentum factors across a largely out of sample data set. Even better, the t-scores exceed the higher thresholds proposed by HLZ, and tests on the asset class universe overcome HLZ’s higher hurdles with substantial margin to spare (full disclosure: ReSolve investment solutions rely largely on asset class momentum and low beta factors).

**The Recipe for Success**

HLZ, Hsu and Kalesnik, AQR, ourselves, and most other reputable practitioners agree that empirical evidence is necessary, but not sufficient to validate prospective investment strategies. Rather, in addition to empirical evidence, Hsu and Kalesnik maintain that, “The factor has [to have] a credible reason to offer a persistent premium”. Specifically, they would find empirical evidence of a factor compelling if:

- It is related to a macro risk exposure, or
- It is related to a deep-rooted behavioral bias that is present in a meaningful fraction of investors, or
- It is related to an institutional feature that cannot be easily changed.

Wes Gray of AlphaArchitect makes almost exactly the same point in a recent article. Basically, Wes says that even if you identify a statistically significant market opportunity, you must still ask yourself these four questions before you can have confidence that the effect is real:

- Who is the sucker – that is, from which investors do we expect to extract excess returns?
- Why are the suckers making mistakes, and why should they be expected to continue making the same mistakes in the future?
- Who are the pros – that is, who are the natural arbitrageurs of the opportunity?
- What is preventing the pros from taking advantage of the opportunity?

If you can answer these four questions with confidence, and the effect demonstrates statistically significant results, then a reasonable practitioner would be remiss in ignoring the potential opportunity.

**Where We Stand**

We firmly believe that the scientific process is alive and well in empirical finance, and that HLZ’s guidelines are an excellent example of the process at work. Financial practitioners should evaluate research with a healthy skepticism, and an awareness of the implications of data mining. Further, investors should be especially skeptical of papers claiming the existence of new factors with no foundation in theories of risk or investor behaviour, and where there are no clear limits to arbitrage.

Where possible, investors should seek out validation through out-of-sample testing. This includes tests on new investment universes; tests on different time frames, and; tests that perturb the definition of the phenomenon. Where a factor has good theoretical roots and proves resilient to a wide variety of empirical tests, rational and dispassionate practitioners must answer a difficult question: why would a responsible fiduciary ignore the opportunity?

Ideology of any kind is the enemy of constructive thinking. The hallmark of a cynic is sweeping disregard for evidence where it runs counter to their worldview. If a person’s worldview holds that all financial professionals are charlatans, he will view all financial research through the prism of this ideology. But this is profoundly counterproductive. After all, the practice of financial advice and management demands real-time decisions every day that affect people’s lives. How is one supposed to act? Worse, how is one supposed to uphold his fiduciary standard?

The truth is, an investor can choose to act in a way that is consistent with how they feel the world should work, or he can choose to act in a way that is consistent with a thoughtful interpretation of the evidence. Empirical finance is the manifestation of this latter worldview, and consistent with all reasonable thresholds of professionalism and fiduciary standard.

We know where we stand, and now so do you.

The post Empirical Finance: Meeting Fiduciary Standards Through Skepticism, Not Cynicism appeared first on GestaltU.

]]>The post Forget “Active vs. Passive”: It’s All About Factors appeared first on GestaltU.

]]>First, some background on ‘passive’ investing. The progenitor of contemporary passive investing is almost certainly Bill Sharpe, who demonstrated in 1964 that, when markets are at equilibrium, the most efficient portfolio is the Global Market Portfolio. This portfolio holds all global financial assets in proportion to their market capitalization (see our article A Global Passive Benchmark with ETFs and Factor Tilts for more background on the Global Market Portfolio and implementation options). Fundamentally, Sharpe’s conclusion is based on that fact that the market cap weighted portfolio represents the current aggregate of all investor bets in the market. This is why ‘passive’ investing is often used interchangeably with market cap weighted indexing.

Market capitalization based indexing has several advantages. First, it is the only portfolio that is consistent with a belief in efficient markets. It is also definitionally the lowest turnover portfolio, as position weights in the portfolio automatically rise and fall in response to changes in relative market capitalization as constituent assets go up and down in price. (Note: This is not precisely true, as stock retirement and issuance will alter ratios through time, but this is small in proportion to total value). In addition, it is the only truly ‘neutral’ portfolio, as it is possible for every investor in the market to own this portfolio in precisely the same weight.

Despite these benefits, and the theoretical case for a passive approach, most investors do not choose to go this route. Granted, most investors are constrained by externalities such as income taxes, estate taxes, regulations, access to alternative products, higher costs, and currency preferences which prohibit passive investment in the Global Market Portfolio. These realities are augmented by behavioural biases such as overconfidence, lottery preferences, and the availability heuristic, which make it difficult for many investors to stick to a passive approach.

Instead, clients and advisors have traditionally adopted an enormous home market bias by setting a policy portfolio with majority allocations to domestic stock and bond sleeves. Then they proceed to compete on the basis of who can pick the best stocks and bonds within their home market. The fact that this represents an active approach because of the pursuit of active security selection is uncontested. But many investors may not realize that, as a result of deviating quite dramatically from the Global Market Portfolio, this methodology also represents a profound, but ultimately implicit, active bet on asset allocation.

Given that most investors default to active management for the reasons described above, among others, let’s spend a moment exploring this approach.

Overwhelmingly, investors pursue active management with the goal of outperforming a passive index by way of astute selection of individual stocks and bonds. The defining characteristic of active management is typically ‘manager as irreplaceable expert’. Ostensibly, the manager possesses certain qualities or unique talents that allow him or her to identify superior investments. Presumably, the manager’s process can not be replicated with simple rules. Typically, active management involves detailed analysis of micro- and macro-economics, industry dynamics, themes, financial statements, and idiosyncratic value drivers of companies. In the end, the manager forms a narrative about why an investment has strong prospects, often with price targets, and monitors the investment to ensure it stays true to this narrative.

This all sounds like complicated and noble work, and it is. Unfortunately however, the track record for traditional discretionary active management leaves much to be desired. Two firm conclusions can readily be drawn from the most up-to-date literature:

- Even the best active equity mutual funds deliver no discernible alpha relative to well specified benchmarks after controlling for luck and fees, and most active managers underperform index funds
*before*fees. - While it’s easy to identify which managers have done well
*in the past*, this carries no meaningful information about which managers are likely to deliver alpha*going forward*. In fact, there is compelling evidence that strong performance over the past 3 to 5 years*negatively predicts*performance over the next 3 to 5 years.

(See Blake here and here, Crane and Crotter here, Fama here, Ferri and Benke here, Vanguard here, SPIVA here, etc.)

This may be difficult to swallow, especially when your manager seems to be blowing the doors off. It’s exciting to hitch a ride on a ‘hot hand’, and self attribution bias causes us to believe that our success is a direct result of our own refined intelligence, process and efforts. The grim reality is that any intermediate term outperformance you may be experiencing is more likely due to some combination of beta (sensitivity to the overall direction of the market), and/or a series of lucky bets. In all probability, you are vulnerable to an equivalent magnitude of laggardly performance down the road.

We acknowledge that there may be a role for some types of active managers in certain portfolios, particularly managers with high levels of ‘active share’, because they may represent complimentary sources of idiosyncratic risk. However, identifying managers on this basis involves a deep understanding of existing portfolio exposures and a sophisticated understanding of how active share might deliver outperformance. Exposure to managers with high levels of active share will also result in high levels of tracking error, which many investors find difficult to tolerate.

Investors may also find sporadic active management opportunities in narrow segments of the market, like complex products or industries which require highly specialized knowledge. But this isn’t particularly helpful for most investors, because the really hard part is identifying when dislocations have occurred in a segment which might allow specialized managers to thrive. For example, even if we identify a superbly proficient manager in the small-cap gold miner space, the manager is unlikely to outperform the broader market during multi-year periods when the gold stock sector is out of favour.

In short, there is no reason for most investors to seek outperformance from traditional discretionary active stock picking in regulated mutual funds or separately managed accounts. Even the most optimistic fan of active management would struggle to find evidence of outperformance in a comprehensive survey of contemporary literature. The logical next step is to conclude that, if active managers can’t beat the benchmarks, investors should invest in the benchmarks. But what are the benchmarks anyway?

In the 1990s the venerable Don Phillips at Morningstar came up with the concept of ‘Style Boxes’ to differentiate between different styles of equity managers. Style boxes were rooted in the seminal research of Fama and French (1992) which demonstrated that companies of different size and valuations represented meaningfully different sources of risk in markets. Thus the style boxes divided managers in terms of the size and value/growth characteristics of their holdings into 9 quadrants as described in Figure 1.

Figure 1. Morningstar Style Boxes

The style box framework dominated institutional and retail portfolio construction for two decades, though it was never proposed as a way to structure passive portfolios. Rather, investors typically applied the concept in an effort to ‘diversify’ active equity portfolios with investments in managers across several style boxes. The hunt was on for the best ‘large cap growth’ managers or ‘small cap core’ managers. Of course, soon after advisors and investors began seeking out managers to fit into these style boxes, they realized there were no relevant benchmarks against which they could evaluate managers in each style.

Russell investments solved the problem by creating tracking indexes for each of the Morningstar style boxes. Eventually, fund companies launched index funds to track these benchmarks, and in the early 1990s investors were offered exposure to these benchmarks with Exchange Traded Funds.

Interestingly, while benchmark strategies like ‘small cap value’, ‘mid-cap core’, and ‘large cap growth’ clearly are not ‘passive’ in the classical sense, they have come to be perceived as passive over time. After all, they represented cheap, investable, systematic alternative to active managers in each style. This was the first step in the process of broadening investors’ perceptions of passive versus active. Fortunately however, the investment management industry didn’t stop there.

Russel’s invention of tracking portfolios for Morningstar’s style boxes caused a subtle shift in investors’ understanding of ‘passive’. Suddenly there were quasi-passive options which allowed investors to take advantage of known sources of outperformance in markets. Style index products inserted themselves firmly in the middle between pure passive methods at one end of the spectrum, and discretionary active management at the other end. Even better, these approaches were simple and rules-based, making them easy for even unsophisticated advisors to utilize. That meant they could be relatively cheap. And when it became clear that managers could not be counted on to beat their style benchmarks, investors began to perceive their investable indexes as attractive alternatives.

As discussed above, the style concept grew out of the identification of systematic sources of risk and reward from the academic literature. But in reality, style boxes were a rather strange way to harness these anomalies. After all, ‘growth’ stocks under this framework were simply defined by the fact that they weren’t ‘value’ stocks. Why would investors deliberately allocate to expensive stocks instead of cheap stocks when the literature clearly demonstrated that expensive stocks persistently *under*perform.

Eventually investors began to adhere more closely to the academic literature by abandoning ‘growth’ tilts and adding other academically identified sources of systematic outperformance, or ‘factors’. Common factor tilts include biasing portfolios toward value metrics like book to market or price to cash-flow; momentum; or low volatility. Each of these factors has deep fundamental roots. For example, it is intuitive that investors should require (and receive) excess returns for bearing the risk of investing in companies which are neglected by other investors (value stocks). Momentum has been explained by theories related to information dispersion, informational cascades (herding), and prospect theory. The low beta effect has been linked to investors’ aversion to the use leverage to achieve return targets, and the so-called ‘lottery’ and/or ‘story’ stock effect.

In addition to strong theoretical roots, systematic equity factors like value, momentum, and low beta have evidenced a high degree of statistical significance over very long horizons. In fact, these factors appear to be even more significant than the ‘equity premium’, which captures the excess required return on stocks relative to risk free assets as a function of stocks’ higher volatility. In other words, there is greater statistical evidence that value, momentum and low beta factors outperform the market capitalization weighted index, than there is evidence that the market cap weighted index outperforms t-bills. This is illustrated in Figure 2, extracted from Harvey, Liu and Zhu.

Figure 2. Published T-scores and statistical significance of select equity market factors at time of publication adjusted for data-mining bias.

Source: Harvey, Liu and Zhu, 2014

In Figure 2 anomalies are marked with a two or three letter code. For example, MRT is the original ‘equity risk premium’ factor first described by Fama and MacBeth in 1973. Each factor’s position along the x-axis identifies the factor’s year of discovery, while the y-axis captures the t-score, or statistical significance of the factor from the seminal paper. MRT demonstrates a T-score of about 2.6, which is of course statistically significant at the standard 5th percentile threshold (t-score of ~2.0), so we can be confident that stocks in fact do deliver higher returns than t-bills. The small cap anomaly (SMB), which posits that smaller capitalization companies outperform larger capitalization companies, is also statistically significant (for U.S. stocks, though this has since been discredited: Shumway and Warther, 1999). Note that HML, representing the value factor, is significant above a T-score threshold of 4.9, as is the momentum premium, indicating a confidence level in excess of 0.9999%. We leave it to the reader to explore some of the more obscure but robust alternative premia on the chart.

The ubiquitous Jason Hsu and Vitali Kalesnik at Research Affiliates recently published their own audit of the most often cited equity factor anomalies, including value, low beta, momentum, and quality factors (proxied by profitability and ROE). Not content to rely on published literature, they performed their own sorts using CRSP/Compustat and Worldscope/Datastream data for four major geographic regions: US, UK, Europe ex-UK, and Japan. The goal was to explore the persistence of these factors across regions as a test of robustness. They also tested alternative formulations of each factor to ensure the observed phenomena were not data-mined noise. Their results are in Figures 3 a) and b).

Figure 3a. Tests of equity factor significance across geographic markets

Figure 3b. Tests of equity factor significance across factor formulations

Source: Finding Smart Beta in the Factor Zoo, Hsu and Kelsnik, 2014

Clearly the value, low beta and momentum factors are highly robust to tests across markets and formulation, while the quality type factors do not stand up to either kind of perturbation. Interestingly, while both value and momentum effects are each not observed in one geographic market (UK and Japanese stocks respectively), value and momentum effects are observed across virtually all markets and asset classes, so we (and the authors) suspect these are outliers. Low beta stocks, on the other hand, are highly significant across all the markets studied.

So far we have largely discussed the active vs. passive debate in the context of equity market investments. However, as we’ve explored at length in previous articles (see Tactical Alpha, Adaptive Asset Allocation, Global Passive Benchmark with ETFs and Factor Tilts), this misses the forest for the trees. The asset allocation decision dominates portfolio outcomes, and therefore deserves attention.

Remember, the EMH specifies that the only truly passive approach to asset allocation is the Global Market Portfolio (GMP). So if we deviate from this portfolio, we are definitionally taking active bets against the EMH. Black and Litterman acknowledged this explicitly in formulating their Black-Litterman model, which uses the weights from the Global Market Portfolio to reverse engineer implied average estimates for asset returns and covariances.

However, there is reason to believe that, if there is any inefficiency in the investment process, it is more likely to manifest *across* large asset classes rather than *between* individual stocks or bonds. In other words, we are more likely to observe dramatic mispricings of a stock market index vs. a bond market index, or two different global stock or bond market indices, than we are to observe mispricings among individual stocks in a given market. After all, there are significant structural impediments to arbitrage away asset class level anomalies, because institutions and private investors have traditionally stuck tightly to established strategic asset allocations with very little dispersion (see Brinson (1991).

We are not alone in espousing this view. Nobel Laureate Paul Samuelson also made the case that markets were likely to be inefficient across asset classes, but efficient within them, in a letter to fellow Nobel Laureate Robert Shiller:

Modern markets show considerable micro efficiency (for the reason that the minority who spot aberrations from micro efficiency can make money from those occurrences and, in doing so, they tend to wipe out any persistent inefficiencies). In no contradiction to the previous sentence, I had hypothesized considerable macro inefficiency, in the sense of long waves in the time series of aggregate indexes of security prices below and above various definitions of fundamental values.

If it is true that investors drive asset classes far from equilibrium, then it may be dangerous to embrace the Global Market Portfolio as a passive approach to asset allocation.

It would be helpful to apply asset level factors to systematically tilt policy portfolios toward assets with higher expected returns in the same way we might tilt individual equity portfolios. Fortunately, the same value, momentum and low beta factors that are observed in equities are also observed across asset classes. For example, Asness, Moskowitz and Pedersen observed value and momentum effects across equity markets, bond markets, commodities and futures. Figure 4 a) and b) illustrate the economic and statistical significance of these effects across all global asset classes.

Figure 4a. Global Tactical Asset Allocation Momentum and Value Return Premia

Figure 4b. Cumulative returns to global value and momentum based asset allocation strategy

Source: Asness, Moskowitz and Pedersen, Value and Momentum Everywhere (2013)

We would highlight two data points in particular in Figure 4a. First, notice the alpha T-stats for the value and momentum factors are 4.69 and 4.76 respectively, which are highly significant, and consistent with the sizes of these factor anomalies in equities. Clearly there are universal phenomena at work across global markets (and in fact this is validated by the paper). Just as interesting, the correlation between the momentum factor and the value factor is -0.6 over the 40 year period studied. Not only do you achieve higher excess returns, but the factor portfolios are substantially better in combination, with a combined zero-cost alpha of 6.9% and a T-stat of 10(!!).

In addition to value and momentum, Frazzini and Pedersen (2014) performed a wide reaching analysis of the low beta factor across global stocks and asset classes and observed a similarly statistically significant effect in virtually every corner of the market. Figure 5 shows the performance of global asset portfolios ranked by beta. Note a nearly universal phenomenon.

Figure 5.

Source: Frazzini and Pedersen, Betting against beta (2014)

Value, momentum and low beta (low volatility) premia exist across individual securities in a market, and across global asset classes. They are observed with greater statistical and economic significance as the universally recognized ‘equity premium’. Empirically minded investors might therefore consider seeking methods of integrating any or all of these factor premia into their investment process to improve long-term results.

It should be evident by now that the investment management process can not be fully captured by sorting strategies or products into active or passive buckets. While there is a strict passive portfolio, the Global Market Portfolio, virtually no single investor actually holds this portfolio in practice. By extension then, there are no truly passive investors. Rather, investors try to balance off competing objectives related to taxes, time horizon, currency risk, home market bias, and a host of other qualities to find a compromise solution. Unfortunately, there is no standard method to optimize these competing objectives, leaving many investors with hodgepodge portfolios which are unintentionally exposed to myriad concentrated and unintentional risks.

While this is clearly a suboptimal solution, investors can be forgiven for not looking toward active management for better options. Some of the most up-to-date papers suggest active mutual fund managers, despite the enormous resources at their disposal, fail to beat simple benchmarks even *before fees**.* After fees, it’s a slaughter.

Factor tilt portfolios are consistent with the systematic, rules-based nature of passive indexing, but are constructed to take advantage of well-known and intuitive market inefficiencies to yield excess returns over time. These excess returns are highly significant; more significant even than the equity risk premium itself. Factors appear to exist because of universal behavioural or risk based phenomena across global markets, and have persisted since the dawn of markets.

It is not obvious how to allocate across global factors in a coherent manner. There are a variety of credible sources of exposure to equity factor ’tilt’ portfolios from several providers. We describe some of our favoured ETFs in our previous post on the Global Market Portfolio with Factor Tilts. These funds will generate most of their returns as a function of being exposed to equity markets in general, with factors exerting a relatively minor, but incrementally positive impact. In contrast, QuantShares manages pure market-neutral factor ETFs for US equities, but it is not obvious how to use these in traditional portfolios.

It has gotten a lot easier to gain access to asset level factors over the past few years as several firms have built promising track records with dynamic asset allocation strategies. However, many of these managers implement ‘discretionary’ approaches which are analogous to traditional active strategies. Which is to say, these managers are not systematically leveraging asset level factors, but are rather executing a more opaque idiosyncratic process which may be very difficult to analyze. In contrast, some approaches such as Adaptive Asset Allocation systematically tilt portfolios toward assets with high momentum and low beta, and can therefore be extensively tested and analyzed.

As with any investment, it pays to do your own homework and have a clear grasp of objectives, risk tolerance, and constraints. That said, some decisions are easy. For example, it’s hard to justify the use of traditional active managers. If you choose to go that route, have a very clear and quantifiable understanding about why your chosen manager(s) have an economically significant edge in their space. On the other hand, many investors would probably benefit from some exposure to systematic factors or tilts in portfolios as an excellent compromise between active and passive.

**(Editor’s Note: A previous version of this article attributed the invention of the Morningstar Style Box to Paul Kaplan. It was actually invented by Don Phillips. We apologize for the mistake.)**

The post Forget “Active vs. Passive”: It’s All About Factors appeared first on GestaltU.

]]>The post All Strategies “Blow Up” appeared first on GestaltU.

]]>We are a quantitative finance shop, right down to the ground. All of our portfolios are driven by supervised quantitative models with no discretionary intervention. As such, I was inspired to respond to a recent article on the risk of quant strategies, as I think the way our team approaches quantitative research diverges from how many outsiders perceive quant, and also from how many quantitative shops work.

This article was inspired by a blog post written by Dominique Dassault at Global Slant, so we’ve loosely organized our comments around that article’s themes. But be warned: we decided to take our comments in a materially different direction. Dassault concentrated on how ‘bad quant’ strategies ‘BLOW UP’, and how these events contribute to systemic risk. In this article, we will explain why even good strategies must test investors’ ReSolve every now and then in order to deliver long-term excess returns. We will address ‘good quant’ vs. ‘bad quant’ and systemic risk at length in a future article.

First, let’s define a BLOW UP. Of course, when most investors imagine a BLOW UP they picture large absolute portfolio losses. And this is certainly the most acute and meaningful type of risk, both from an emotional and a financial standpoint. After all, large losses impair a portfolio’s ability to sustain distributions, such as during retirement, or to support endowment or pension liabilities. But investors also find it hard to endure other types of portfolio outcomes, such as:

- Long periods of meaningful underperformance relative to widely observed benchmarks;
- Long periods of no returns, which cause investors to question the viability of the strategy; and
- Social exclusion, such as from owning so-called ‘sin stocks’ like tobacco and firearms companies.

Investors experience fear and discomfort from these and myriad other less tangible risks, and in their own way, each of these experiences can feel like a BLOW UP. However, while these risk qualities may feel as painful as real losses, they inflict much less financial damage to portfolios; falling behind for a while, or having a materially different experience than your peers, is not the same as losing 30% to 50% of your money when it comes to sustaining portfolio objectives over the long-term.

But here’s the rub: without occasional highly unpleasant periods, investors could not expect to earn any excess returns over safe cash. To see why, consider the excess returns to stocks versus cash or bonds. An equity index, like the ubiquitous S&P 500, is a simple quantitative strategy which systematically holds qualifying stocks in proportion to their respective market capitalizations. But stock markets have historically BLOWN UP about every 5 to 7 years in the form of explosive bear markets. In return, equity investors are compensated for bearing this risk; this compensation is the called the ‘equity risk premium’. Many investors, who are not steadfastly convinced of the persistence of the equity risk premium, capitulate to fear and sell their stocks at the depths of bear markets. As Michael Batnick at Irrelevant Investor blog correctly pointed out, these people are the equity risk premium. They donate capital to those who are long-term true believers that equities will outperform.

We can expect the equity premium to deliver a persistent premium through time, so long as equity markets are expected to inflict regular BLOW UPs, which shake out weak hands. In fact, it is unreasonable to expect to harvest returns from the equity risk premium without enduring regular BLOW UPs.

Some investors try to attenuate the risk of the equity risk premium by timing exposure to equity markets in order to avoid the inevitable large drawdowns during bear markets. Many of these investors believe that they are investing in the equity premium, but this is not strictly true. Rather, these investors are harvesting some returns from the equity premium, and some returns from other market anomalies.

For example, investors who try to time equity markets by moving out of equities when they appear expensive relative to historical averages or other asset classes are, perhaps unwittingly, attempting to harvest the ‘value’ factor. That is, they are trying to overweight cheap assets and underweight expensive assets. Similarly, many investors try to manage equity exposure by employing moving averages or other technical indicators. In fact, these investors are, whether they know it or not, attempting to harvest the momentum premium. In other words, they are taking advantage of the fact that markets ‘trend’.

Investors who attempt to take advantage of alternative sources of risk and return, such as value or momentum premia, should not be under the misapprehension that they have successfully avoided risk. If that were true, they would have also successfully avoided excess return! Rather, investors in these alternative premia have simply substituted one risk for another.

One risk that both value and momentum premia exhibit is the risk of under-performing the assets being ‘timed’ for extended periods of time. This can be quite painful for investors, as they watch their friends’ more traditional portfolios appreciate while their portfolios stagnate. As a result, investors become infected with the suspicion that the factors they are harvesting are somehow ‘broken’, or no longer exist. This fear and doubt compels many investors to abandon these strategies toward the tail end of under-performing periods, leaving money on the table for more disciplined investors to reap. If these unpleasant periods did not exist, everyone would follow the strategy and no one would abandon it; thus no one would leave behind any excess returns!

If you are finding all of this confusing and counter-intuitive, you’re not alone. But this is precisely the kind of second and third-order thinking that is required to be a successful investor. The point, however, is that all investment strategies that are expected to deliver long-term excess returns must be expected to very seriously test your ReSolve on occasion. These tests are mostly unpredictable, but sometimes can be attenuated with subtle quantitative techniques. We will discuss good and bad techniques, and potential systemic impacts to markets, in a future article.

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]]>The post Global Tactical Asset Allocation: Just the Facts appeared first on GestaltU.

]]>With all due respect to these distinguished financial professionals, we’re here to tell you that the analyses these authors have used to dismiss TAA is flawed. Specifically:

- The authors are under the misapprehension that TAA requires discretionary market calls;
- They’ve lumped vastly different strategies together for judgment; and
- They have evaluated the success of TAA relative to a poorly specified benchmark, and over a biased time period.

This article will discuss each of these issues in turn, and comprehensively demonstrate why TAA will probably improve the performance of any diversified portfolio.

**TAA Does Not Require Discretionary Market Views**

First, it should be abundantly clear from previous articles that those ‘strategists’ who purport to be able to call market tops and bottoms based on their own discretionary analyses are doomed to fail. We’ve spilled a lot of ink on this topic in the past, which we will not recapitulate here, but we would encourage those who are not yet persuaded of this fact to read our article, “Predicting Markets, or Marketing Predictions” here. But in truth, this issue is a red herring because **discretionary market calls are not required for successful TAA**.

The best TAA strategies systematically harness well documented market anomalies, most notably value and momentum. These anomalies, which have been observed in markets as diverse as commodities, fine art, tulip bulbs, wine, real estate, interest rates, and equities, do not require successful discretionary judgment. Rather, they are endogenous to all markets because of pervasive behavioural biases; structural issues, and; risk exposures.

Now, some skeptical market commentators dismiss these factors (like value and momentum) on the basis that, once these anomalies have been broadly identified, rational actors will arbitrage away the opportunity. However, both value and momentum have compelling theoretical foundations which explain their ubiquity and persistence. Furthermore, they exhibit levels of statistical significance that are difficult to ignore. In fact, the statistical evidence in support of the value and momentum factors is even stronger than the evidence that stocks produce higher returns than t-bills. Don’t believe us? Consider Figure 1. below from a recent paper evaluating the statistical evidence for a wide variety of proposed market factors. Note that the HML (value) and MOM (momentum) factors exhibit t-scores of almost 5 (circled in green), while MRT (CAPM market excess return factor, circled in red) yields a t-score of just over 2.5 (note that higher t-scores indicate higher levels of statistical significance – more on this below).

Source: Asness, Moskowitz, Pedersen, Value and Momentum Everywhere

In more basic language, this table illustrates two important points. First, it shows that momentum and value effects exist at highly significant levels across both global stocks and global asset classes. Second, it would be very difficult for a commentator to acknowledge the persistence of these factors as they pertain to stocks without also acknowledging their persistence across global asset classes. If you acknowledge one, you must logically acknowledge the other. A person who asserts any other conclusion is selling something.

In summary, while the evidence is clear that no one can successfully forecast market turns, this fact is unrelated to the potential of GTAA. Rather, the key to successful Global Tactical Asset Allocation is to rely on proven factors by systematically biasing portfolios toward the cheapest or highest momentum sectors of global markets.

**Defining GTAA**

Commentators who dismiss GTAA often cite the performance of the Morningstar Tactical Asset Allocation fund category over the past few years. We’ll address the issue of poorly specified benchmarks below, but in fact the issue runs deeper than this. The problem is that, unlike most Morningstar categories where funds are grouped according to clear investment styles and factors, the TAA category is more of a hodge-podge of funds, which Morningstar can’t easily classify elsewhere in its index lineup.

For example, consider the Horizon Active Asset Allocation fund (AAANX), with the ability to invest in ETFs tracking equity markets, REITs, commodities, currencies, credit and rates around the world. The fund has a turnover of 600%, and a quick look back through monthly reports shows a very active and diverse set of holdings representative of a broad investable universe. While their stated benchmark is the S&P 500 equity index, and a quick scan of historical holdings does show a bias toward global equities, the fund is clearly both ‘global’ and ‘tactical’.

On the other extreme, the Morningstar TAA category also includes the Good Harbor Tactical Core US strategy, which has a narrow investible universe of U.S. equity sectors and U.S. Treasury bonds. There is clearly nothing ‘global’ about this strategy, though it is certainly tactical, switching into 100% bonds or 100% stocks in any given month.

The Morningstar TAA category also includes U.S. sector rotation funds such as Innealta Capital Sector Rotation Fund, as well as global risk parity funds, target risk funds, and other mandates which may or may not be either tactical or global. Obviously, we need a better classification methodology that creates a more homogenous group of true GTAA mandates.

Fortunately, Morningstar also publishes a quarterly “Morningstar ETF Managed Portfolios Landscape Summary” report, which provides a more granular taxonomy of tactical strategies. In addition, the proposed taxonomy aligns well with what we believe are the obvious hallmarks of GTAA strategies, namely:

- Diverse global universe of investible asset classes
- Flexible mandates with few portfolio constraints
- Process involves large tactical shifts in portfolio holdings to take advantage or short- or intermediate-term opportunities
- Liquid investment vehicles primarily composed of passive beta products including ETFs

The Morningstar Landscape “Global All Asset” category maps very closely to these criteria. It includes both ‘hybrid’, ‘strategic’ and ‘tactical’ funds with appropriate global universes and flexible mandates. In our estimation, Tactical strategies in the Global All Asset category best match the criteria for GTAA.

Now that we have defined a category for GTAA and identified a group of strategies that fall into the category, it’s time to talk about performance – but against what benchmark? We discuss this next.

**Performance and Benchmarking**

One of the most common failings of the investment industry is the prevalence of poorly specified benchmarks. This is of critical importance because it is easy for a knowledgable but disingenuous professional to manipulate the facts in order to make any point they want. Want a simple way to boost results? Choose an easy benchmark for comparison. Want to dismiss performance? Choose a challenging benchmark. Of course, the choice of benchmark for persuasive purposes is highly sensitive to the time period under analysis.

Investment commentators who dismiss TAA often compare the results of TAA strategies to a U.S. 60/40 balanced fund like the Vanguard Balanced Fund (VBINX). And this benchmark does have one thing going for it, especially if a commentator’s goal is to malign TAA strategies: It is a very tough benchmark to beat over the past one, three and five years – perhaps the toughest in the world in USD terms. Unfortunately, it’s hard to see how this portfolio represents an appropriate bogey for GTAA strategies over the long-term.

For one, this portfolio is insulated from global currency effects, which have been especially pronounced in the past few years with global QE programs in effect. Second, it ignores non-U.S. equity beta; while a focus on U.S. equities at the expense of international stocks has been a lucky bet for the past few years, it ignores the broader scope of GTAA strategies. Also, since the goal of GTAA strategies is to harvest premia from as many liquid global sources as possible, the strategies often incorporate alternative investments, like REIT and commodity ETFs, into their investible universe. These are not represented in a U.S. balanced fund benchmark.

Fortunately, Morningstar takes a broader view in their Landscape report. Their Global All Asset benchmark, copied below (Figure 3.) is composed of 55% global stocks, presumably distributed geographically by market cap; 35% global bonds, split evenly between US and international; and 10% commodities. Clearly the folks at Morningstar are trying to be more representative of the space, and their mix is certainly in the right ballpark. But it is also still rather arbitrary – how did they arrive at their weights? Have they weighted toward historical GTAA holdings? If so, is there any guarantee that historical holdings will be representative of future holdings? These are dynamic strategies after all. Do commodities deserve a 10% strategic weighting or is this informed by recency bias? In addition, the Morningstar benchmark is over 80% weighted to U.S. dollars. Does this represent a neutral currency policy?

Source: Morningstar

It’s worth spending a moment on how we might judge the adequacy of a benchmark in general. At root, a well specified benchmark should be expected to meet the following criteria:

- It is passive;
- It is investible; and,
- It reflects the investing opportunity set of the manager.

Sharpe (1962) showed that in order for a portfolio to be truly ‘passive’, it must be structured such that it can accommodate all participants in the market at the same time. Axiomatically, a passive portfolio must be representative of the average investor portfolio, because this is the only portfolio that all participants can hold at once. For proof, let’s simplify the problem. Consider 20 marbles divided among 4 people: Jane with 3, Alex with 9, Stephen with 7 and Marco with 1. On average they hold 5 marbles (3 + 9 + 7 + 1 = 20 / 4 people = 5); it follows that the only configuration of marbles where each of the 4 people can hold the same ‘portfolio’ of marbles is if each person has 5 marbles. In markets, the neutral portfolio that represents the average positions of all market participants is the portfolio that holds each asset in proportion to its market capitalization. In other words, the market cap weighted portfolio.

This is not a new concept; U.S. large cap equity managers are typically benchmarked against a market cap weighted index of large-cap U.S. stocks. U.S. Investment Grade bond managers are be benchmarked against a market cap weighted index of U.S. listed investment grade bonds. Cap weighted indexes are common and intuitive when they are constructed within a major asset class.

But the concept is also easily extended into a multi-asset class context. In this case we would expect a passive portfolio to hold all asset classes in proportion to their respective market capitalizations. Consider a simple example where the aggregate global market has a value of $100 trillion, where $50 trillion is stocks and $50 trillion is bonds. In this case, a passive investor would hold 50% of their portfolio in bonds and 50% in stocks. Every participant in the markets could hold this exact portfolio without changing the overall composition of the market, so it is the only passive, neutral portfolio.

As discussed in prior posts (see here and here) Doeswijk et. al. determined the actual market value of every global financial asset (as of year-end 2012) and published their relative market capitalization weights in a 2014 paper. These weights describe the most passive portfolio possible: the global market cap weighted portfolio (GMP). Fortunately, an investible version of this portfolio can be very closely replicated with low-cost, U.S. listed ETFs (see Figure 5.) This portfolio uniquely meets all the criteria for an appropriate benchmark: it is definitionally the only passive portfolio; it is definitionally investible; and it covers the investible opportunity set for GTAA mandates because it includes all global investible assets.

Figure 5. Investible Global Market Portfolio.

Source: Interpreted from Doeswijk et. al.

We would note that the global market cap weighted portfolio definitionally holds all assets in their native currency, and therefore reflects currency fluctuations in non-domestic asset classes. Over 50% of both global equity and bond sleeves in our proposed global market portfolio reflect non-US currency exposure (the foreign equity exposure is hidden inside our global equity ETF).

All of the ETFs in our GMP proxy portfolio have been trading for more than five years, which makes it simple to construct a total return index for this portfolio to be used as a benchmark. **We believe this is the most appropriate benchmark for GTAA strategies.** The chart and performance of the GMP over calendar 2014, the three years from 2012-2014, and the five years from 2010-2014 are shown in Figure 6.

Figure 6. Performance of the Global Market Portfolio

Source: CSI Data

Now that we have specified the most appropriate benchmark, we can get down to the business of evaluating how well GTAA strategies have delivered on their promise. How should we judge success? We submit that for GTAA strategies in particular we should judge results on both an absolute and a relative basis. When judging absolute results, it is our core belief that there is no way to properly evaluate performance without observing both rewards and risk. It’s like describing all the features of a product without any discussion of the cost:

- Do I want a private jet so that I can travel whenever and wherever I want without the hassle of airport lineups? Sure. Do I want it for $6 million plus $250k per year in maintenance costs? No.
- Do I want to invest in a strategy that might make 10% per year? Sure. Do I still want it if the strategy experiences a drawdown of 40% or more about one year in 5? Probably not.

While many managers would debate our preferences, we first look to a strategy’s Sharpe ratio when evaluating GTAA approaches. Many thoughtful consultants and advisors object to the Sharpe ratio because they assert that investors are unconcerned with upside volatility, and focus exclusively on downside risk. While this may be true, in our experience ‘what goes up with volatility is likely to drop with volatility’. This assertion is supported by the tendency for volatility to cluster; the largest down days are often adjacent in time to the largest up days. As such, we perceive the symmetrical character of volatility as a better way to capture the true risk of a strategy than, say downside deviation. That said, we are also interested in non-parametric measures or risk, such as drawdown and ulcer index, as these capture the true risk of a strategy when markets become non-normal, as they often do during crises, and the linearity of the return experience.

Unfortunately, the Morningstar report does not provide *absolute* risk information, so on an absolute basis we can only observe the benefits (returns) of the strategies, not the costs (risk). However, we can evaluate the relative performance of GTAA strategies by comparing them to our two benchmarks. Morningstar has also blessed us with *relative* risk-adjusted metrics, so that we can judge the relative merits of a strategy vis-a-vis the benchmark in terms of both relative benefits (alpha) and costs (beta). We extracted the results of the Global All Assets – Tactical strategies with at least 5 year track records in Figure 7.

Figure 7. GTAA performance vs. appropriate benchmarks

Source: Morningstar, CSI Data

A comparison of just the annualized returns for the GTAA strategies relative to the benchmarks shows that they track each other very closely at each horizon, though the average GTAA strategy tracks the GMP more closely than the Morningstar benchmark, especially in 2014. In fact, this is a sign that the benchmarks are well specified. It is also, perhaps, to be expected; the GMP is, after all, the average of all active asset class bets!

On average, the GTAA strategies edged out their benchmarks over the 2014 calendar year, and were even with benchmarks over 3 and 5 year periods. But the story is more interesting once we observe the risk-adjusted characteristics. Note that the GTAA strategies tracked or exceeded their benchmark with less risk, as GTAA betas averaged just 0.8 over the past 5 years. As such, since GTAA strategies provided similar returns with less systematic risk, they delivered alpha of about 1% per year above their passive, globally diversified benchmark. Furthermore, while the average GTAA annualized returns appear to track closely to benchmark annualized returns, the Morningstar benchmark explains less than 70% of GTAA returns, as measured by average R-Squared values. We can therefore conclude that, while the benchmark is relatively well specified, GTAA strategies are harvesting returns from sources other than passive global beta exposures. In other words, their active bets appear to be paying off.

The fact is, the past 5 years have been an extraordinary period for global markets, characterized by a massive recovery in global risky assets coincident with a huge compression in global volatility. Many markets have experienced record consecutive periods without the meaningful corrections we typically observe, even during bull market cycles. As a result, GTAA strategies, which are typically constructed to really shine during crises, have yet to see their day in the sun. In fact, I’m mildly surprised to see that GTAA strategies have competed so well during this bull market phase of the cycle. We won’t get to see just how resilient these strategies are until they stand tall above the detritus of the next bear market.

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]]>The post We’re Launching Our 2nd Blog: SKEW appeared first on GestaltU.

]]>Every day, we consume a formidable amount of information. Some of the content is intriguing, some amusing, and some infuriating. And we have thoughts on many of those pieces. Yet, rather than writing on topics outside GestaltU’s characteristic long-form investment research, we have thus far chosen to focus on the single content style that long-time readers have come to expect. In order to maintain such high standards, we’ve rarely ventured outside of those confines. But as we’ve grown as writers, it’s become more difficult to contain the breadth of topics we’d like to post on, and the voice we’d like to write with.

Hence, Skew.

Among the many reasons for launching Skew, we hope to:

**Be respectful of your time.**We know that not everyone has the time or inclination to consume 1,500 word essays. Skew, wherever possible, will present short-form content.**Write in English**. Many of the posts on Gestalt are highly technical and difficult to understand. With Skew, we want to distill long articles down to the salient points and translate technical information into understandable prose with actionable intelligence.**Post more frequently.**It takes a remarkable amount of time to research, write, polish and publish a long-form essay. This is why we’re scarcely able to post more than an 1-2 articles per month. Our goal for Skew is to publish more frequently, on issues that are informative, relevant and timely.**Write a bit off-topic.**Did you see last year’s foray into inane NCAA March Madness pool rules? That kind of post has Skew written all over it!**Clarify our thinking.**We find that writing helps us clarify our own thinking on complex issues. Skew provides us with an additional outlet to help us process our own thoughts on markets, economies and the world at large.

For our long-time readers, let us be clear: **GestaltU** **will continue to bring you the same style of content you’ve come to expect from us.** We’re adding the Skew blog in addition; we don’t expect to draw resources away from the development of our long-form content.

One last thing, since the timing seems so good. We just published our 2015 update to last year’s March Madness blog post. You can find our 2015 update here.

Enjoy!

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]]>The post Winning By Not Losing: Bootstrap Quantile Clouds appeared first on GestaltU.

]]>If you are an average investor with a typically basic understanding of investing, **Rule #1** above will probably make perfect sense. However, if you are a financial professional, you will probably have to read the statement a few times before it becomes clear.

Here’s why: from the moment you enter into the field of finance, you are taught to think of risk in terms of volatility. But in the context of Rule 1, it is impossible to quantify risk in this way. That’s because financial goals are usually framed in terms of target wealth, and wealth outcomes are a function of both volatility and expected returns. As such, risk is the range of wealth outcomes that might be expected at the investment horizon. (Note that, from a financial standpoint wealth and portfolio income are inextricably linked – maximizing one will necessarily maximize the other – so we will focus on wealth. Note also that the sequence of returns matters too, but we won’t address that here.)

Investors will therefore prefer portfolios that provide for the highest expected return, in excess of their minimum required return, under adverse assumptions, and that match their tolerance for failure. Conservative investors may wish to invest in the portfolio that provides the highest expected return above their minimum required return of 3% for example, under the 5% least favourable conditions. More adventurous investors might tolerate a 25% chance that terminal wealth falls below their target. Only investors with lottery-like preferences will choose portfolios based on the best outcomes under the most favourable conditions.

Note that this is further complicated by the fact that investors’ time horizons are, in practice, just a small fraction of their true financial time horizons. For example, a 50 year old investor may have a life expectancy of another 35 years, and wish to leave a legacy amount with a much longer time horizon still. However, data on investor behaviour suggests that this investor is unlikely to stick with a strategy for much longer than 4 or 5 years. Figure 1. from Dalbar’s 2014 Quantitative Analysis of Investor Behaviour report, shows that investors in stock and bond mutual funds tend to stick with their strategy for about 3 years, while diversified investors (‘asset allocation’) have historically held on for almost 5 years.

Figure 1. Average Mutual Fund Retention Rates (1995 – 2014)

From a modelling and planning perspective, there is little value in setting investor portfolio preferences for a 35 year time horizon if they are going to change their portfolio every 5 years or less. Rather, the objective should be to recommend a portfolio that the investor is likely to stick with through thick or thin, but also where the investor is likely to come to the least amount of harm if he or she abandons the strategy after experiencing an adverse period.

The fundamental question to answer is this:

- If an investor can tolerate
*p*probability of not reaching target wealth and; - If an investor’s
*emotional*time horizon before abandoning a strategy under adverse conditions is*y*years and; - The investor requires a minimum return of
*r*to reach his wealth target then; - Which portfolio minimizes the probability that the investor will NOT reach his financial goals

You will note that this question is just a more detailed way to frame **Rule #1**.

There are complex analytical models that can answer this question with great precision, but most have a subtle but important flaw: they assume portfolio returns are independent and identically distributed, and; they assume returns are normally distributed. It turns out that these assumptions are actually not very impactful, and it would have been relatively easy to solve the problem by applying a multi-period Roy’s Safety First model, or through traditional Monte Carlo analysis. But we thought we’d go the extra mile.

Boostrapping is a simulation method, much like Monte Carlo, which provides a way to generate sample paths for wealth. However, where Monte Carlo analysis generates random returns from the normal distribution, bootstrapping generates sample returns from the empirical distribution described by actual historical observations. For example, when creating a random return path for the S&P 500 through bootstrapping, actual observed historical monthly returns from the S&P 500 are drawn at random, usually with replacement. To create a 5 year sample path, you would draw 60 monthly returns; to create 1000 5-year sample paths you would choose 60 monthly returns 1000 times.

Each 5-year sample path represents an alternative history for the S&P 500. As a result, this process illuminates a fascinating and rarely contemplated reality for investors: they have observed just one of an (almost) infinite number of possible trajectories that the S&P 500 might have taken. While the path we observed evokes the only narrative that we can possibly understand, and seems positively *inevitable* in hindsight, any one of the alternative paths we created were equally likely *ex ante*. Only after time has passed, and the actual path has unfolded, can we look back and identify the one line that fits with our experience.

Now let’s look in the other direction – into the future. Remember, before history unfolded, we knew that their was a murky cloud of infinite possibilities for how the S&P 500 could have evolved. We now sit at the beginning of a new timeline that reaches out into the future before us. As such, we look out on the same murky cloud of possibility. Fortunately however, this cloud has structure, and we can quantify this structure in meaningful ways.

Figure 2. is what we call a ‘Quantile Cloud’ for the S&P 500. It is formed by generating 100,000 alternative 5-year paths, randomly drawn from actual monthly **total returns including dividend reinvestment** observed over the period 1880 – 2014, using bootstrap with replacement. Again, bootstrapping preserves the *empirical distribution* of realized returns rather than imposing a distribution on the data.

Figure 2. 5-Yr Bootstrap Quantile Cloud for S&P 500

Let’s take a minute to get to know the Quantile Cloud. Each barely perceptible microscopic line on the chart (not the multi-colored thicker lines) represents 1 path of 100,000. Where the density of lines is high, near the middle of the cloud, the colour shifts into the pink spectrum. Where there are few observations, near the edges of the cloud, the colour shifts into the blue end of the spectrum. The very densest middle of the cloud, highlighted by the green line, represents the median, or average outcome. The individual thin blue lines which can be distinguished near the very top and very bottom of the cloud are statistically possible, but extremely unlikely. The black line running through the middle of the chart represents the ‘break-even’ line; that is, where the portfolio has returned 0% over the period.

The coloured lines on the chart represent the quantile wealth at each horizon. For example, the red line at the very bottom represents the 5th percentile wealth outcome for the S&P 500 each month. Notice that the red 5th percentile and the orange 10th percentile lines fall below the black line at all periods, which means over 5 years there is at least a 10% chance of seeing your wealth fall below starting wealth when investing in the S&P500. In fact, the pale green 20th percentile line falls below the black line for over 30 months, which means there is a 20% change of seeing your wealth fall below starting wealth over almost 3 years.

There is a summary of quantile geometric returns over the full 5 year period at the top left of the chart. Note that the 5th and 10th percentile growth rates are negative, consistent with what we observed above – negative wealth over all periods. All quantiles at the 20th percentile and above show positive returns. The median growth rate is 8.8%.

Now let’s apply this quantile chart in the context of our **Rule #1**. Let’s assume an investor has a history of switching strategies or advisors about every 5 years, which represents her true time horizon. Let’s also assume the investor requires 2.5% return to achieve her minimum target wealth, and can tolerate a 10% chance of failure. How appropriate is a 100% investment in the S&P500 in the context of these preference?

Note that the 10th percentile return from our S&P 500 Quantile Cloud is -1.1% over this investor’s time horizon of 5 years. But the investor requires a 90% chance of achieving 2.5% over 5 years to meet her minimum target wealth. Clearly, the S&P 500 portfolio is not a good match for this investor’s preferences.

If an all stock portfolio will not meet this investor’s objectives, let’s consider some other portfolio options. Figures 3-5 present 5-year Quantile Clouds for a U.S. 60/40 balanced portfolio, the Global Market Portfolio[1], and a Global Risk Parity[2] (Equal Risk Contribution ERC) portfolio respectively, all rebalanced quarterly. All data is total return including reinvested dividends and interest, but not accounting for fees, transactions, or taxes. [See notes [1] and [2] at the bottom of this article for a description of these portfolios.]

Figure 3. U.S. Balanced 60/40 S&P 500/US 10-year Treasury Quantile Cloud

Figure 4. Global Market Cap Weighted Portfolio Quantile Cloud

Figure 5. Global Risk Parity (Equal Risk Contribution) Quantile Cloud

Let’s see if we can come closer to meeting our investor’s preferences with these alternative portfolios. Recall that we are searching for the portfolio which we expect to achieve at least 2.5% cumulative growth over a 5 year horizon, 90% of the time; that is, at the 10th percentile. First note that the median expected returns for US balanced, Global Market Cap, and Global Risk Parity (ERC) portfolios are 7.6%, 5.7%, and 5.3% respectively. All of these portfolios present median expected returns that are lower than the median return from the all-stock S&P 500 portfolio.

Yet, as we glance down the quantile returns a different story emerges. In fact, at the 10th percentile risk tolerance reflected by our model investor, the expected returns to stocks, balanced, global market cap and global risk parity portfolios are -1.1%, 1.4%, 1.9% and 2.5% respectively. The order of returns is reversed. In fact, despite the fact that the Global ERC portfolio reflects the lowest average return over 5 years, it presents the highest return at the investor’s risk tolerance of 10% chance of failure.

The goals of this exercise were threefold:

- First, reframe the primary investment objective in terms of the risk of not achieving a client’s financial target;
- Provide a visual model for the extreme random nature of returns, and;
- Illustrate how high average expected returns do not necessarily mean an investor is more likely to meet their financial goals over a finite horizon

By framing **Rule #1** with Quantile Clouds, we can see how portfolio return and risk interact under a true random process to meet different investor preferences. Obviously there are ways to solve these problems with greater precision, but the intuitive visualization offered by Quantile Clouds may make it easier for clients to understand the risk/return tradeoff, and potential value of global diversification.

**Notes**

1. The Global Market Cap portfolio is an approximation based on USD Global Financial Data extensions for US equities, EAFE equities (manually assembled by Wouter Keller), emerging market equities, U.S. corporate bonds, 10-year U.S. Treasury bonds, U.S. high-yield bonds, international government bonds, REITs, and TIPs. Returns for the period 1880 to the mid 1920s are from S&P 500 and U.S. Treasuries only. TIPs enter the portfolio in 1973. Weights are contemporary market cap weights and do not reflect changes to portfolio constitution that occurred through time. For illustrative purposes only.

*2. The Global ERC portfolio is rebalanced quarterly to Equal Risk Contribution weights for all of the assets described in Note 1. The variance-covariance matrix is formed from rolling 12-month returns.*

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]]>The post The Narrative is Reality appeared first on GestaltU.

]]>― Umberto Eco, Foucault’s Pendulum

Back in the days when I still thought markets were driven by fundamentals I used to be a big fan of Don Coxe’s monthly commentaries. Don was at the epicenter of the commodity / BRIC narrative, and his commentaries were dense with historical context, pithy quotes, and compelling analysis. He was the progenitor of the concept of a ‘triple waterfall crash’, of which the prolonged bear market in Japanese equities was the prototype. He also coined the rule that investors should focus on areas of the market where, “those who know it best, love it least, because they’ve been disappointed most”. For him, this was the dominant driver of the commodity trade, as long-time CEOs of major mining and energy companies would be slow to bring on new production in the face of high current prices, because they would be terrified that the next secular bear market for those commodities would be just around the corner.

For me in the mid-naughts, Don was the “Guardian of the Trend”. And I was a full-on, card carrying member of this cult.

**Secular Cults**

In secular (that is, non-religious) cults, confidence in the narrative is fuelled primarily by “Confirmation Bias” and the “Illusion of Knowledge”. In other words, people search out as many facts as possible to support their narrative, and believe that more information increases the accuracy of their forecasts. To wit, I became an expert in fields that supported my world view.

I could quote all the relevant stats on Saudi’s oil fields and why we shouldn’t believe them. I knew the NPV of the major Canadian oil-sands companies based on reserves in the ground at a range of long-term oil price forecasts. I tracked the relative cost curve for on-shore vs. deep water drilling, as well as the lease prices for different classes of exploration and production platforms. I watched the crack spread and the term structure of crude futures. I watched Saudi CDS as a leading indicator of oil price movements. I read Dennis Gartman.

In addition, I knew the relative global reserves of potassium and phosphorus and the largest and lowest cost producers. I could cite all manner of statistics on global demographics, and the likely increase in meat consumption due to the rise of the emerging middle class, and implications for corn and oat prices. I watched Caterpillar, Joy Global, and Manitowoc stocks and listened to management calls about the state of construction and mine development in emerging economies. I understood the difference between laterite and magmatic sulphide nickel deposits, and their relative cost structure.

But those are just facts, and facts only serve to *support* the narrative; they have no power in themselves. The narrative is based on *faith, *and all new information is filtered through the prism of that faith. *Faith* in peak oil. *Faith* in China’s emerging middle class need for meat and infrastructure. *Faith* in scarcity. *Faith* in monetary profligacy and the inevitability of inflation. *Faith, faith, faith!*

**Ghosts of Bubbles Past and Present**

In each cycle, there are a handful of pied pipers diligently manning required posts as “Guardians of the Trend”, assuring us that the narrative is reality. In the “Greed is Good” era of the 1980s, the narrative was fed by such characters as Martin Zweig, Michael Milken, and Ivan Boesky, with the fictional “Gordon Gekko” as the archetype.

In the technology bubble the ‘animal spirits’ were lifted by such characters as Henry Blodgett, Mary Meeker, Jack Grumman, and Frank Quattrone. During the emerging markets / commodity bubble the narrative was led by Jim O’Neil (who coined the term BRICs), Jim Rogers, Marc Faber, Peter Schiff, T. Boone Pickens, and Eric Sprott. The coincident housing bubble narrative was fostered by Louis Cavalier, Abby Joseph Cohen, and others.

The new new new narrative of central bank omnipotence has its own cast of “Guardians”. The leading cast members are Paul Krugman, Ben Bernanke, Janet Yellen, Shinzo Abe, Mario Draghi, and perhaps Mark Carney. David Tepper and his ilk are zealous acolytes. The members of the ‘passive posse’ (you know who you are) also play supporting roles by overwhelming protests of ‘asset inflation’, ‘expensive markets’ or ‘low future returns’ with chants of ‘efficient markets, efficient markets, efficient markets’. Paul Samuelson, who stated that markets are “micro efficient” but “macro inefficient” is rolling over in his grave.

Or maybe the current narrative really is ‘the truth’, and the market’s tree really can grow to the sky. I no longer care either way.

**Breaking the Spell**

“One might be led to suspect that there were all sorts of things going on in the Universe which he or she did not thoroughly understand.”

― Kurt Vonnegut, Slaughterhouse-Five

The collapse of the emerging markets / commodity bubble was an intensely traumatic experience, and left a gaping vacuum in my understanding about how the world works. If I knew as much as I did about the markets I was involved with, and the gurus I followed knew as much as they knew, and everyone got the trade completely wrong in the end, what did that mean? I can now empathize (abstractly) with members of doomsday cults who forecast a ‘rapture’ which never arrives.

The months immediately following the Global Financial Crisis were some of the most challenging of my life. I had linked my value as an investment professional to my ability to predict markets based on superior knowledge and understanding. But my superior knowledge and understanding had not translated into better forecasting ability or investment performance. Therefore I had no value as an investment professional. Should I seek out a different career?

But no one I followed – in fact, no one I’d heard of – had been able to do any better. Sure, there were a few ‘gurus’ who nailed the bear market, and a much smaller number that nailed both the bear and the bounce. But their narratives and methods were inscrutable and unconvincing. And as the bull market matured, even these gurus quickly lost their prescience. Which way do you move when you have no direction?

**Tetlock’s Gift**

It was during this period of existential crisis in 2009 that I stumbled upon Philip Tetlock. Of course, this was only partly by accident. At any other previous point in my life I would have tripped over Tetlock, picked myself up and walked on as if nothing had happened. But at that particular time I was an empty vessel, waiting to be filled with a new understanding of the world. I was ready to *receive*.

For those who haven’t heard of Philip Tetlock, and who may be ready to embrace the terrifying (but liberating!) reality that he has validated with his decades long research, I encourage you to read this article, and watch this video.

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 28,000 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. For example, models that forecast that the next period would continue the recent trend worked well. Models that forecast a return to a long-term mean also performed well. Chock one up for systematic momentum and value investors.

In any event, you may not be in a cognitive/emotional state where the facts presented above can be assimilated into your worldview. If you are a research analyst that is paid to make predictions about whether to buy or sell a stock at the current price, or an economist who is paid to forecast interest rates or oil prices, then these facts undermine your ability to make a living. Few people can operate for long with this level of cognitive dissonance, so you will necessarily ignore these conclusions.

Many readers are in a self congratulatory mood since their ‘long and strong’ equity bets have paid off so handsomely over the past five years or so. Self attribution bias prevents these readers from understanding that their success is due to luck, not skill. As such, they probably are not ready to receive Tetlock’s wisdom either. These readers may regret their hubris in the depths of the next crisis, when they are 25% to 50% poorer. C’est la vie.

If however, like me in 2009, you are disenfranchised with the analysts on TV, and in the newspaper, and at your firm, opining ad nauseum on topics they can’t possibly forecast, and with no accountability, then Tetlock’s wisdom might just be the right medicine at the right time. Who knows, perhaps five or six years down the road, you may find that you’ve reconstructed yourself in many delightfully unexpected ways, and produced some pretty neat new ideas based on concepts that actually work.

Of course, the market narrative exists whether you pay attention to it or not. But when you embrace the great unknown, you’re able to disengage and observe the mania for what it is: the Jungian collective unconscious acting to manifest its own destiny. It’s a movie playing out in real time in front of your eyes, with all the humour and drama and, eventually, tragedy that makes any great movie worth watching. And just as any faith requires sacrifice, most of these participants sacrifice a meaningful slice of their savings in order to avoid the physical pain of social exclusion. As such this drama, which is no more or less than the moment to moment expressions of faith by millions of market participants, fed by oscillating tantrums of greed and fear filtered through a grimy prism of amorphous identity and values, presents incredible opportunities for the enlightened few.

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]]>The post Your Alpha is My Beta appeared first on GestaltU.

]]>Incorrect casual use of the term alpha

This complaint may stem from the statistician in me, but the casual use of the term alpha irritates me quite a bit. Returning to very basic regression techniques, the term alpha has a very specific meaning.rp = α + β1 r1 + β2 r2 + β3 r3 + … + εAlpha is just one of the estimated statistics of a return attribution model. The validity of the regression outputs, whether parameter estimates such as alpha or various betas, or risk estimates such as standard errors, depend on the model used to specify the return stream. Independent variables should be chosen such that the resulting error residuals cannot be meaningfully explained further by adding independent variables to the regression. In the most prevalent return attribution model, the typical one factor CAPM model, returns are explained by one independent variable – broad market returns.Defining an appropriate return attribution model is necessary to estimate a manager’s alpha. I find it ironic that the use of the term alpha is most frequently applied to a subset of asset managers called hedge funds where defining the return attribution model is often the hardest. Long-short equity managers can display non-constant beta as their net exposures change. Fixed income arbitrage managers typically display very non-normal return distribution patterns. Managed futures traders can capture negative coskewness versus equity markets that provide additional benefits beyond their standard return and risk profile. Calculating these managers’ alpha is a difficult task if for no other reason that specifying the “correct” return attribution model is problematic.Consider the specific example of a hedge fund manager whose net exposure is not constant. In this case, a one factor market model is not necessarily optimal and other factors such as the square of market returns might need to be added to account for time varying beta. If a manager makes significant use of options, the task of specifying a proper model becomes even harder. Also, consider a manager whose product specialty is volatility arbitrage and an appropriate market benchmark may not be available. How then to estimate alpha?I prefer using the term “value-add” to be a generic catch-all for strategies that increment a portfolio’s value. Whether that incremental value is generated though true alpha, time varying beta, short beta strategies with low return drag, cheap optionality, negative coskewness to equity markets, or something else that is not able to be estimated directly from a return attribution model, it saves me from having to misuse the term alpha.

Lars raises great questions about the relevance of alpha derived from a linear attribution model with Gaussian assumptions when a strategy may exhibit non-linear and/or non-Gaussian risk or payoff profiles. Unfortunately, this describes many classes of hedge funds. While this is true, his comments took me in a different direction altogether.

It’s interesting to contextualize alpha not just in terms of the factors that an experienced expert might consider, but rather in terms of what a *specific* *target* investor for a product might have knowledge of, and be able to access elsewhere at less cost. In this way, a less experienced investor might perceive a product which harnesses certain non-traditional beta exposures to have delivered ‘alpha’, or more broadly ‘value added’, where an experienced institutional quant with access to inexpensive non-traditional betas would assert that the product delivers little or no alpha whatsoever.

Let’s start with the simplest example: imagine a typical retail investor who invests through his bank branch. A non-specialist at the bank branch recommends a single-manager balanced domestic mutual fund, where the manager is active with the equity sleeve, exerting a value bias on the portfolio. The bond sleeve tracks the domestic bond aggregate. The fund charges a 1.5% fee.

Subsequently, the investor meets a more sophisticated Advisor and they briefly discuss his portfolio. The Advisor consults his firm’s software and determines the fund’s returns are completely explained by the bond aggregate index returns, domestic equity returns, and the Fama French (FF) value factor. In fact, after accounting for these factors, the mutual fund delivers -2% annualized alpha.

The Advisor suggests that the client move his money into his care, where he will preserve his exact asset allocation vis-a-vis stocks and bonds, but invest the bond component via a broad domestic bond ETF, and use a low-cost value-biased equity ETF for the equity sleeve. The Expense Ratio (ER) of the ETF portfolio is 0.1% per year, and the Advisor proposes to charge the client 0.9% per year on top, for a total of 1% per year in expenses. The Advisor, by identifying the underlying exposures of the client’s first fund, and engineering a solution to replicate those factors with lower cost, has generated 1% per year in alpha (1.5% mutual fund fee – 1% all-in Advisor fee + 0.5% by eliminating the negative mutual fund alpha).

At the client’s next annual review, the Advisor recommends that the client diversify half of his equities into international stocks, at a fee of 0.14%. An unbiased estimate of non-domestic equity returns would be similar to domestic returns, minus the 0.6*0.5*(0.14-0.1) = 0.012% increase in total portfolio fees. However, currency and geographic diversification are expected to lower portfolio volatility by 0.5% per year, so the result is similar returns with lower risk = higher risk adjusted returns = higher value added = higher alpha.

After another year or so, the new Advisor discusses adding a second risk factor to the equity sleeve to compliment the existing value tilt: a domestic momentum ETF with a fee of 0.15%. Based on the relatively low correlation between value and momentum tilts (keeping in mind they are all long domestic equity portfolios), the Advisor believes the new portfolio will deliver the same returns over the long-run, but diversification between value and momentum tilts will slightly reduce the portfolio volatility, by another 0.2%. Same returns with less risk = higher alpha.

At each stage, the incremental increase in returns and reduction in portfolio ‘beta’ (vis-a-vis the original fund) results in a higher ‘alpha’ for the client. Now obviously the actions that the Advisor took are not traditional sources of alpha – that is, they are not the result of traditional active bets – but they nevertheless add meaningful value to the client.

Now let’s extend the logic into a more traditional institutional discussion. The institution is generally applying attribution analysis for one or both of the following purposes. The two applications are obviously linked in process, but have substantially different objectives.

- To discover how well systematic risk factors explain portfolio returns over a sample period. For example, we might determine that a long-short equity manager derives some returns from idiosyncratic equity selection, some from the Fama French value factor, and some returns from time-varying beta. If we hired the manager for exposure to these factors, this would confirm our judgement. Otherwise it might prompt some questions for the manager about ‘style drift’ or some other such nonsense.
- To determine if a manager has delivered “value added”, or alpha. For example, perhaps the manager delivered excess returns, but we discover that the excess returns can be explained away by adding traditional Fama French equity factors to the regression. Since it is a simple and inexpensive matter to replicate these risk factor exposures through ‘passive’ allocations to these factors (using ETFs or DFA funds for example), it might be reasonable to discount this source of ‘value added’ for most investors, and trim the alpha estimate accordingly.

This should be pretty straightforward so far. Using a long-short equity mandate as our sandbox, we discussed how a manager’s returns might result from exposure to the FF factors, time-varying exposure to the market, and an idiosyncratic component called alpha. But now let’s get our hands dirty with some nuance.

Let’s assume the long-short manager has been laying on a derivative strategy with non-linear positive payoffs. Imagine as well that a wily quant suspects he knows the method that the manager is using, can replicate the return series from the derivative strategy, and includes this factor in his attribution model. Once this factor is added, the manager’s alpha is stripped away. While the quant may feel that there is no ‘value add’ in the derivative strategy because he can replicate it for cost, surely an average investor would have no way to gain exposure to such an exotic beta. As such, the average investor might perceive the strategy as ‘value added’, or ‘alpha’ while the quant would not.

Ok, let’s back out the derivative strategy, and assume our long/short manager exhibits positive and significant alpha after standard FF regression. In other words, the manager’s excess returns are not exclusively due to systematic (positive) exposure to market beta or standard equity factors, such as value, size, or momentum. Of course, since it is a ‘long/short’ strategy, the manager can theoretically add value by varying the portfolio’s aggregate exposure to to the market itself. When he is net long, the strategy should exhibit positive beta risk, and when he is net short it should manifest negative beta risk. How might we determine if this time-varying beta risk explains portfolio returns?

Engel (1989) demonstrated how regressing portfolio returns on squared CAPM returns will tease out time-varying beta effects. So let’s assume that adding a squared CAPM beta return series to the attribution model explains away a majority of this ‘alpha’ source. Therefore, including this factor in the model increases the explanatory power (R2) of the model, and reduces the alpha estimate. But is this fair or relevant in the context of ‘value added’? After all, while we can say that the manager is adding value by varying CAPM beta exposure, we have not demonstrated how an investor might generate these excess returns in practice. I have yet to see a product that delivers the squared absolute returns of CAPM beta, but please let me know if I’ve missed something.

I submit that it’s useful to identify the time-varying beta decisions for attribution purposes. This source of returns may represent true “value add” or (dare I say alpha), because it can not (presumably) be inexpensively and passively replicated by the investor. To the extent an investor is experienced enough, and/or sophisticated enough to identify factors which can inexpensively replicate the time-varying beta decisions (such as via bottom-up security selection, or top-down timing models), then, and only then, might the investor discount this source of ‘value added’.

So far we’ve discussed hypothetical examples, but a recent lively debate on APViewpoint is a great real-life case study. Larry Swedroe at Buckingham has long militated against traditional active management in favour of DFA style low-cost factor investing. It took many by surprise, then, when Larry wrote a compelling argument for including a small allocation to AQR’s new risk premia fund (QSPIX) in traditional portfolios. After all, at first glance this fund is a major departure from Larry’s usual philosophy, with high fees, and leveraged long and short exposures to a wide variety of more exotic instruments. Thus ensued 100 short dissertations from a host of respected and thoughtful Advisors and managers on APViewpoint’s forum about why the fund’s leverage introduces LTCM style risk; why the factor premia the fund purports to harvest can not exist in the presence of efficient markets, and; why the fund’s high fees present an insurmountable performance drag.

Notwithstanding these potentially legitimate issues, I’m uniquely interested in how one might view this fund in terms of alpha and beta. The fund’s strategy involves making pure risk-neutral bets on well documented factors, such as value, momentum, carry, and low beta, across a variety of liquid asset classes. In fact, AQR published a paper describing the strategy in great detail. Presumably even a low-level analyst with access to long-term return histories from the factors the fund has exposure to could explain away all of the fund’s returns. From this perspective then, the fund would deliver zero alpha. However, it is far easier to gather the return streams from these more ‘exotic’ factors than it is to operationalize a product to effectively harvest them. So for most investors, this product represents a strong potential source of ‘value add’.

The goal of this missive was to demonstrate that, when it comes to alpha, where you stand depends profoundly on where you sit. Different investors with varying levels of knowledge, experience, access, and operational expertise will interpret different products and strategies as delivering different magnitudes of value added. At each point, an investor may be theoretically ‘better off’ from adding even simple strategies to the mix, perhaps at lower fees, and even *after* a guiding Advisor extracts a reasonable fee on top. More experienced investors may be able to harness a broader array of risk premia directly, and thus be willing to pay for a smaller set of more exotic risk premia.

It turns out that ‘alpha’ is a remarkably personal statistic after all.

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]]>The post Dow 20,000: Is 2015 the Year? appeared first on GestaltU.

]]>But I digress. We don’t make predictions on this blog, but it is constructive to understand generally what the range of probable outcomes might be. Is our hero, Dr. Siegel, taking a brave stand against the bearish hordes, or is he making safe proclamations from behind a sturdy statistical moat? We aim to find out.

First, the low hanging fruit. What is the unconditional probability that the Dow Jones Industrial Average, which currently sits at approximately 18,000, closes out 2015 above 20,000? First, let’s assume that returns are normally distributed and *iid*. Next, let’s take long-term average (arithmetic) U.S. stock returns to be 5.3% per year (this is the average 12 month arithmetic price-only returns to U.S. stocks from the Shiller worksheet – remember, index returns do not include dividends), with annual standard deviation of 20%.

If the mean annual return to the price index is 5.3%, then the unbiased expected value of the Dow at the end of 2015 is 18,000 * 1.053= 18,950. A finish at 20,000 would represent a return of 20,000/18,000 = 0.111 or 11.1%, which is 11.1% – 5.3% = 5.8% more than expected. Given the standard deviation of returns is 20%, this represents a 5.8/20 = 0.29 standard deviation event. We can now apply the cumulative normal distribution function to determine the probability of a positive 0.29 sd event. In Excel, it is

1 – NORM.S.DIST(0.29,TRUE) = 0.386, or 38.6%

So the unconditional probability that the Dow closes at 20,000 or greater at the close on the last trading day of 2015 is almost 40%. This is not quite a coin toss, but Jeremy is not exactly going out on a limb.

Keep in mind that stock market price returns *approximate* a geometric random process. They don’t just climb in a steady curve, and close each day at a new high. Surely Jeremy would take credit for his “Dow 20,000” call if the index exceeds the magical 20,000 threshold *at any point* during the year, even if it doesn’t actually finish the year above this level. For simplicity however, let’s just examine the probability that it *closes* above 20,000 on any trading day of the year; so we won’t take into account intra-day periods.

Recall that if the annualized return is 10%, then the expected return at the close on day 1 is (using a 252 trading day year):

1.053^(1/252)-1 = 0.0002, or 0.02% with a range of 20% * sqrt(1/252), or 1.26%

Were the Dow to close at 20,000 on trading day 1, that would represent an 11.1% return in 1 day. Given the 1 day expected return is 0.02%, with a 1 day SD of 1.26%, this would be a (0.111 – 0.0002) / 0.0126 = 8.8 standard deviation event. The probability of a positive 8.8 sd event under a normal sample distribution is a decimal number preceded by 20 zeroes. Essentially no chance.

But that’s just on day 1. What about on day 63, which is about 3 months into the year?

The expected return after 63 days is 1.053^(63/252)-1 = 1.3%, with a standard deviation of 20% * sqrt(63/252) = 10%. Were the Dow to have risen 11.1% to close at 20,000 on trading day 63 (about the end of March), that would represent a (0.11 – 0.013)/0.1 = 0.98 standard deviation event. The probability of a positive 0.98 standard deviation event is about 16.3%. Now are are talking a 1 in 6 chance that the Dow hits 20,000 at the end of March, the same odds as throwing a 6 on a standard die.

The following chart was formed by performing essentially the same analysis at each daily period, and shows the probability that the Dow will meet or exceed 20,000 at the close of each sequential trading day of the year. We highlighted the 16.3% probability at a 3 month horizon described above for illustrative purposes.

Figure 1. Probability of Dow > 20,000 at each sequential trading day of 2015

We now know the probability of the Dow closing above 20,000 on any given day, but we still haven’t answered the question, “What is the probability that the Dow closes at or above 20,000 at any time in 2015?” To answer this, first consider Figure 2, which shows just 20 of the virtually infinite number of possible paths for the Dow over the next year, given our mean return and standard deviation assumptions.

Figure 2. Sample paths for the Dow in 2015

By visual inspection we can see that a substantial portion of the potential paths in Figure 2 cross above 20,000 at some point during the year. We ran a Monte Carlo simulation of 1 million possible paths, and discovered that about 64% of paths would cause the index to rise above 20,000 at some point during the calendar year.

Particularly astute readers may recognize that the former problem, where we solved for the probability of a price exceeding a specific value at a certain point in time, is a problem of similar nature to that of solving for the value of a European call option, which can be exercised only at expiration. This problem has a known closed-form analytical solution. In contrast, the latter problem has elements that are similar to finding the value of an American call option, which can be exercised at any time up to and including expiration. This problem has no known closed-form solution, and must be solved numerically or by simulation, such as our Monte Carlo method.

It’s critical to understand the random element in stock market activity so that we don’t get so emotionally attached to silly milestones. There is a 64% chance that the media and the top 0.01% will be able to break out party hats and champagne this year to celebrate an arbitrary milestone in a poorly constructed index. Siegel isn’t making a bold statement; far from it. Rather, he is playing the (unconditional) odds. And that is precisely what you should do as an investor.

The question is: do you feel lucky? We can think of a few reasons why you shouldn’t feel so sanguine, and might humbly suggest a better way of thinking about markets anyway.

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]]>The post A Century of Generalized Momentum appeared first on GestaltU.

]]>To this end, about two months ago we were honoured when Wouter J. Keller, CEO of Flex Capital and Professor Emeritus at Vrije University Amsterdam, invited us to collaborate on a paper exploring a new heuristic optimization, Elastic Asset Allocation, which follows from his previous work on Flexible Asset Allocation (FAA) and the more esoteric Modern Asset Allocation (MAA). These are excellent contributions to the existing literature on dynamic asset allocation, and complement our Adaptive Asset Allocation concept.

From the abstract of the new paper:

“In this paper we generalize [Flexible Asset Allocation] FAA, starting from a tactical version of Modern Portfolio Theory (MPT) proposed in Keller (2013). Instead of choosing assets in the portfolio by a weighted ordinal rank on R, V, and C as in FAA, our new methodology – called Elastic Asset Allocation (EAA) – uses a geometrical weighted average of the historical returns, volatilities and correlations, using elasticities as weights.”

We hope you enjoy the read. The full paper is below.

A Century of Generalized Momentum (Wouter and Butler, SSRN Id2543979)

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]]>The post Measuring Tactical Alpha, Part 2 appeared first on GestaltU.

]]>Figure 1. Performance comparison of Global Tactical Asset Allocation products vs. ETF Proxy Global Market Portfolio, Jun 1, 2011 – Nov 28, 2014

Figure 2. Performance comparison of global risk parity products vs. ETF Proxy Global Market Portfolio, Jun 1, 2011 – Nov 28, 2014

Analysis: GestaltU, Data from Yahoo Finance and Bloomberg

A few notes about these tables. First, where stats are labeled (Incep), they are calculated from June 2011, or the product’s inception if it launched subsequent to that date, through the end of November 2014. Second, CAGR numbers are annualized, except where a fund has been operating for less than 1 year. All risk-adjusted performance numbers are annualized from daily data, regardless of the length of track record (daily ratios are multiplied by sqrt(252)). Betas, alphas and t-scores are all since inception, and all relative metrics (IR, alpha, beta, t-scores) are relative to the Global Market Portfolio and based on daily observations.

So what story do these tables tell? Well, first off the Global Market Portfolio hasn’t been a tough bogey to beat in terms of raw returns over the past three years or so, with less than 6% annualized returns. For comparison, the S&P (SPY ETF) has returned over 16% annualized over the period, and a US balanced fund (Vanguard US Balanced ETF) has gained 11% per year. Bear in mind US markets represent over 30% of the global index, so international diversification has been quite a performance drag.

I know many of you with US-centric portfolios are patting yourself on the back. Ain’t self attribution bias grand? Make no mistake, you are US-centric because of home market bias, not superior forecasting abilities, but I will be the first to admit that it’s better to be lucky than smart. I can state with some confidence that US-centric investors are unlikely to experience the same relative success over the next three years. If that’s the case, what are you going to do about it?

In terms of returns relative to the GMP, GTAA funds are a mixed bag. The fund with the highest returns appears to be SMIDX, the SMI Dynamic Allocation fund, but this is somewhat of a red herring because the fund has less than 1/2 the operating history of most other funds. On a risk adjusted basis, JP Morgan’s Efficiente (EFFE) mandate has delivered the highest risk adjusted performance, in terms of Sharpe, Sortino, and Omega over the entire observation period. More importantly, given its low beta and high alpha scores, EFFE has generated its returns with very little reliance on performance from the underlying indexes. This is a critical point, as funds with a high correlation to the GMP are vulnerable to a negative shift in performance when global markets turn at the end of this cycle.

Investor legend Rob Arnott’s GTAA behemoth, PAAIX, managed under the PIMCO banner, deserves an honourable mention. It also surpassed the GMP’s Sharpe ratio over the past few years, and delivered the second lowest alpha and beta of any fund, despite lower absolute returns.

We included the Good Harbor Tactical Core US fund in our analysis, despite the fact that it is US focused, because it highlights the risk of trying to market time strictly between the stocks and bonds of one market. **This is the difference between market timing and GTAA: you make just one bet.**We deal with this concept in more detail in our new paper (see below). In our testing, we’ve observed that market timing between stocks and bonds or stocks and cash is a much more difficult challenge than spreading bets across multiple asset classes, and Good Harbor’s unfortunate recent performance lends credence to our own findings.

Given higher average structural allocations to bonds in risk parity funds, products in this class have clearly benefitted from the global race to the bottom in long rates, as average Sharpe ratios are meaningfully higher than average GTAA Sharpe ratios. I strongly suspect this will reverse when the rate cycle finally turns (which admittedly could be quite a while). Setting aside QSPIX for a moment as a special case, note that Invesco’s Balanced Risk portfolio sports the highest Sharpe, Sortino, and Omego ratios over the past 3+ years, as well as the lowest beta and highest alpha. This is a large fund, with $10 billion in AUM according to Morningstar, yet it continues to deliver stellar returns year after year. Not for nothing, it has also generated the highest annualized returns over this recent period.

We mentioned QSPIX is a special case, and it is. This fund, managed by AQR’s esteemed Andrea Frazzini and Ronen Israel, is based on a concept described in a 2012 paper by Antti Ilmamen, Ronen Israel, and Tobias Moskowitz, entitled “Investing with Style: The Case for Style Investing” (currently behind AQR paywall). Antti Ilmamen is one of the greatest investment thinkers alive today, and his books are required reading for every aspiring asset allocator. The authors present compelling evidence of the magnitude, persistence, and structurally low correlations, of the four primary sources of style premia: value, momentum, carry and ‘defensive’. Across all asset classes covered, the authors demonstrate that style premia correlations averaged -0.22, and ranged between -0.6 and +0.21 from 1990 – 2012. Long-term Sharpe ratios for style premia composites across all asset class buckets range from 0.9 for value to 1. 37 for carry over the same period. In simulation, when normalized to a 10% volatility, a combination style premia composites across all asset classes delivered a Sharpe of 2.52 before fees and expenses.

Of course, the authors are aware of the many frictions and pitfalls involved in implementing the strategy, so they included an analysis of the net historical performance after accounting for trading costs (Sharpe declines to 1.9); discounting for model overfitting (Sharpe declines to 0.98), and; risk-management and fees (Sharpe ratio declines to 0.85). This seems to be to be quite a conservative target (see Figure 5.)

Obviously, given the low expected average correlation with traditional 60/40 portfolios, and the high expected Sharpe ratio, QSPIX should substantially improve overall portfolio Sharpe, even with small allocations. For example, a 10% allocation to QSPIX carved out of a 60/40 portfolio might raise overall Sharpe from 0.3 to 0.44, according to the authors.

Overall, I’d say the short snapshot of performance we’ve seen over the past year since inception would not cause me to reject the possibility that QSPIX will deliver against expectations. However, the fund may be mildly vulnerable to liquidity shocks, as it has a gross leverage ratio of 8x (!!), so it should not play the role of a tail hedge in portfolios. In my opinion, the best structural tail hedge is a good CTA fund.

So what can we conclude from our analysis? This article wasn’t meant to recommend, or point fingers, at any particular strategy, but rather to highlight how we might think about the performance of global allocation funds, and what observed performance features might make them attractive. Above all, before committing any capital to these products, we would focus our scrutiny on the process underlying the strategy. What factors do the managers believe are driving returns? What evidence do they have that their methodology is effective? We would want to see much longer trading histories, analyze performance in multiple trading regimes, and understand how the strategy might interact with other holdings in portfolios. Where a long-term live history isn’t available (or even if one is available), we would be keen to see simulations of historical performance using the same process, and understand all the ‘moving parts’ that might affect the character of the strategy.

That said, if we only have live returns to go on, we would focus on performance relative to the only true passive global benchmark, the GMP, rather than making comparisons with specific regional indexes. Specifically, we would seek to harvest as much true alpha as possible relative to the GMP, as strategies with high alphas are less reliant on strong global market performance to deliver returns. After all, aren’t we after diversification? Next we would look at overall risk metrics, especially volatility, but with one eye on drawdowns and beta. Only then would we start to care about absolute returns and Sharpe ratios.

One other metric, Omega ratio, stands out as meaningful, since unlike all of the other performance metrics above, it makes no assumptions about the distribution of returns. The utility of Sharpe, Sortino, alpha, and beta all depend on the assumption of normally distributed returns, but Omega accounts for the fact that returns often stray far from normality, especially over shorter horizons. The formula for Omega ratio looks fancy, but it’s actually easy to calculate. First, since the Omega ratio reflects the relative probability of achieving returns above a minimum required return (MRR), we must first choose an MRR. We chose to use the risk free rate, which is currently zero, and which makes our calculations really easy. But here is the general formula in Excel-friendly language.

Omega={SUM(IF(returns>MRR,returns-MRR))/(SUM(IF(returns<MRR,MRR-returns)))}

Note that the returns variable refers to the vector of returns, so this is a matrix formula. In order for Excel to calculate it, you must hold down both the CTRL key and the ENTER key at the same time.

In any event, you will note that on this measure, and relative to a 0% risk free rate over the period studied, GTAA funds compare favourably relative to the GMP, almost across the board. This suggests that, after accounting for higher moments of the return distributions, an investor would have a higher probability of achieving positive returns using GTAA than the GMP. An interesting observation indeed.

Overall, there are a few worthy examples of successful GTAA mandates and several risk parity products worth considering for active global diversification. I should also mention that Meb Faber’s Cambria has recently launched a very interesting new GTAA ETF, GMOM, based on newer additions to Meb’s ubiquitous paper, “A Quantitative Approach to Tactical Asset Allocation“. Well worth a look.

Lastly, we are excited to get our own GTAA track record audited so that we can add our own numbers to this list as we launch our new firm, ReSolve Asset Management, in the new year.

**In the meantime, we would encourage those who are interested in global allocation strategies to give our new Tactical Alpha paper a read. Again, this is unique offer to our blog’s readers, since we’ve yet to distribute this widely. We believe it provides a strong argument for investors to consider a larger allocation to active asset allocation strategies in general. You’ll be granted immediate access to a pre-release copy here.**

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