Business and trading will roll on, but the blog will be napping while I’m away.

Looking for your fix of trading geekery? Check out our most popular posts of the last month:

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Strategy #1 for Trading Volatility ETPs: Term-Structure Following

Strategy #2 for Trading Volatility ETPs: Timing the VIX

The Evolution of “Sell in May”

Visualizing the Bear

“Sell in May” Debunked?

Trading Volatility ETPs: Obey Thy Stops

VXX/XIV Performance in Advancing & Declining Markets

Free Historical VXX Data

EconomPic’s Seasonality Strategy

Deciphering the VIX:HV Ratio

Happy Trading,
ms

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Most of the stock market’s volatility comes in the daytime (open-to-close), but most of the market’s gains come overnight (close-to-open).

[growth of $1, logarithmically-scaled]

The graph above shows two hypothetical traders. The first (grey) is only long the SPY from each day’s open to close (daytime), and the second (red) from each day’s close to the following open (overnight).

Note that (a) the daytime session is about 60% more volatile, and (b) all of the SPY’s long-term gains since 1993 have come overnight and most of its long-term losses during the day.

That’s not the case this year, with all the market’s gains coming in the daytime session and both sessions being about equally volatile. Same chart, YTD…

[growth of $1, linearly-scaled]

Significance? Not sure.

In my past tests, I’ve never found a strong use for the daytime versus overnight relationship, other than polite dinner conversation.

I was digging back into the subject, and thought an updated chart was in order. As always, more to follow.

Happy Trading,
ms

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In the table to the right (click to zoom) I show how the stock market’s best 6 months of the year has evolved over the last 80+ years. Each row represents 20 years. Red cells denote the “best” 6 months.

Recall that the “sell in May” rule is based on November through April being the best half of the year.

Given the results in my previous post, I was surprised by how consistently Nov – Apr (or at least Dec – May) was the best performing period.

Happy Trading,
ms

OOPS: in my rush to get this post out I botched the table I initially posted. I was showing the best 6 months from 1930 to whatever year was listed on the table (rather than that particular 20 year period). Sincerest apologies!

Geek note: the “best” 6 month period was chosen based on volatility-adjusted (not absolute) dividend-adjusted S&P 500 returns.

It’s hard to buy in to the idea that such a simple approach could have such divining powers, but the results are (on the surface) compelling.

I’ve been pondering how best to put the strategy through the paces. Thoughts…

[growth of $1, logarithmically-scaled]

Usually a graph like the one above accompanies these discussions. Here I’ve shown the S&P 500 (dividend-adjusted) from Nov-Apr (red) vs May-Oct (grey), since 1950.

Awesome results. Great strategy.

The problem is of course that this is all prepared with the benefit of hindsight. Surely in 1950, we wouldn’t have known that Nov-Apr would turn out to be such fortuitous months for stocks. So in the next graph I’ve taken a different approach.

I’ve assumed that each year the investor only looked at the data available from 1930 up to that point in time, and invested in whatever 6 months of the year had been the best for stocks.

This is called “walking the test forward”, and (to some degree) removes the benefit of hindsight.

[growth of $1, logarithmically-scaled]

The graph shows that most of the benefit of choosing seasonally strong months disappears because the investor wouldn’t have made the “right” choices given the information available at that time.

The investor would have done well since the 1990’s, but that’s a much less robust observation than the first graph would imply.

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So what if rather than choosing seasonally strong months based on ALL data available up to that point in time, the investor only looked at say the last 10 years?

Same conclusion.

20 years?

Same conclusion.

If we go out to about 30 years (i.e. the investor is choosing seasonally strong months based on the previous 30 years of S&P 500 data), the strategy soars again…

But the fact that only 30 years (as opposed to say, 20) works so well is most likely because it’s a curve-fit solution.

So does the data totally debunk “sell in May”?

No. I wouldn’t base a trading decision solely on the rule, but results in all tests were impressive enough in recent history that the observation at least deserves to be on the radar.

But that really misses what I think is the more important point:

The graph like the first I showed would lead the reader to think that the “sell in May” rule is much more robust than it actually is. In truth the rule is at best a questionable observation, and at worst, simply a product of randomness.

Happy Trading,
ms

P.S. This post isn’t meant to dump on the quantitative minds who I respect very much that have discussed this subject recently. I’m just one nerd with $0.02 and I recognize that on this one, I am probably out on a long branch all by myself.

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Strategy results since 1962 (adding about a decade to EconomPic’s results):

[growth of $10,000, monthly-intervals, logarithmically-scaled]

In the graph above I’ve shown the S&P 500 in blue (dividend-adjusted), US Treasuries in grey, and EconomPic’s strategy in red (frictionless).

EconomPic uses the Long Gov/Credit bond index when not invested in the S&P 500. I prefer the 10-year UST index (IEF) because I think it represents a better risk/reward tradeoff (and I have more data on hand). Differences between the two are small for the purposes of this test.

Numbers for the number lovers…

Obviously “the red line is higher”, but that’s a simplistic way to assess a strategy. From this 30,000 foot view, all the dips that make trading so hard to stomach get washed out.

I think something like the graph below is a better test. Here I’ve shown the rolling 5-year Sharpe Ratio of the S&P 500 (blue) versus EconomPic’s strategy (red).

EconomPic’s strategy outperformed the S&P 500 (in risk-adjusted terms) in 82% of all 5-year periods. That’s impressive.

The usual warnings about curve-fitting notwithstanding (especially for a strategy that trades so infrequently), it’s interesting that EconomPic first described this strategy nearly four years ago and since then it’s continued to outperform.

Big ups to EconomPic for posting this strategy. This is just meant to be a primer. In a follow up post, I’ll break down the strategy’s results further.

Happy Trading,
ms

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My vol. trading is a big return generator today, but I recognize that I’m exploiting market imbalances that may not exist long-term.

On the other hand, TAA isn’t going to light the world on fire, but I can rest well knowing that we’re chasing opportunities that have existed for a century and more.

The TAA model has underperformed its benchmark in the 19 mos since inception.

As I’ve shown before, the model would historically have gone through long periods of underperforming, especially when the benchmark has been strong. This is a “generational” model, and I’m much more concerned with returns over the next decades than any one month or year.

But I think it’s still a worthwhile exercise to drill down on where the model has done well and not so well, and where it could be better.

Things the Model has Done Well

I’ve held U.S. Treasuries (IEF) and Gold (GLD) for most of the last 19 months. Those trades have done well – so well that ALL of the model’s returns since inception have come from just those two asset classes.

Things the Model has NOT Done Well

The model has done a poor job at both selecting specific equity asset classes to invest in AND timing the % of the portfolio to invest in equities each month.

Note that when I say equity asset classes I include real estate (VNQ) and commodities (GSG), because in today’s market, all are highly correlated.

To illustrate, in the graph below I’ve shown two portfolios. The first (grey) are the model’s actual “equity-driven” returns. The second (blue) are the results of simply investing in the volatility-adjusted equivalent of the S&P 500 (SPY) each month.

What I’m testing is the model’s success in picking specific equity asset classes (grey), versus just dumping each month’s equity exposure in to the S&P 500 (blue).

[growth of $1, linearly-scaled]

The fact that the grey line consistently trails the blue means that the model has done a bad job selecting equity asset classes.

A bit of that is due to bad luck (ex. taking a big position in EWJ right before the Tohoku earthquake), but most of it is bad timing.

But the suck doesn’t stop there.

Recall the blue line in the graph above, which is a different % of the portfolio invested in SPY each month. What if I just took the average exposure of all months, and invested it on day one. Here I’m testing the model’s success timing the % of the portfolio to invest in equities each month.

[growth of $1, linearly-scaled]

The fact that the blue line (slightly) trails the red means that the model has also done a bad job timing the % of the portfolio to invest in equities.

Next Steps

The first of these shortcomings (selecting the specific asset class) is an issue I need to continue analyzing. The model would have been better off just plowing equity exposure into the S&P 500 most months so far and that’s unacceptable.

The second shortcoming (timing the equity exposure) I chalk up to “stuff happens”. Like Mebane Faber (the inspiration for my own model) I’m using long-term moving averages to guide entry/exits in to equities, and that’s a concept that’s served investors well for a century plus (given enough time to let the averages play out).

I’m at my self-imposed word limit. More perhaps in a future post.

Happy Trading,
ms

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Our Tactical Asset Allocation (TAA) model selects up to four assets from a diverse basket of asset classes on the final trading day of each month. Below is the new allocation for today’s close. Click to read more about the TAA model.

I eat my own cooking, so I’ve devoted a healthy share of my own net worth to the TAA model (read why). On the last day of each month I share my new allocation (see above) and real-time performance (see below).

The model performed in line with its benchmark in April, returning (as of 04/27) +1.2% versus 1.1%.

For May, the model is holding the same 4 asset classes, but reducing exposure to gold in favor of the S&P 500. We’ve had a gold position on for over a year and a half, and it’s become a little bloated with gains.

The model has underperformed its benchmark in the 19 months since inception.

As I’ve discussed before, the model would historically have gone through extended periods of underperforming its benchmark, especially when the benchmark has been strong. This is a “generational” model and I’m much more concerned with returns over the next decades than any one month or year (read more). Real-time results have most definitely been in line with backtests.

In a follow up post later this week I’m going to drill down on exactly where the model has done well so far (gold and treasuries) and not so well (timing equities and selecting specific equity asset classes). Be on the lookout.

. . . . .

Happy Trading,
ms

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For the uninitiated, the VIX (which is an estimate of future volatility) is closely tied to recent past volatility of the S&P 500, as the graph below demonstrates. Here I’ve shown the VIX on the y-axis versus the 21-day standard deviation of the S&P 500 (i.e. historical volatility) on the x-axis.

[HV = annualized 21-day std. dev. of the natural log of daily S&P 500 changes * 100]

Note three things: (a) how the relationship is roughly linear, (b) the slope is less than 1.0 (m=0.7539), and (c) the large y-intercept (b = 8.3713).

That means that when historical volatility (HV) is low, the ratio of the VIX to HV tends to be high. But when HV is high, the ratio will be near or even less than 1.0.

That also means that simply comparing the VIX to historical volatility is meaningless without considering whether HV is high or low.

To illustrate, the graph below shows historical volatility (x-axis) versus the VIX:HV ratio (y-axis).

[HV = annualized 21-day standard deviation of the natural log of daily changes * 100]

Note how when HV is low, the VIX:HV ratio tends to be high, but as HV increases, the VIX:HV ratio approaches and eventually falls below 1.0.

Why is all this important?

Pundits often make hay about the VIX:HV ratio as if it had predictive value all by itself. It doesn’t.

What does have predictive value is comparing the VIX to where you would expect the VIX to be at that level of historical volatility.

In a follow up post I’ll dive deeper into the topic by using this observation to predict next-day changes in the S&P 500, the VIX, and volatility ETPs VIX and XIV.

Happy Trading,
ms

P.S. as always, I’m standing on the shoulders of giants here. I’m definitely not the first to talk about the VIX:HV ratio and how it relates to historical volatility (ex. VIX & More has pounded this drum on many occasions).

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Below I’ve colored red all S&P 500 declines of more than 5% since 03/2004 (which is as far back as we can estimate VXX/XIV).

Next I’ve shown the daily performance of VXX during those advancing (blue) and declining (red) markets (you can more or less flip these results for XIV).

And for good measure, the results of two hypothetical (frictionless) portfolios. The first (blue) only trades VXX during advancing markets, and the second (red) only during declining markets.

[growth of $10,000, logarithmically-scaled]

The fact that VXX goes down in advancing markets and up in declining ones isn’t the surprise. The surprise (at least to me) is how “symmetrical” that observation is.

I expected VXX’s performance in declining markets to be more inconsistent because most of these declines were small enough that, with the exception of the 2007-08 and 2011 bear markets, VIX futures stayed mostly contangoed (which is a drag on VXX returns).

But by comparing the stats in the table above we see that (adjusted for volatility) VXX’s outperformance in advancing markets was just as strong as it’s underperformance in declining ones.

Even after removing the 2007-08 market crash, that observation holds.

That makes a small case for trading VXX/XIV by timing the broader stock market (something I’ve poopooed in the past).

One last thought: notice the skew in the results for declining markets (i.e. average VXX returns are much larger than median returns) indicating gains during declines are the result of a smaller number of big days.

It’s more difficult to be right about a long VXX position in declining markets, but the payoff for being right is greater. That’s because the VXX tends to increase in spikes, but decrease in increments (the opposite of equities).

Key takeaway: despite the mostly negative (positive) impact of the VIX futures term structure, the performance of VXX (XIV) is, on average, equally positive (negative) in advancing markets as it is negative (positive) in declining ones.

Happy Trading,
ms

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Here’s another look at the same data. Below I’ve colored red all declines in the S&P 500 of 20%, 10%, and 5% or more. Click on images to zoom.

Key takeaway? Declines happen…often.

[growth of $10, logarithmically-scaled, click to zoom]

[growth of $10, logarithmically-scaled, click to zoom]

[growth of $10, logarithmically-scaled, click to zoom]

Happy Trading,
ms

Geek note: I’ve used the S&P 500 price-only index to measure declines, but used dividend-adjusted data in all charts above.

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