The chart below shows the longest active day-of-week winning streaks for the DJIA since 1900 (regardless of the day of the week).

The red arrow marks our current winning streak of 18. It hasn’t been since the 1920’s that we’ve seen anything close when the DJIA posted multiple 15 day-of-week winning streaks.

I should note that had we looked at the S&P 500 (which for the purpose of an analysis like this is more or less the same thing as the DJIA) the streak stands at just 8 Tuesdays, a much less impressive feat.

Of course this is all just polite dinner conversation and chart porn, and I put no stock in this as a useful timing indicator.

Happy Trading,
ms

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– Turnkey Analyst

– Doug Short

– Bloodhound Exchange + follow up

– Woodshedder

– Paststat + follow up

– UK Stock Market Almanac

– MarketSci + follow up

– Plus 99% of posts from the Stock Trader’s Almanac.

Hat tip to The Whole Street for all links. Feel free to comment with any I might have missed.

Happy Trading,
ms

. . . . .

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Below is the DOM seasonality calendar for next month, broken out by quartiles (read why), with quartile 1 indicating the strongest days and quartile 4 the weakest.

Results in April were (beyond) abysmal, but real-time results since I began sharing the calendar in October have been mostly inline with the historical test.

The S&P 500 has averaged 0.09% (24% annualized) on the best half of days versus 0.05% (14% annualized) on the worst half.

Quartile 4 days (the worst of days) have been particularly bad, with an average return of -0.17% (-35% annualized).

As I stressed when I introduced the concept, day-of-month seasonality never justifies a trade all by itself, but I do think it deserves to be one of many tools in the trader’s toolbox.

Happy Trading,
ms

. . . . .

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The graph below shows how each day is weighted in a 10-day simple moving average (grey) versus exponential moving average (red). For the uninitiated, the SMA and EMA are the two types of moving averages most commonly employed by traders.

In the 10-day SMA, each day from 0 (the most recent) to 9 (the most distant) is equally weighted (10%).

In the EMA, day 0 makes up 18.2% of the average. That falls to just 3.0% by day 9. The left tail on the graph (day 20 and beyond) extends indefinitely, but in total makes up just 1.8% of the average.

The next graph show the daily weighting for a 50-day SMA/EMA, and the graph below that compares a 10-day EMA to a 50-day EMA.

For those familiar with how these averages are calculated, none of this is new information, but I thought it was interesting to see it visually.

For me personally it’s a reminder of how arbitrary an SMA is, weighting the very last day in the average equally with the most recent day, and how much of an impact it can have when that last day falls out of the average despite not telling you much about what’s going on today.

Happy Trading,
ms

. . . . .

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I (humbly) disagree with folks who poo-poo VXX (long 1-month VIX) as a bad investment.

Let me rephrase that. I think it’s very worthwhile to educate investors about why buying VXX is usually a bad choice (read more), and why buying VXX for the long-term is always a bad choice, but VXX isn’t in and of itself broken. It’s just an investment whose brief moment in the sun hasn’t come yet.

Investors would be forgiven for losing sight of that. Behold the horror show that has been VXX since inception in 2009:

[growth of $1, logarithmically-scaled]

But there’s a lot more data to consider than most realize. Recall the graph below that I’ve shown previously estimating VXX back to 2004, adding an additional 5 years of data prior to the ETF launch ⁽¹⁾.

[growth of $1, logarithmically-scaled]

Some notable VXX runs: a 97% gain within 2 months (2007), a 183% gain within 3 months (2011), and the big daddy, a 336% gain within 3 months (2008).

The problem is of course that investors too often try to trade VXX by timing the market. They preemptively buy VXX when the market gets overbought, and then get decimated by the water torture that is contango if the market does anything but go straight down.

A much better approach is to let the state of the VIX futures term-structure (i.e. backwardation) be the guide as to when VXX might be a viable play, and then (and only then) attempt to time the broader market.

That day will come, because the return of big volatility is necessary and inevitable. And when it happens, investor darlings like XIV (inverse 1-month VIX) will get crushed. Contrary to what is becoming conventional wisdom, XIV is only slightly more appropriate as a blind long-term play than VXX is.

To illustrate, the same extended historical data set for XIV back to 2004:

[growth of $1, logarithmically-scaled]

The difference between them is that XIV is usually the wise choice, but when it’s a bad choice, it’s really a bad choice. Flip that on its head for VXX. VXX is usually the unwise choice, but when it’s the right choice, it’s really the right choice.

VXX isn’t broken, it’s just an investment whose next brief moment in the sun hasn’t come yet.

Shameless self-promotion: to see MarketSci’s own approach to timing VXX and XIV, check out our Volatility ETF Strategy.

Happy Trading,
ms

(1) VXX data through 12/2005 estimated based on VIX futures, through 01/2009 based on the underlying VIX Short-Term Futures Index, and to date based on actual VXX ETF data.

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The strategy applies the popular short-term indicator RSI(2) to the VIX index and uses the result to time the S&P 500.

[logarithmically-scaled, growth of $1]

The graph above shows the S&P 500 (grey, dividend-adjusted) versus strategy results (red) since 04/1987.

Strategy rules: Buy the S&P 500 (SPY) at the close when RSI(2) of the VIX will close above 90 and the S&P 500 is above its 200-day moving average. Sell when RSI(2) of the VIX will close below 30.

Note that I’ve ignored STS’s ATR-based position sizing and assumed 100% of the portfolio was invested on each trade. Also note that because the VIX is strongly negatively correlated with the S&P 500, this is a short-term mean-reversion strategy (i.e. buying when VIX is high = buying when the S&P 500 is low).

Geek notes: S&P 500 results are dividend-adjusted (VFINX prior to 01/1993 and SPY thereafter). VXO is used in place of VIX prior to 01/1990. Return on cash = half the nearest 13-week UST. Transaction costs/slippage ignored.

Numbers for the number lovers…

Note that in the stats above I also included a variation of the strategy without the 200-day moving average requirement (middle column).

I haven’t shown it for the sake of brevity, but even based on a cursory examination, an argument could be made that the additional filter isn’t doing much to benefit the strategy.

Same test, but with 200-day MA requirement removed:

[logarithmically-scaled, growth of $1]

As a standalone strategy, both variations have failed to be big return drivers; the strategy is just too selective in its trades (time in market = 15% of all days). The strategy would need to be coupled with other ideas to increase exposure to the market.

But when the strategy has signaled a trade, those trades have been much more productive than the average day (note daily return stats).

One fly in the ointment: the strategy has lost steam in recent years.

To illustrate, below is the rolling 3-year daily volatility-adjusted return (average return / standard deviation of returns) of the strategy when invested (red) versus buy & hold (grey).

Note how the strategy is on the low end of its historical performance and hovering around even with buy & hold. Obviously, anyone considering this strategy would need to keep a careful eye on this.

Big ups to STS for resurrecting this strategy from Larry Connors. Note that this wasn’t meant to be an exhaustive analysis, just keeping the ball bouncing through the blogosphere.

Be sure to check out STS’s post for another angle of attack looking at various buy & sell thresholds.

Happy Trading,
ms

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SPLV and SPHB are on opposite ends of the large cap spectrum. SPLV tracks the 100 stocks from the S&P 500 with the lowest volatility, and SPHB the highest beta.

[growth of $1, logarithmically-scaled]

An interesting difference between the two ETFs is how differently each has responded to short-term mean-reversion (STMR) strategies. When I say STMR, I mean indicators like RSI(2), DV(2), etc.

To demonstrate, below I’ve shown the result of trading SPLV (low vol) using the simplest of STMR strategies, daily mean-reversion. I’ve assumed we went long SPLV at the close when SPLV closed down for the day, otherwise to cash, from 01/2007.

This is a proof of concept, so I’ve ignored transaction costs, slippage, and return on cash.

[growth of $1, logarithmically-scaled, frictionless]

Note the consistent positive performance, even through the 2008/09 crises.

I would never suggest that anyone trade the overly simple way I’ve shown here, but I would note that this tendency of the market to reverse its most recent direction, is exactly why more sophisticated indicators like RSI(2), DV(2), etc. work.

For comparison, below is the same strategy trading SPHB (high beta).

[growth of $1, logarithmically-scaled, frictionless]

Clearly, daily mean-reversion has not been nearly as effective trading SPHB. I see similar results with other measures of STMR like RSI(2).

I can’t comment on the reasons behind the discrepancy, but I do think it’s important beyond simply trading SPLV.

I’ve covered many times the fact that popular STMR indicators like RSI(2) or DV(2) have lost most of their predictive power (relative to their glory days), but this test shows that’s not so true for the lowest vol stocks.

Perhaps that observation provides some clues as to why STMR has lost some of its mojo in recent years.

More to follow perhaps in a future post, just meditating on the data at the moment.

Happy Trading,
ms

. . . . .

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SPLV (SPHB) tracks the 100 stocks from the S&P 500 with the lowest volatility (highest beta) over the previous 12 months. Using data available at S&P, we can get an extended view of how both ETFs might have performed all the way back to 04/2008 (adding an additional 3 years of data). SPLV is in red, SPHB in grey.

[growth of $1, logarithmically-scaled]

Below I’ve also included the rolling 1-year Sharpe Ratio of both ETFs (for simplicity’s sake, rf = 0%).

Note how, when adjusted for volatility, both ETFs performed similarly during the 2008 crash and immediate recovery. Also note the widening gap in their most recent performance.

The question I’m rolling around in my noggin is…

What degree of the outperformance (relative to volatility) that we see in SPLV is a result of the well-documented observation that low vol stocks outperform over the long-term because the market doesn’t properly compensate for volatility and/or risk (read more at Falkenblog), and what degree of that outperformance is a result of the type of stocks/sectors that tend to fall into the low beta bucket going through a sunny period where they just so happened to outperform (bearing in mind that even extending the data back to 2008 covers a very small period of history for such a long horizon observation)?

Happy Trading,
ms

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In this post, using a simple walk-forward test to minimize hindsight bias, I’ll look at trading the strongest non-contiguous 6 months of the year (i.e. unlike my last post, the months do not have to be sequential).

First, here is how such a strategy is usually touted…

[growth of $1, logarithmically-scaled, dividend-adjusted S&P 500, frictionless]

The graph above shows the results of trading the S&P 500 during the best (non-contiguous) 6 months of the year in red, versus the worst 6 months in grey, since 1950. Wowzahs.

The problem of course is that this graph is prepared with the benefit of hindsight. The trader would not have known in 1950 what the best months would be in the future, so below I’ve rerun the same test using a simple 20-year “walk-forward” test.

That means the trader now chooses the best/worst 6 months based on the 20-years prior to that point in history. Why is that important? Because if history couldn’t accurately predict the future before, why should we think history will accurately predict the future now?

Note that I’ve defined “best” as the months with the highest average return divided by standard deviation (like a Sharpe Ratio without a risk-free discount).

[growth of $1, logarithmically-scaled, dividend-adjusted S&P 500, frictionless]

On first blush, trading the best months still appears effective. Not as effective as our first test, but still worthwhile: annualized return for the best 6 months was 14.7% (versus 7.5% for the worst), a Sharpe Ratio of 0.88 (versus 0.38), and 67% of months were positive (versus 59%).

But “first blushes” can be deceiving. Digging a little deeper into the data…

. . . . .

First, if these results were robust, we’d expect to see consistent outperformance. Below is the rolling 20-year Sharpe Ratio of our best (red) and worst (grey) 6 month strategies.

Check. Outperformance has been consistent over the last 60+ years (i.e. the red line is consistently above the grey line).

Second, if these results were robust, we would expect stronger results for better ranked months. In other words, the best ranked month would be better than the second best month, the second best would be better than the third best, etc.

Data is never quite that clean, but we should see a general trend in that direction. Below is the annualized return in months ranked 1/2, 3/4, etc.

Not impressive. Top ranked months have been middling, bottom ranked months have been above average, and there’s no clear trend to the results.

Lastly, if these results were robust, we would expect the strategy to be similarly effective using other similar lookbacks. I used 20 years in the walk-forward test above, but what about 15 years, 25 years, etc?

Below I’ve run the same rolling Sharpe Ratio for other lookback periods (click to zoom).

Results are inconsistent using other similar lookbacks.

. . . . .

Am I debunking calendar month seasonality?

No. In all tests, results have been more impressive in recent history, especially since 2000, so calendar month seasonality will continue to be a little itch in the back of my brain, especially during particularly strong or weak calendar months.

But I think these more in depth tests show that calendar month seasonality (like the “sell in May” rule) is not nearly as effective as tests prepared with the benefit of hindsight would imply.

Happy Trading,
ms

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This time every year the “sell in May and go away” strategy rears its head again.

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.

. . . . .

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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