Skewness factor

I’d like to test a skewness factor in my models. For example, I want to test going long (short) momentum stocks within the lowest (highest) skewness quintile. Can anyone here suggest how to write such a rule?

Thx,
Ed

See: https://www.portfolio123.com/mvnforum/viewthread_thread,7323#36740

Not doable based on my attempts.
You can get a mean return through LoopSum in a Custom Formula but cannot then call that in the formula to create skewness.

$MeanReturn50d: LoopSum(“((Close(CTR)/Close(CTR + 1))-1)*100”, 50, 0, 1) / 50

Ok, good to know. Hope it’s possible here before too long.

What is the formula for skewness? I woud like to give it a shot.

Easiest approximation is 3 (mean - median).
Next is skewness coefficient: (3 (mean - median)) / std dev
Next level is proper statistical formula. See Wikipedia.

Thanks Shaun. The statistical formula in Wikipedia is a bit too much for my simple brain. I’ll take your word for it that it’s not possible in P123.

What I did gather from Wikipedia is that:

  • Skewness is conceptually a measure of the length of the right tail vs. the left tail.
  • And that one of its contributers went out of his way to point out that “The skewness is not strictly connected with the relationship between the mean and median: a distribution with negative skew can have the mean greater than or less than the median, and likewise for positive skew.”
    Since there is (surprisingly) no Median function in P123, that last point is anyways irrelevent.

Questions:

  • What type of returns are used to measure skewness, daily total returns? Over how many trading bars?
  • What is a theoretical basis for using skewness to predict returns?
  • Can skewness be approximated by using minimum, maximum, average and standard deviation (which are available in P123)? (More specifically, I was considering estimating the relative skewness by using Average (of all the data) - Midpoint (between min and max) scaled by standard deviation.)

Thanks.

Recent interest on skew: http://blog.alphaarchitect.com/2015/05/11/momentum-investing-skewness-enhanced-momentum-yields-double-alpha/

Abstract: Motivated by the time-series insights of Daniel and Moskowitz (2014), we investigate the link between expected skewness and momentum in the cross-section. The three factor alpha of skewness-enhanced (-weakened) momentum strategies is about twice (half) as large as the traditional momentum alpha. In fact, skewness is among the most important cross-sectional determinants of momentum. Our findings do not neatly fit within a specific prominent theory of momentum. Due to the simplicity of the approach, its economic magnitude, and its existence among large stocks and in the recent past, the results appear difficult to reconcile with the efficient market hypothesis.

Reviews on the blog note that the main benefit is on the short side, which in my experience is not properly addressed in academic papers that ignore borrow-ability and short costs.

We should have access to the return series in P123 just as we have access to the price series. Just as with Close(), it would be nice to have RetPrice() or RetTotal(). These could then be used with mean, median, std dev, skewness, kurtosis functions which of course we’d want next.

As for [quote]

I have yet to read the paper so I may be way (way) off-base on offering it up as being relevant. Please let me know what you think.

Walter

That is the paper that alpha architect reviewed. Better to read their review than the paper.

Thanks! Here it is; http://blog.alphaarchitect.com/2015/05/11/momentum-investing-skewness-enhanced-momentum-yields-double-alpha/

Alpha Architect’s executive summary: This paper documents some interesting findings. However, as the paper points out, the skewness measure has no impact on the long leg of the portfolio. Thus, the results are driven by the short leg, which can have much higher costs.

Walter

Yes, it is that research that prompted this thread. Hoping the team here at P123 might look into adding a skewness factor or calculation as more and more research points to skewness as a useful tool. As it stands now the best I can do to simulate a skewness factor is by excluding the top “x” results (say, the top 2-4) in a screen. But that functionality is not available in a simulation, and it’s not truly measuring skewness, somewhat of a blunt instrument (though it has helped my returns in my short models).

Skewness was part of my old (very old) time MBA thesis; I recomputed Markowitz wighting by doing mean-skewnwss optimizations instead often-variance. As I recall, the results were pretty good, and still better when I hypothetically assumed all stock-stock covariance’s were zero given the lack of persistence in the covariance metric (each piece worked on its won too).

Skewness would probably wind up pointing toward stocks similar to what you’'d get from models using Sortino.

The danger, though, is that every high-right-tail stock is at the same time a potential high left-tail stock, the difference being in how events happen to have played out during the sample period. Risk-relevant fundamentals relate to the length of the he tail; events relate to the direction. So if things change, companies could easily flip flop, So if we were to add skewness (Have you posted this as a Feature Request? You may want to do likewise for Kurtosis.) it would be important to model them in tandem with factors that suggest that the future, the right tail is more likely than the left tai.

Hi all,

another area where skewness plays an interesting role is options volatility. The CBOE measures the relative demand for low strike puts in the Skew-Index, published here:

http://www.cboe.com/micro/skew/introduction.aspx

When trading options, but also when I want to have a quick impression of market sentiment in addition to VIX, the SKEW index is helpful as a trading signal. I came across this when reading THE INDOMITABLE INVESTOR by Steven M. Sears. Here is the relevant passage:

https://books.google.de/books?id=9u_sBQAAQBAJ&pg=PA90&dq=indomitable+investor+skew&hl=de&sa=X&ei=7BNeVYyMEcuasgHBxoDgDw&ved=0CCEQ6AEwAA#v=onepage&q=indomitable%20investor%20skew&f=false

Hi Marc:

Thanks, good observations.

As to your point about the instability of high right-tail stocks, my understanding of the findings from the AA research is that they confirm your hunch … i.e., that one using momentum should avoid right-tail stocks in a long portfolio (and likewise avoid the left-tails in a short portfolio). Rather, one should buy the momentum stocks in the lowest corresponding skewness quintile (and short negative momentum stocks in the highest corresponding skewness quintile). So there’s a double sort, both on momentum and skewness. Note that the research concludes this system is far more effective for shorts than longs, as there was little/no discernible value-added when factoring skewness into long-momentum portfolios.

Thx,
Ed

Ed,

I just checked the paper. I didn’t haver time to get into it deeply, but I think I have a sense of what’s going on.

It looks to me like the study is, in effect, using the momentum/skewness combination in a way that gives a different slant on the basic mean-reversion thing, or the overbought correction/oversold bounce. What’s different is tat they seem to use skewness to measure the degree on the extreme. I may not be saying it quite right; the vocabulary that most of us use doesn’t really account for skewness. But maybe you get the point.

It seems to me, though, you might be able to replicate the most essential aspects of the strategy using momentum and sortino. I’ve often found that papers like that tend to be most valuable for the ideas that underlie the model rather than the model’s specs per se. My first glance leads me to suspect that you may be able to capture the core idea on p123 right now; all you need do is revise the factor vocabulary to account for the absent of a skewness factor. Maybe I’ll have a better sense of that when I get a chance to read more closely.

Well, maybe “replicate” isn’t the right word. Perhaps I should say I think you may still be a blue to build p123 model that lets you benefit from the ideas, even if you have to salter the details of implementation.

Hey Marc:

Good idea, I’ll give that Momentum/Sortino combination a test drive here, maybe that’ll do the trick. And completely agree with your observation that one need not get hung up on the particular factors, necessarily, if a similar combination is a reasonably valid substitute both in theory and in practice.