Small Cap Outperformance Debunked?
I break from conventional wisdom on the subject of the “size effect”, or the tendency for small-cap stocks to outperform large caps over the long-term.
Some negligible small cap hoodoo might exist, but it pales in comparison to what really drives this Wall Street mantra: a “volatility (beta) effect”.
Proponents of the size effect might use a chart like the one above to make their case. Here I’ve shown the annual difference since 1927 between small and large cap performance in grey, with the average of all years (+2.89%) in red.
Geek note: I’m using the Fama/French benchmarks to represent large/small-caps. These differ from tradable large/small-cap benchmarks like the S&P 500 and Russell 2000, but are sufficiently correlated that I think the analysis is sound.
At first blush, it would appear that small caps have more often than not, and with a fair amount of consistency, trounced large caps by about 3% a year.
But that’s only half the story…
It’s All about the Vol.
Imagine we used a pairs-trade, 50% long small-caps and 50% short large-caps, to isolate just small-cap outperformance. Our results from 1927 (frictionless and rebalanced monthly) would have been:
[logarithmically-scaled, monthly interval, growth of $10,000]
There’s that size effect again, still going strong.
But next let’s imagine that we instead ran two portfolios. In the first, we only took the pairs trade when the market (average of large and small caps) rose, and in the second only when it fell. Remember, we’re just looking at outperformance so the direction of the market shouldn’t matter.
Results (up markets in green and down in red) from 1927:
[logarithmically-scaled, monthly interval, growth of $10,000]
Clearly small-cap outperformance has been strongly tied to market direction – small caps have consistently out/underperformed in up/down months.
It’s pretty simple: because small-caps are pretty well correlated to large-caps but about 30% more volatile, when the market goes up they tend to go up more (and vice-versa). So because of the general upward bias of the market, small-caps have naturally tended to outperform large caps. That’s NOT a size effect, that’s a volatility/beta effect.
But is Vol. the ONLY Effect?
I’m not going to say with absolute certainty that no size effect exists. Academics (purportedly) far smarter than I have built careers saying it does. But I’ll leave you with this chart which I think speaks for itself.
Here we have the same pairs-trading portfolio, but rather than an even 50/50% split, I’ve balanced the trade (monthly) to account for the expected volatility of each leg (based on observed volatility over the previous 5-years).
Put another way, I’ve allocated more to large caps and less to small caps to truly isolate just the size effect without that pesky volatility/beta-effect getting in the way. The results:
[logarithmically-scaled, monthly interval, growth of $10,000]
Take out the volatility/beta-effect and all you’re left with is a meandering graph. Whatever “size effect” exists is far smaller and more fleeting than most financial professionals realize.
Happy Trading,
ms
Three random thoughts: (a) CXO Advisory has done a number of great reviews of papers discussing the size effect (most of which would disagree with me) and I highly recommend starting there to read more about this issue, (b) in this analysis we looked at indexes so I can’t say whether any of the above holds true for individual stocks (because that’s not what we do), and (c) I realize that I’m not the first to make the case above, but in classic me fashion, I had to reinvent the wheel on my own before I’d attach it to my apple cart.
. . . . .
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Filed under: Stock Market Mechanics | 21 Comments
Very nice post, thanks.
Here’s a Hulbert column (just 4 days ago, which is why I popped into my mind) that
says that the small cap advantage is January only.
http://www.marketwatch.com/story/after-end-of-january-size-does-matter-2010-01-27
And here’s another column from earlier in the month.
http://www.marketwatch.com/story/small-cap-strength-comes-on-schedule-2010-01-12
RE to Blue: once again, you stole my thunder…I’m covering Hulbert’s post tomorrow =)
In a nutshell, I think there’s a small bit of truth in January small-cap outperformance, but it’s still mostly a volatility/beta effect (caused by the fact that January has historically been a very good month for the market). michael
Hi Michael, thanks for all your thought-provoking posts and excellent blog.
I was wondering if the data you use above includes dividends?
RE to Bryan: thanks for the kind words, and yes, I always use dividend-adjusted data. michael
I’m a little confused about this post as it relates to the vix based pairs trading strategy. In the pairs trading strategy the small cap / large cap positions are adjusted for volatility. Wouldn’t you want to capture that extra beta (eg the combined red/green curves in the chart above)?
RE to Mike: if I understand your question correctly, you’re asking if it would be better not to adjust each side of the VIX-based pairs trading strategy to balance vol. and instead make use of the difference in beta between the Russell 2000 and S&P 500?
If so, good question. I thought about taking that approach, but then you lose the benefit of market neutrality. If we’re willing to take on beta risk, then I think there are more effective directional plays.
For other readers, the posts Mike is referring to are:
http://marketsci.wordpress.com/2010/01/20/vix-based-pairs-trading-market-neutral-strategy/
http://marketsci.wordpress.com/2010/01/21/follow-up-to-vix-based-pairs-trading-strategy/
michael
Great post Michael! I always appreciate your work, and am happy you are back to your blog. Definately among the top 5 quant bloggers out there. Keep it up!
Mike,
Academia speaks to the risk premium in small caps over large caps (the size effect). Higher beta is exactly what they expect with small caps. I don’t think academics claim superior risk-adjusted returns or that performance in down markets is superior. Academia further assumes a buy and hold strategy, so given that markets have drifted upward over the long run, they are in fact correct that small caps outperform large caps for the buy and hold investor. For a trading portfolio, however, choosing small caps will magnify your error both up and down due to the higher beta.
RE to Ryan: I’m not sure I agree with that. Academia DOES claim asymmetrical outperformance (or put another way, that small cap stocks don’t underperform in down markets as much as they outperform in up markets). Here’s a CXO review of such a paper: http://www.cxoadvisory.com/blog/external/blog3-28-07/
Saying that something is “good” simply b/c it carries higher beta/vol and will outperform in an upward drifting market is dishonest and exposes investors to risks they don’t understand (I’m railing against the financial community here, not you).
michael
Well done, Michael. I can never understand how people can make comparisons w/o normalizing volatility/beta…you did a great job of that here
Hello Michael. Wonderful post.
Here’s what Fama & French said today regarding Jan effect.
“History provides a cautionary tale. Another anomaly that was all the rage among academics was the January effect. Small stocks tend to have high returns in January and lower return in other months. Interestingly, this anomaly seems to be weak in the live returns of small cap mutual funds, raising the possibility that there is something weird in the quoted prices for small stocks around the turn of the year on major databases.”
http://www.dimensional.com/famafrench/2010/02/qa-can-investors-profit-from-momentum.html#more
RE to Henry: funny you should mention that. I held off on releasing my own “small-caps in January” post b/c I found similar oddities in small-cap index/MF quotes around January. I don’t think it’s a problem in “quoted prices” (that sounds a little overreaching to me) but there is drift with the fama/french benchmarks. More to follow.
michael
Very good work mate.
Hi Michael,
In original paper that brought major attention to the size effect, the authors (Fama & French, 1992) do adjust for beta. Here’s a few quotes from a defunct blog summarizing their method:
“To estimate beta, the authors form portfolios based on size using the familiar NYSE breakpoints. Doing so makes the estimates of beta more precise (as in Fama and MacBeth 1973). But since beta is often correlated with size, the authors break up these portfolios on the basis of pre-ranking betas and then make a new set of 100 size-beta portfolios.”
“By subdividing the size portfolios on the basis of pre-ranking betas we can see a strong relation between size and return, but no relation between return and beta.”
“Thus, variation in beta that is tied to size is positively related to average return, but variation in beta unrelated to size does not lead to higher returns.”
I would imagine the vast difference between your results and Fama/French’s is due to your testing the entire small vs. large asset class, whereas they’re sorting all stocks by beta first, so as to compare apples to apples. My personal theory on why small caps outperform (over the long haul) is that they don’t. Its actually the large caps that underperform due to the basic law of diminishing returns.
Here’s the link to the original paper:
http://www.bengrahaminvesting.ca/Research/Papers/French/The_Cross-Section_of_Expected_Stock_Returns.pdf
And here’s a link to research showing that high volatility is a predictor of underperformance for stocks:
http://www.connorsresearch.com/CR_Historical_Volatility.pdf
I know this is an older post but I’d very interested in knowing what you think.
Cheers mate,
Josh
RE to Josh: thanks for the well researched comment.
You are correct, I combined the high/med/low beta stocks in the manner suggested by F&F to form just one “small cap” group and one “large cap” group.
My issue is much less with the academic work than how it’s been interpreted on the Street. The research has gone from “comparing X beta small cap stocks w/ equal beta large cap stocks” (which might very well be a valid point) to “small cap stocks outperform large cap stocks…period”.
The former is a nuanced point that requires a very careful understanding of the very specific assumptions that the author used in his research. The latter is a gross overstatement that (I hope) we’ve shown is utterly bunk.
michael
I couldn’t agree more…
I found something that sheds a little more light on the volatility effect. It especially highlights how important that the way you slice and dice your data effects your conclusions. This is more individual stock type research so maybe not particularly relevant to you.
http://www.cxoadvisory.com/blog/external/blog3-31-10/
Josh
This actually proves the point that you should be long small cap stocks in an up market. The up market can be defined in several ways, for example, market above 52 week moving average. This may not work well with your typical investor but can easily be incorporated by managed funds/mutual funds etc. My own small time research on small cap stocks published data shows that if you move just between bonds and small cap fund based on 52 week moving average with some extra room, your returns will be ahead with lot less draw downs and volatility.
Sorry if I’m talking to the wrong crowd .. apologize in advance :)