Sunday, December 10, 2006

Market-cap and growth-value arbitrage

Predicting whether small-cap or growth stocks will outperform large-cap or value stocks in the next quarter is a favorite pastime of financial commentators. To many financial economists, however, the question is long ago settled by the so-called Fama-French Three-Factor Model. This model postulates that the returns of a stock depend mainly on 3 factors: the general market index returns, the market-cap of the stock, and the book-to-price ratio. Furthermore, as an empirical fact, over the long term (i.e. for any 20-year period), small-caps beat large-caps by an average compounded annual rate of 3.12%, and value stocks beat growth stocks by 4.06% (the latter result applies when we confine ourselves to the large-cap universe).

This model is very convenient to us arbitrageurs. Statistical arbitraguers generally don’t know how to predict market index returns, but we can still make a living in a bear market by buying a small-cap, value portfolio and shorting a large-cap, growth portfolio, and expect to earn 3-4% (on one-side of capital) a year. For example, despite the much anticipated imminent demise of small-caps over the last year or so, I found that if we long the small-cap value ETF IJS, and short the large-cap growth ETF IVW from November 15, 2005 to November 15, 2006, we would have earned about 10% return. The 3-4% average returns look meager, but note that since this is a market-neutral, self-funding portfolio, your prime broker (if you trade for a hedge fund or a proprietary trading firm) will allow you to leverage this return several times.

Some traders will find 20 years a bit too long. Is there any help from academic theory on whether small-cap value will outperform large-cap growth next month, and not next 20 years? A recently published article by Profs. Malcom Baker and Jeffrey Wurgler says there is. (Mark Hulbert wrote a column explaining this in the New York Times recently.) The gist of this article is that when market sentiment is positive, expect small-caps to underperform large-caps by 0.26% a month, and value stocks to outperform growth stocks by 1.24% a month. Conversely, when the market sentiment is negative, expect small-caps to outperform large-caps by 1.45% a month, and value stocks to underperform growth stocks by 1.04% a month. How one computes “sentiment” is complicated: it is a linear combination of 6 variables: closed-end fund discount, NYSE share turnover, number and first-day returns on IPOs, equity share in new issues, and the dividend premium. (The authors used data from 1963-2001 for this study.) Now, without actually computing all these variables, most would agree that the current sentiment (as of December 2006) is fairly positive. This implies, as Mr. Hulbert noted, that small-cap will underperform large cap in the coming months, contrary to the long-term trend. However, the other long-term trend, that value will beat growth, will still hold in the near future. It is up to the reader to find a pair of ETF’s that will take maximum advantage of this prediction, but I will help here by tabulating some of the available funds.


Further reading:

Bernstein, William (2002), The Cross-Section of Expected Stock Returns: A Tenth Anniversary Reflection.
O’Shaughnessy, James P. (2006), Predicting the Markets of Tomorrow. Penguin Books.


Yaser Anwar, CSC (Trader- Equities & FX) said...

Ernie to be honest I'm quite surprised that small-caps do better when sentiment is negative vs. large-caps.

Conventional thinking is- you'd expect sentiment to be bad when economy is not so good. Thus people turn to large caps for predictable earnings growth.

However the sentiment indicators you pointed out are different, thus I'm guessing the results that during positive sentiment (assuming economy is going to do well) large-caps do better.

Great stuff-

Ernie Chan said...

Yaser: I think what the researchers found was that people's sentiment is a contrarian indicator. When they feel bad, expect good times to come! So when sentiment is bad now, the future returns of the stock market will be good, and small-caps will rally especially strongly. -Ernie

Yaser Anwar, CSC (Trader- Equities & FX) said...

Ernie- I think right now sentiment is quite positive! 4 months back if you threw "darts" and picked stocks you would have done well.

Right now in my view you have to carefully select the stocks. I expect to see a year end rally as you know PMs will be "window dressing" and massive M&A (read: banker bonus). In my view we should see a correction around Jan-Feb when earning season starts.

Although I wouldn't mind the current rally to keep going on and on! Have a good day!

Ernie Chan said...

Yaser: Yes, the sentiment is very positive now, as I mentioned in the article. (I should have used a hypothetical tense in my comments above.) Since the sentiment is so positive now, the researchers expect future returns to be bad, especially for small-cap returns. Take care! -Ernie

Chris said...

Ernie -- You mention that the research was done on data through 2001. Has anyone tested the findings out of sample since then?

Ernie Chan said...

Chris: good question. I am not aware of anyone testing the model out-of-sample yet, since the original research was published only recently. (Yes, that's right, it sometimes take that many years to get a research paper published!) Of course, I could have done the out-of-sample testing myself -- but the data requirements of this study are non-trivial. If you have access to these data: let me know! -Ernie

chris said...

I wish I did. I searched around for time series data on any sentiment index and had no luck. Some of the I-banks do bullish/bearish surveys, and these would presumably be a good substitute, but I wasn't able to find any of them publicly available. Maybe some of your former hf colleagues could get a hold of this kind of stuff from their sell-side salesmen?

SPH said...

Ernie - to your earlier point re: sentiment as a contrarian indicator, I think you've nailed it. Although I've no data to support such a claim, I recall a study that suggested the best time to buy a security was AFTER the majority of sell-side institutions had downgraded to Underperform/Sell. Albeit not directly related, this same logic also transfers/applies well to other arenas of analysis, such as technical analysis (i.e. Sub-.30 RSI indicates oversold & prepare to buy), and classic value investing (i.e. buy only when securities are trading sub-fair value, and garner a risk-adjusted margin of safety).

Of course, much of this debate centers around the theory of behavioural finance, which not surprisingly, is tightly embraced by deep value investors such as Buffet/Dreman/Miller.

Solid debate. Cheers, Steve H.

Anonymous said...

Any idea why Fama hasn't modified the Three-Factor Model to include PEAD and momentum, especially when he's publicly acknowledged that they're robust?

Ernie Chan said...

Dear anonymous,

It may be that there are so many ways to define PEAD and momentum factors that it is not clear what the "ideal" definitions should be. If you email Professor Fama and/or French and get some responses, I would appreciate very much if you post them here!