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.

	Value	Blend	Growth
Large cap	IVE	IVV/SPY	IVW
Mid cap	IJJ	IJH	IJK/JKH
Small cap	IJS	IJR	IJT

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.