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There is an interesting New York Times article on a mathematician and cryptologist who used to work for the wildly successful hedge fund Renaissance Technologies and is now famous for decoding DNA's. This article caught my eyes because quite a few of my former colleagues from the speech recognition research group at IBM also went over to Renaissance as researchers and portfolio managers. Renaissance is an extraordinary hedge fund in Long Island that has an average annual return of 35% since 1989, after charging 5% management fee and 44% incentive fee. They profess to hire only scientists, engineers and mathematicians with as little background in finance as possible. They started off trading futures, but has since then diversified into equities models, and is reportedly raising a $100 billion fund at the moment.
A lot of people want to know the secrets of their success. From the people they hire, one can always guess. The common thread among DNA decoding, cryptography, and speech recognition is information theory, the discipline founded by legendary Bell Labs mathematician Claude Shannon. There are a few tools in information theory that have found wide-spread applications: hidden Markov model is one, expectation-maximization (EM) algorithm is another, and then of course the grandfather of prediction: Bayesian statistics. Needless to say, I have tried them all in my own trading research, but have not met much success so far. Aside from the limitations of my imagination, I suspect the reason is that these tools work much better with higher frequency data than the daily data that I have thus far worked with. Therefore I am not ready to give up yet. (Readers of my earlier article on artificial intelligence may think that I am being inconsistent here, as I was less than enthusiastic about the application of that discipline to trading. There is, however, quite a big difference between information theory and artificial intelligence. The former is characterized by sophisticated theory with very few parameters, the latter, simple theory with a lot of parameters.)
There is one published trading model that is based squarely on research in information theory. It is called Universal Portfolios, created by Stanford information theorist Prof. Thomas Cover. It is an elegant and quite intuitive model, but I don't know how well it performs under realistic conditions. I hope to write about some of my research on this and a related class of models in a future article.
Further reading:
Cover, Thomas M. and Thomas, Joy A. (1991), Elements of Information Theory. John Wiley & Sons, Inc.
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.
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.
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