The Statistics of Statistical Arbitrage

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Abstract
Hedge funds sometimes use mathematical techniques to “capture” the short-term volatility of stocks and perhaps other types of securities. This sort of strategy resembles market making and is sometimes considered a form of statistical arbitrage. This study shows that for the universe of large-capitalization U.S. stocks, even quite naive techniques can achieve remarkably high information ratios. The methods used are quite general and should be applicable also to other asset classes. Market makers in financial markets generate profits by buying low and selling high over short time intervals. This process occurs naturally because, as market makers, they offer a stock for sale at a higher price than they are willing to pay for it and because the more urgent buyers and sellers have to accept the market makers’ terms. Market making, particularly that of NYSE specialists, has been studied in the normative context of academic finance. This article describes a market-making type of trading strategy. High-speed trading strategies similar to market making have putatively been used by hedge funds in recent years—a type of strategy sometimes referred to as “statistical arbitrage” (or “stat arb” in the abbreviated patois of the Street). Statistical arbitrage of this nature can be studied in the context of portfolio behavior and is thus amenable to the methods of stochastic portfolio theory. We use these methods to examine the potential profitability of such a strategy applied to large-capitalization U.S. stocks, but the methodology is quite general and should be applicable also to other asset classes. Dynamic stock portfolios can be constructed that behave like market makers. Equal-weighted portfolios are dynamic portfolios in which each of the stocks has the same constant weight. In an equal-weighted portfolio, if a stock rises in price relative to the others, it generates a sell trade in the stock, and if the price declines, it generates a buy. Hence, such a portfolio sells on upticks and buys on downticks, the way a market maker would. We estimate the return and risk parameters of equal-weighted portfolios and use these parameters to determine the efficacy of statistical arbitrage in the universe of large-cap U.S. stocks. In the absence of trading commissions and with adequate order flow, we find that a hedged strategy that is long an equal-weighted portfolio that is rebalanced at 1.5 minute intervals and short an equal-weighted portfolio that is rebalanced only at the open and close of trading during the day can generate an annual information ratio as high as 32. Editor’s Note: INTECH markets unique mathematical investment processes that attempt to capitalize on the random movement of stock prices.

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