Statistical Trading Strategies

The finance theories underlying Chapters 8 and 10 assume the absence of arbitrage, leading to pricing models that are martingales after adjustments for the market price of risk. Since the martingale models preclude making risk-adjusted profits via trading strategies, these theories imply that the derivatives markets would only attract hedgers, who use derivatives to reduce the risk they face from future movements of stock or bond prices. However, as pointed out by Hull (2006, Chapter 1), derivatives markets have also attracted speculators and arbitrageurs who try to take advantage of the discrepancies between the arbitrage-free theories and the actual market prices. Hedge funds have now become big users of derivatives for all three purposes, namely hedging, speculation, and arbitrage.

Statistical learning of market patterns can proceed with different levels of resolution. As pointed out in Section 3.1.2, the highest resolution can be obtained from transaction-by-transaction or trade-by-trade data in securities markets. In Section 11.2, we describe statistical models and methods to study market microstructure. It illustrates these statistical methods with intraday transactions of IBM stock from January 2 to March 31, 2003 and gives a brief introduction to real-time trading, which has become popular for hedge funds and investment banks.

Although the Markowitz, CAPM, and Black-Scholes theories in Chapters 3 and 8 assume the absence of market friction and in particular no transaction costs, transaction costs are an important consideration in the design and evaluation of statistical trading strategies. Section 11.3 gives an introduction to estimation and analysis of transaction costs and discusses how transaction costs and the dynamic nature of trading have introduced challenges to the development of statistical trading strategies.