Financial Signal Processing and Machine Learning

Chapter 3Mean-Reverting PortfoliosTradeoffs between Sparsity and Volatility

Marco Cuturi¹ and Alexandre d'Aspremont²

¹Kyoto University, Japan

²CNRS - Ecole Normale supérieure, France

Mean-reverting assets are one of the holy grails of financial markets: if such assets existed, they would provide trivially profitable investment strategies for any investor able to trade them, thanks to the knowledge that such assets oscillate predictably around their long-term mean. The modus operandi of cointegration-based trading strategies (Tsay, 2005, §8) is to create first a portfolio of assets whose aggregate value mean-reverts, and then to exploit that knowledge by selling short or buying that portfolio when its value deviates from its long-term mean. Such portfolios are typically selected using tools from cointegration theory (Engle and Granger, 1987; Johansen, 1991), whose aim is to detect combinations of assets that are stationary and therefore mean-reverting. We argue in this chapter that focusing on stationarity only may not suffice to ensure profitability of cointegration-based strategies. While it might be possible to create synthetically, using a large array of financial assets, a portfolio whose aggregate value is stationary and therefore mean-reverting, trading such a large portfolio incurs in practice important trade or borrow costs. Looking for stationary portfolios formed by many assets may also result in portfolios that have a very small volatility and that require significant ...