On the Market-Neutrality of Optimal Convergence Trading Strategies

In this talk, we study the utility maximization problem for assets whose prices are cointegrated. This problem arises from the investment practice of convergence-trading which is one of the oldest forms of statistical arbitrage strategies used by active portfolio managers such as hedge funds.

After providing background knowledge on convergence trading and cointegration, we focus on investigating the assumption of market-neutrality of the optimal convergence trading strategies. This assumption is a ubiquitous assumption taken by practitioners and academics alike, but, lacks a theoretical justification. Indeed, to the best of our knowledge, the only relevant study is Liu and Timmermann (2013) which implies that the optimal convergence strategies are, in general, not market-neutral.

We start by considering a minimalistic pairs-trading scenario with two cointegrated stocks and solve the Merton investment problem with power and logarithmic utilities. We pay special attention to when/if the stochastic control problem is well-posed, which is overlooked in the study done by Liu and Timmermann (2013). In particular, we show that the problem is ill-posed if and only if the agent's risk-aversion is less than a constant which is an explicit function of the market parameters. This condition, in turn, yields the necessary and sufficient condition for well-posedness of the Merton problem for all possible values of agent's risk-aversion. The resulting well-posedness condition is surprisingly strict and, in particular, is equivalent to assuming the optimal investment strategy in the stocks to be market-neutral. Furthermore, it is shown that the well-posedness condition is equivalent to applying Novikov's condition to the market-price of risk, which is a common sufficient condition for imposing absence of arbitrage. To the best of our knowledge, these are the only theoretical results for supporting the assumption of market-neutrality of convergence trading strategies. We then generalize the results to the more realistic setting of multiple cointegrated assets, assuming risk factors that effects the asset returns, and general utility functions for investor's preference. In the process of generalising to multivariate case, we also obtained some well-posedness conditions for matrix Riccati differential equations which are, to the best of our knowledge, new.

References:
Angoshtari, B.: On the market-neutrality of optimal convergence-trading strategies, preprint, 2013.

Angoshtari, B.: Portfolio choice with one pair of cointegrated assets, preprint, 2013.

Liu, J. and A. Timmermann: Optimal convergence trade strategies. Review of Financial Studies, volume 26, no. 4: pp. 1048–1086 (2013).