Optimal Portfolios of Mean-Reverting Instruments

In this paper we investigate portfolios consisting of instruments whose logarithms are mean-reverting. Under the assumption that portfolios are constant, we derive analytic expressions for the expected wealth and the quantile-based risk measure capital at risk. Assuming that short-selling and borrowing are allowed, we then solve the problems of global minimum capital at risk and the problem of finding maximal wealth subject to constrained capital at risk. We illustrate these results with some numerical examples that show the strong effect of the mean-reversion rates on the portfolio choice.