Foster-Hart optimal Portfolios

We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the 'Foster–Hart risk'—a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster–Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA–GARCH process with multivariate 'normal tempered stable' innovations. We demonstrate that the Foster–Hart optimal portfolio’s performance is superior to those obtained under several techniques currently in use in academia and industry.