Foster-Hart optimization for currency portfolios

We examine the effectiveness of Foster-Hart optimization for currency portfolios. Compared to stock trading, short selling is quite common in currency trading. Combining long and short positions leads to maintaining positive expected portfolio returns. Foster-Hart optimization is more applicable to currency portfolios than to stock portfolios because the Foster-Hart risk measure is not defined for the gamble whose expected returns are negative. Our sample portfolio consists of ten European currencies. For time series analysis, we employ a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals in order to capture fat-tailedness, skewness, and asymmetric interdependence of exchange rate dynamics. Statistical tests indicate that the model is recommendable among the candidate models. We establish that Foster-Hart optimization is more profitable than standard techniques in this context.