Estimation and arbitrage opportunities for exchange rate baskets

This paper analyses short-term portfolio investment opportunities in a capital market where a currency is defined as a currency basket. In line with the mean-variance hedging approach, a self-financed optimal investment strategy is determined which minimizes the expected quadratic cost function. The successful implementation of the speculative strategy requires a precise estimate of the basket weights, which are possibly non-constant over time. To this end, an adaptive non-parametric procedure is suggested which provides satisfactory results both on simulated and real data. The optimal investment strategy is applied to the case of the Thai Baht basket whereby the weights are computed by means of the adaptive estimator. A recursive estimator, a rolling estimator and the Kalman filter, are implemented and serve as benchmark models. Results are compared with the literature. The different estimators are evaluated with profit-based criteria and the performance of the adaptive estimator turns out to be the best one.