Estimation and arbitrage opportunities for exchange rate baskets

This paper analyzes short term portfolio investment opportunities in a capital market where a currency is defined as a currency basket, i.e. a linear combination of foreign currencies. In line with the mean-variance hedging approach, we determine a self-financed optimal investment strategy which minimizes an expected quadratic cost function. In order to implement such a strategy an estimate of the basket weights is required. To this end we suggest an adaptive nonparametric procedure, which, if compared with standard procedures, provides very satisfactory results both on simulated and real data. We apply the optimal investment strategy to the case of the Thai Bath basket. The basket weights are computed with the adaptive estimator. We also implement a recursive estimator, a rolling estimator and the Ka1man filter which serve as benchmark models. The different estimators are compared with profit based criteria.