Optimal multi-currency investment strategies with exact attribution in three Asian countries

Abstract

The exact and complete return attribution framework of Singer and Karnosky (1995) does not account for risk, since it ignores accumulated historical information. Its implied investment strategy selection is based on simple return maximization and ignores that investment strategies are correlated via intra- and intermarket risks. Using simple tensor algebra we extend their exact accounting framework to include market risk measurements for n countries. The resulting n 2× n 2 strategy risk matrix exactly decomposes into a tensor sum of the n× n fundamental market risk matrices. Since the strategy risk matrix is singular with rank=2 n−1< n 2, the resulting portfolio choice problem is degenerate. But, the portfolio constraints imposed by the exact accounting framework allows one to solve the conventional Markowitz' mean-variance optimization problem as a nondegenerate lower dimensional problem of fundamental investment choice between stock markets and currency overlays, with a nonsingular 2 n×2 n risk matrix. The original n 2 investment strategy allocations are then uniquely retrieved from the resulting 2 n optimal investment choices. Thus, we solve also the problem of the optimization of complete, exact investment strategy portfolios, like RiskMetrics ™ and CreditMetrics ™. Our complete and exact return-risk attribution accounting framework is applied to monthly return data of Singapore, Malaysia and Indonesia from July 1992 through June 1997. The average historically maximal simple and risk-adjusted investment strategy returns are compared with the efficiency frontier computed for the 5 year horizon of an `efficiency-seeking' global investor to determine their implied minimal risk levels. Furthermore, the paper analyzes which markets exhibit most risk in these Asian countries. The evidence shows that most of the risk is attributable to the magnitudes of the risks of the stock markets, followed by those of the currency markets and the cash markets.