Optimal Multi-Currency Investment Strategies with Exact Attribution in Three Asian Countries

Singer and Karnosky's (1995) exact and complete return attribution framework 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 inter-market risks. Using simple tensor algebra we extend their exact accounting framework to include market risk measurements for n countries. The resulting n^2 x n^2 strategy risk matrix exactly decomposes into a tensor sum of the n x n fundamental market risk matrices. Since the strategy risk matrix is singular with rank = 2n-1< n^2, the resulting portfolio choice problem is degenerate. But the portfolio constraints imposed by the exact accounting framework allow to solve the conventional Markowitz' mean- variance optimization problem as a non-degenerate lower dimensional problem of fundamental investment choice between stock markets and currency overlays, with a nonsingular 2n x 2n risk matrix. The original n^2 investment strategy allocations are then uniquely retrieved from the resulting 2n optimal investment choices. 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 five year horizon and of 'efficiency-seeking' global investors 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.