Markov Chain Approach for Bond Portfolio Selection
Mean-variance framework has been established as a standard portfolio management scheme since Markowitz’s (1952) seminal work, and we have observed its many extensions and modifications since then. In spite of its simplicity and analytical tractability, however, it imposes some difficulties in practical implementation. The most difficult part is to forecast the future return and risk of individual investment assets, which has been most studied topics but has yielded few satisfactory results yet.
In this paper we propose a new approach modeling the ex-post optimal portfolio weights as a Markov process. We pay attention to the fact that the ex-post optimal investment is not a diversified investment but an all-or-nothing investment and we can classify individual assets as “invested” and “not-invested” each period. We model that the evolution of two states, “invested” and “not-invested”, for each asset follows a Markov process. By modeling the portfolio weights directly, we can eliminate the uncertainty engaged with forecasting the future return and risk of assets.
We apply the new approach of Markov process into bond portfolio selection with U.S and German treasuries. The cumulative return by applying the new approach proves to be superior to those by some simple traditional methods based on mean-variance framework. Thus, we suggest that our approach could be seriously considered as an alternative asset allocation strategy.