Investor’s portfolio decision: perspective of parameter uncertainty

Abstract

During the process of portfolio decision, the investor usually assumes that the distribution of asset return is known in order to identify the optimal investment strategy. In fact, the distribution of asset return is unknown and the investor often uses the historical data to estimate its distribution, which is uncertainty and should be taken into account during the process of portfolio decision. In this paper, we use the relative entropy to measure the uncertainty degree of risk premia and covariance matrix, build the model of mean-variance portfolio, and obtain the portfolio’s risk premia and variance under the worst scenario. At last, a comparative empirical study based on the portfolio’s effective frontier is performed. Results show: parameter uncertainty has significant effect on portfolio decision, and the effect of risk premium uncertainty is more than that of covariance matrix uncertainty; for the investor of risk-aversion, the higher the degree of parameter uncertainty is, the lower the portfolio performance is, and the stronger the relationship of assets in portfolio is, the weaker the effect of parameter uncertainty on portfolio is.