Optimization Makes Estimation Much More Worse

Abstract

Mean-variance optimization as a modern portfolio theory is a major model for theoretical purposes, however, in practice portfolio managers don’t have enough interest despite some other ad hoc methods for many reasons such as estimation errors. Recently, the significance of modern portfolio theory has been analyzed that it doesn’t beat the simple naïve 1/N rule not only in many real empirical databases but also in a simulation. By this paper, due to inherent weakness of Sharpe ratio we first express more common use and adjusted measurements such as adjusted expected utility of portfolio under ambiguity aversion to analyze their effects on portfolio optimization after this consideration, because using only sample mean and variance (Sharpe ratio) to evaluate performance value for the portfolio models may be subject to considerable bias. Second, we propose a new model based on the new measurement (adjusting ambiguity Sharpe ratio) to improve portfolio optimization problem. Our result states that by using the new measurement mean- variance optimization beats the naïve rule by applying the adjusted measurement and also the novel model outperforms Markowitz in terms of Sharpe ratio while the interesting is that for adjusting Sharpe ratio inverse result exists. Therefore, our study expresses optimization makes estimation almost worse when we try to use a measurement as an optimization target.

Keywords: portfolio selection, optimization, measurement, Sharpe ratio.