Optimal portfolio selection using maximum entropy estimation accounting for the firm specific characteristics

Abstract

The estimated return and variance for the Markowitz mean-variance optimization have been demonstrated to be inaccurate; thereafter it could make the traditional mean-variance optimization inefficient. This paper applied the Maximum Entropy (ME) principle in portfolio selection while accounting for firm specific characteristics; they are the firm size, return on equity and also lagged 12 months return. Since these characteristics are found not only related to the stock’s expected return, variance and correlation with other stocks, they can be good variables to estimate the weights. Furthermore, this method used Generalized Cross Entropy to shrink portfolio weights to the equal weights; therefore solving the problem of concentrated weights in Markowitz mean-variance framework. Also in our empirical study, six stocks are used to investigate the effect of maximum entropy based methods. The results show that the in-sample forecasts that are in comparison with other traditional methods are good, however, in the out-of-sample forecasts the results are mixed.