Portfolio optimization based on generalized information theoretic measures

Abstract

In this article, we compare the efficiency of the traditional Mean-Variance (MV) portfolio model proposed by Markowitz with the models which incorporate diverse information theoretic measures such as Shannon entropy, Renyi entropy, Tsallis entropy, and two-parameter Varma entropy. We put these measures as the objective function of the portfolio optimization problem with constraints derived from the mean and variance of the financial market data. Our approach is substantiated by an application to the 10 most liquid NIFTY indices of the Indian financial market and our findings show that using portfolio performance measures like Award Risk Ratio (ARR) and diversity index, the model with generalized information entropy measures yields higher performance than those with other traditional portfolio optimization techniques, like MV model. Furthermore, including the additional condition on variance as a constraint in maximum entropy models reduces portfolio diversity and makes allocation of assets less feasible than the models without incorporating variance.