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.

摘要

在本文中，我们将 Markowitz 提出的传统均值方差 (MV) 投资组合模型的效率与包含香农熵、Renyi 熵、Tsallis 熵和两参数 Varma 熵等多种信息论度量的模型的效率进行了比较。我们将这些度量作为投资组合优化问题的目标函数，约束来自金融市场数据的均值和方差。我们的方法通过对印度金融市场 10 个最具流动性的 NIFTY 指数的应用得到证实，我们的研究结果表明，使用奖励风险比 (ARR) 和多样性指数等投资组合绩效指标，具有广义信息熵指标的模型产生的性能高于那些具有其他传统投资组合优化技术的人，例如 MV 模型。此外，