Entropy Augmented Asset Pricing Model: Study on Indian Stock Market

Abstract

This study explores the effectiveness of entropy as a proxy of aggregate market risk, in explaining the cross-section of excess returns in asset pricing model, after controlling for established factors like market excess returns, size, book to market and momentum. The analysis considers Indian firms, given that Indian capital markets are characterized by relatively thin trading and higher volatility compared to developed markets. Entropy is estimated using Shannon Entropy. Factor mimicking portfolio is constructed based on Shannon Entropy, whose returns are used as additional risk factor in Fama–French–Carhart four factor asset pricing model. Gibbons Ross Shanken-F statistic and Adjusted R² are used to judge the efficacy of this factor in capital asset pricing model. All analysis is done using built in functions of python. Market beta, size and Book-to-Market are found to impact equity returns significantly. Entropy factor also impacts equity returns, but to a lesser extent. Explanatory power of asset pricing model is found to improve after inclusion of entropy factor, as indicated by GRS-F Statistic and Adjusted R². Entropy augmented Capital Asset Pricing Models can be used by firms to decide hurdle rate for project evaluation and by asset managers for identifying over-valued/under-valued securities. This is the first study that investigates the role of entropy in explaining asset returns, in addition to other established priced factors. This study is limited to Shannon Entropy only. Other forms of entropy may improve results further, and should be explored in future research.