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The paper establishes entropy as a measure of risk in asset pricing models by comparing its explanatory power with that of classic capital asset pricing model’s beta to describe the diversity in expected risk premiums. Three different non‑parametric estimation procedures are considered to evaluate financial entropy, namely kernel density estimated Shannon entropy, kernel density estimated Renyi entropy and maximum likelihood Miller‑Madow estimated Shannon entropy. The comparison is provided based on the European stock market data, for which the basic risk‑return trade‑off is generally negative. Kernel density estimated Shannon entropy provides the most efficient results not dependent on the choice of the market benchmark and without imposing any prior model restrictions.

Comparing Entropy and Beta as Measures of Risk in Asset Pricing