We develop a new approach to determine investors’ risk compensations for all distributional moments of a security. Using the concept of entropy, which is a summary of all moments of a risky security, we derive the relationship between expected returns and their compensation for entropy risk. Entropy risk premium (ERP), which is entropy under the physical minus the risk-neutral measure, indicates the hedging cost against changes in risks associated with all moments of the return’s distribution. Applying our model to the commodity markets, we find that ERP carries economically significant information for the cross-section of returns that is different from individual or combined moments.

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永远不会沉闷：商品市场的熵风险

我们开发了一种新方法来确定投资者对证券所有分配时刻的风险补偿。使用熵的概念，它是风险证券所有时刻的总结，我们推导出预期收益与其对熵风险的补偿之间的关系。熵风险溢价 (ERP) 是物理熵减去风险中性度量的熵，表示针对与收益分布的所有时刻相关的风险变化的对冲成本。将我们的模型应用于商品市场，我们发现 ERP 携带了与单个或组合时刻不同的收益横截面的经济重要信息。