What are coherent risk measures?
Within financial economics, there are many ways to describe risk, and each method of measuring risk will be able to cover certain factors. A coherent risk measure is a function that considers translational invariance, monotonicity, homogeneity and sub-additivity.
Key takeaways
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Coherent risk measures are mathematical functions that must satisfy four properties: translational invariance, monotonicity, homogeneity, and sub-additivity.
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These mathematics-based measures help investors and traders determine the amount of risk an investment could potentially incur.
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Expected shortfall is a favored coherent risk measure used to calculate credit or market risk of an investment portfolio.
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Value at risk is not considered coherent because it excludes sub-additivity, which can lead to potential portfolio under-diversification.
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Other coherent risk measures include entropic value at risk, the Wang risk measure, and the superhedging price.
Where have you heard about coherent risk measures?
Most experienced investors or traders will have encountered, if not used, a coherent risk measure at some point. These mathematics-based measures can be very useful for determining the amount of risk an investment could incur.
What you need to know about coherent risk measures.
A risk measure qualifies as coherent if it meets certain basic mathematical properties, and there are a number of coherent risk measures, all ranging in popularity. A favoured coherent measure is expected shortfall, which is used to calculated the credit or market risk of a portfolio. However, it is generally accepted that value at risk is not a coherent measure, due to its exclusion of sub-additivity – leading to potential under-diversification. Other coherent risk measures include entropic value at risk, the Wang risk measure and the superhedging price.