CVaR with Risk Appetites: A New Tail Risk Measure and its Application in Portfolio Optimization


Student thesis: Master's Thesis

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Award date11 Jan 2023


Conditional Value at Risk (CVaR) is a well-known tail risk measure used in portfolio optimization. Compared to another popular tail risk measure, Value at Risk (VaR), CVaR estimates the risk more conservatively since it stands for average losses exceeding VaR. Besides, it possesses an excellent coherence property, and the CVaR optimization approach can calculate VaR and optimize CVaR simultaneously. However, it fails to distinguish risk appetites of different individuals by generating different portfolios. Therefore, we propose a new tail risk measure called utility value at risk (UVaR). The main idea is to compute a weighted average loss similar to CVaR, where the weights are captured by a utility function, and the parameter in that utility function determines the risk preference. By varying the utility parameter, UVaR provides distinct values with risk-seeking, risk- neutral, and risk-averse features. In addition, we derive a series of analytical solutions under distributional assumptions, prove the coherence property in both continuous and discrete settings, and apply it to the traditional CVaR optimization framework.