A Generalisation of the Mean‐Variance Analysis
考虑一个在参考点处有拐点且扭曲客观概率的决策者，将其期望效用近似为均值和部分矩的函数，推广了均值-方差和均值-半方差效用，并推导出风险溢价、最优资本配置和推广的Sharpe比率。
Abstract In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This ‘mean‐partial moments’ utility generalises not only mean‐variance utility of Tobin and Markowitz, but also mean‐semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first‐order impact on risk measurement even when the risk is small.