解析没看懂

问题如下：

A risk analyst at a wealth management company is calculating the ES of a portfolio. The portfolio’s returns are expected to follow a uniform distribution, with all returns between 18% and −16% being equally likely. What is the 97% ES of the portfolio?

选项：

A.

−15.49%

B.−15.15% C.−14.98% D.−14.30%

解释：

A is correct. Begin by calculating the 97% VaR. The range of returns is 18% − (−16%) = 34%. The left 3% tail therefore covers the range found as follows:

x/34% = 3%

x = 3% * 34% = 1.02%

Thus, the 97% VaR is −16% + 1.02% = −14.98%. The ES is halfway between −14.98% and −16%, or −15.49%.

B is incorrect. This is the 95% ES. (The 95% VaR is −16% + (5% * 34%) = −14.30%. The ES is therefore halfway between this and −16%, or −15.15%.)

C is incorrect. This is the 97% VaR.

D is incorrect. This is the 95% VaR.

Learning Objective: Explain and calculate ES and compare and contrast VaR and ES.

Reference: Global Association of Risk Professionals, Valuation and Risk Models (New York, NY: Pearson, 2023). Chapter 1. Measures of Financial Risk [VRM–1]