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:

$$x / 34\% = 3\% \\ x = 3\% \times 34\% = 1.02\%$$

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 $-16\% + (5\% \times 34\%) = -14.30\%$. 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]