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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A portfolio's daily returns are normally distributed with mean zero and standard deviation 1.5% of a USD 80 million portfolio. Using z-values of 1.645 (95%) and 2.326 (99%), what is the one-day 99% VaR, and how does it compare with the 95% VaR?

The 99% VaR is about USD 2.79 million, roughly 41% above the 95% VaR of 1.97 million. Daily volatility is 1.2 million, and the ratio of the normal quantiles, 2.326 to 1.645, is about 1.414.

  1. AUSD 2.79 million, which is about 41% higher than the 95% VaRCorrect
  2. BUSD 2.79 million, which is about 14% higher than the 95% VaR
  3. CUSD 1.97 million, which is about 41% higher than the 95% VaR
  4. DUSD 4.19 million, which is about 41% higher than the 95% VaR

Explanation

Daily sigma = 0.015 × 80 = 1.2 million. 99% VaR = 2.326 × 1.2 = 2.79 million; 95% VaR = 1.645 × 1.2 = 1.97 million. Ratio = 2.326/1.645 = 1.414, so 41% higher. The 14% option misreads the ratio; 4.19 uses 3.49 as the multiplier by mistake (1.5 × 2.326 × 1.2).

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