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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A manager has a 100 million portfolio with expected excess return over the risk-free rate of 5 million annually and a 95% one-year VaR (normal) of 16.45 million. Using a z-value of 1.645 for 95%, what is the portfolio's annual volatility in return terms, and the ratio of excess return to VaR?

Volatility is 10% and the excess return to VaR ratio is about 0.30. Dividing the 16.45 million VaR by 1.645 gives 10 million, or 10% of 100 million. Dividing the 5 million excess return by the 16.45 million VaR gives roughly 0.30.

  1. AVolatility 10%; excess return to VaR ratio about 0.30Correct
  2. BVolatility 16.45%; excess return to VaR ratio about 0.30
  3. CVolatility 10%; excess return to VaR ratio about 0.50
  4. DVolatility 5%; excess return to VaR ratio about 0.30

Explanation

Assuming zero mean in the VaR, VaR = 1.645 x sigma x 100m, so sigma = 16.45/164.5 = 10%. Ratio = 5/16.45 = 0.304. Sharpe = 5%/10% = 0.50, which is the trap in option C; B treats VaR% as volatility.

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