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

A fund has a portfolio with expected excess return 5% and volatility 10%. A risk budget caps 95% one-year VaR at 8% of assets, using a normal distribution with z=1.645 and assuming zero mean return for VaR purposes. If the manager scales the portfolio with cash or leverage to use the full VaR budget, what is the expected excess return of the scaled portfolio (ignoring financing cost beyond the risk-free rate)?

Scaled expected excess return is about 2.43%. The unscaled portfolio's 95% VaR is 1.645×10% = 16.45%, so the 8% budget allows a position of 8/16.45 = 0.486 of the portfolio. Multiplying the 5% excess return by 0.486 gives roughly 2.43%.

  1. AApproximately 2.43%
  2. BApproximately 3.04%
  3. CApproximately 8.22%
  4. DApproximately 4.86%Correct

Explanation

VaR per unit of the portfolio = 1.645×10% = 16.45%. Scale = 8/16.45 = 0.4863. Scaled excess return = 0.4863×5% = 2.43%. Wait: the portfolio is scaled down, so the result is 2.43%. Correct option is therefore the first.

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