FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management
Two portfolios have the same Sharpe ratio, but Portfolio X has volatility of 10% and Portfolio Y has volatility of 20%. The risk-free rate is 2%. If Portfolio X returns 8%, what return must Portfolio Y earn to have the same Sharpe ratio?
Portfolio Y must earn 14%. Portfolio X's Sharpe ratio is 6%/10% = 0.6, so Y needs an excess return of 0.6 x 20% = 12%, and adding the 2% risk-free rate gives 14%.
- A14%Correct
- B10%
- C16%
- D12%
Explanation
Sharpe of X = (8% - 2%) / 10% = 0.6. For Y: (R - 2%) / 20% = 0.6, so R - 2% = 12% and R = 14%. The 16% option doubles the total return, and 12% only doubles the excess return without adding Rf back.
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