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

Two sub-portfolios are combined. Portfolio X has volatility 8% and excess return 4%; portfolio Y has volatility 10% and excess return 3%. Using the Sharpe ratio rule for optimal allocation across uncorrelated strategies, which is correct about adding Y to X when the correlation is zero?

Y should receive a positive allocation. Because its correlation with X is zero, the test for improving the portfolio is that Y's Sharpe ratio exceeds the existing Sharpe ratio times the correlation, which is zero. Y's 0.30 passes, so diversification benefits justify holding it.

  1. AY should be excluded because its Sharpe ratio (0.30) is lower than X's (0.50)
  2. BY should receive a positive allocation because zero correlation provides diversification, even though its Sharpe ratio is lower than X'sCorrect
  3. CY should receive the larger allocation because its volatility is higher
  4. DY should be excluded because its excess return is lower than X's

Explanation

Sharpe X = 0.50, Y = 0.30. A new asset improves the optimal portfolio if its Sharpe ratio exceeds the existing portfolio's Sharpe times correlation; with correlation zero, 0.30 > 0, so Y adds value. Optimal weights are proportional to excess return divided by variance, which are positive for both.

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