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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio has an expected excess return of 5% and a volatility of 10%. An asset in the portfolio has an excess return of 7.5% and a beta of 1.5 relative to the portfolio. A manager considers whether the portfolio is optimal with respect to this asset. What is the conclusion?

The portfolio is consistent with optimality for this asset. Its excess return divided by beta is 7.5%/1.5 = 5%, matching the portfolio's own 5% excess return. Since the ratios are equal, shifting weight would not improve the Sharpe ratio.

  1. AThe asset is over-weighted because its return is above the portfolio's
  2. BThe asset has a ratio of excess return to beta equal to 5%, consistent with optimalityCorrect
  3. CThe asset is under-weighted because its beta exceeds 1
  4. DThe asset should be removed because its beta is above 1

Explanation

Optimality requires excess return/beta to equal the portfolio's excess return (beta of 1). Here 7.5%/1.5 = 5%, equal to the portfolio's 5%, so no rebalancing improves the Sharpe ratio. High beta alone does not imply a misallocation.

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