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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

Portfolio X has a Treynor ratio of 8% and a beta of 0.9. Portfolio Y has a beta of 1.5 and an excess return of 10%. The risk-free rate is 3%. Which statement is correct?

Portfolio X has the higher Treynor ratio. Portfolio Y's Treynor ratio is its 10% excess return divided by beta of 1.5, giving 6.67%, which is below X's 8%. Y's larger excess return is simply compensation for higher systematic risk.

  1. APortfolio X has the higher Treynor ratio, because 8% exceeds 6.67%Correct
  2. BPortfolio Y has the higher Treynor ratio, because its excess return is larger
  3. CBoth have the same Treynor ratio
  4. DPortfolio X has an excess return of 8% over the risk-free rate

Explanation

Y's Treynor ratio = 10% / 1.5 = 6.67%, lower than X's 8%. X's excess return is 8% x 0.9 = 7.2%, so the last option is wrong. Y's larger excess return reflects higher beta, not better reward per unit of systematic risk.

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