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

Two funds are evaluated with risk-free rate 2%. Fund X: return 10%, beta 1.0, standard deviation 16%. Fund Y: return 9%, beta 0.6, standard deviation 20%. An investor will hold the fund as her entire portfolio. Which statement is correct?

Fund X has the higher Sharpe ratio, 0.50 versus 0.35, while Fund Y has the higher Treynor ratio, 11.67% versus 8.0%. The rankings differ because Y has lower beta but higher total risk. Sharpe is the relevant measure when the fund is the investor's entire portfolio.

  1. AFund X ranks higher on Sharpe (0.50 vs 0.35) and Fund Y ranks higher on Treynor (0.117 vs 0.08)Correct
  2. BFund X ranks higher on both Sharpe and Treynor
  3. CFund Y ranks higher on both Sharpe and Treynor
  4. DFund Y ranks higher on Sharpe and Fund X ranks higher on Treynor

Explanation

Sharpe X = 8/16 = 0.50; Sharpe Y = 7/20 = 0.35. Treynor X = 8%/1.0 = 8.0%; Treynor Y = 7%/0.6 = 11.67%. So X wins on Sharpe and Y wins on Treynor. For an undiversified whole portfolio Sharpe is the appropriate measure, so X is preferred.

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