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CMA Final · Strategic Financial Management · Asset Pricing Theories

The risk-free rate is 6% and the market portfolio has an expected return of 12% with a standard deviation of 15%. An investor builds a portfolio on the Capital Market Line with a standard deviation of 22.5%. Treating borrowing at the risk-free rate as allowed, what are the proportion invested in the market portfolio and the expected return of the investor's portfolio?

The investor puts 150% of own funds in the market portfolio by borrowing 50% at the risk-free rate, and earns 15%. The weight is 22.5 divided by 15, and the return is 1.5 times 12% minus 0.5 times 6%, which equals 15%.

  1. A150% in market (borrowing 50%); expected return 15%Correct
  2. B150% in market (borrowing 50%); expected return 18%
  3. C66.7% in market; expected return 10%
  4. D150% in market (borrowing 50%); expected return 13.5%

Explanation

Weight in market = 22.5/15 = 1.5, so 50% is borrowed at 6%. Return = 1.5 x 12 + (-0.5) x 6 = 18 - 3 = 15%. Equivalently CML: 6 + (6/15) x 22.5 = 6 + 9 = 15%. The 18% option ignores the borrowing cost.

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