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CMA Final · Strategic Financial Management · Asset Pricing Theories

The risk-free rate is 6% and the market return is 12% with a standard deviation of 15%. Under the Capital Market Line, an investor wants a portfolio with a standard deviation of 20%, financed by borrowing at the risk-free rate and investing everything in the market portfolio. What is the expected return, and what proportion of own funds is borrowed?

The expected return is 14.0% with borrowing of 33.3% of own funds. Needing 20% risk against the market's 15% means a weight of 1.333 in the market portfolio. Return is 1.333 times 12% less 0.333 times 6%, equal to 14%.

  1. A14.0% return; borrowing equal to 33.3% of own fundsCorrect
  2. B14.0% return; borrowing equal to 20% of own funds
  3. C12.0% return; borrowing equal to 33.3% of own funds
  4. D10.0% return; no borrowing, 66.7% in market

Explanation

Weight in market = 20/15 = 1.3333, so borrowing is 0.3333 of own funds. CML return = 6 + (6/15) x 20 = 14%. Check: 1.3333 x 12 + (-0.3333) x 6 = 16 - 2 = 14%. The 20% borrowing option confuses the excess standard deviation with borrowing.

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