IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory
The risk-free rate is 6% p.a. The market portfolio has expected return 14% and standard deviation 16%. An investor wants a portfolio on the capital market line with standard deviation 24%. What expected return does it offer?
The expected return is 18%. The CML slope is (14%-6%)/16% = 0.5, so at 24% standard deviation the return is 6% + 0.5 x 24% = 18%, equivalent to holding 150% in the market financed by borrowing at the risk-free rate.
- A18%
- B20%Correct
- C21%
- D24%
- 26%
Explanation
Sharpe ratio of market = (14-6)/16 = 0.5. CML return = 6% + 0.5 x 24% = 18%. Check: weight in market = 24/16 = 1.5, so return = 6 + 1.5 x 8 = 18%. The option 20% is wrong here. Correct value 18% corresponds to option index 0.
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