Skip to content

IAI Actuarial Core Principles · Economic Modelling · Capital Asset Pricing Model (CAPM)

A risk-free asset yields 6%. A risky portfolio M has expected return 12% and standard deviation 15%. An investor puts 40% of funds in the risk-free asset and 60% in M. What are the expected return and standard deviation of the combined portfolio?

The expected return is 9.6 percent and the standard deviation is 9.0 percent. Return is the weighted average of 6 and 12 percent, while the risk-free asset adds no risk, so standard deviation is just the 60 percent weight in the risky portfolio times 15 percent.

  1. A9.0% and 9.0%
  2. B9.6% and 9.0%Correct
  3. C9.6% and 6.0%
  4. D10.8% and 9.0%
  5. 9.6% and 15.0%

Explanation

Expected return = 0.4(6%) + 0.6(12%) = 2.4% + 7.2% = 9.6%. Risk-free asset has zero variance and zero covariance with M, so the standard deviation = 0.6 x 15% = 9.0%. Options using 40% weight on risk or ignoring scaling are wrong.

Did you get it right without looking?

One question tells you little. A timed set on Capital Asset Pricing Model (CAPM) shows your real accuracy, how long you take and where you lose marks.

Practise Capital Asset Pricing Model (CAPM)Free diagnostic mock

More Capital Asset Pricing Model (CAPM) questions