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IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns

A two-factor model for a portfolio's excess return has factor loadings of 0.9 on the market factor and 0.5 on an interest-rate factor. The expected factor risk premiums are 6% and -2% respectively. The risk-free rate is 7%. What is the portfolio's expected return under the model, assuming zero alpha?

The expected return is 11.4%. Add the risk-free rate of 7% to 0.9 × 6% = 5.4% and 0.5 × (-2%) = -1%, giving 7 + 5.4 - 1 = 11.4%.

  1. A11.4%Correct
  2. B12.4%
  3. C13.4%
  4. D11.9%
  5. 10.4%

Explanation

Expected return = risk-free + sum of loading × premium = 7% + 0.9×6% + 0.5×(-2%) = 7% + 5.4% - 1% = 11.4%. Ignoring the negative sign on the second premium would give 12.4%, which is the key error.

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