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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

Two assets have expected returns 8% and 14%, standard deviations 10% and 20%, and correlation 0.5. A portfolio holds 60% in the first and 40% in the second asset. What are its expected return and standard deviation?

The expected return is 10.4% and the standard deviation about 12.2%. Return is the weighted average of 8% and 14%. Variance is 0.0036 plus 0.0064 plus 0.0048, equalling 0.0148, whose square root is roughly 12.2%, below the 14% weighted average because correlation is under one.

  1. A10.4% and 12.2%Correct
  2. B10.4% and 14.0%
  3. C11.0% and 12.2%
  4. D10.4% and 10.6%
  5. 11.0% and 15.0%

Explanation

Return = 0.6*8+0.4*14 = 10.4%. Variance = 0.36*0.01 + 0.16*0.04 + 2*0.6*0.4*0.5*0.1*0.2 = 0.0036+0.0064+0.0048 = 0.0148. Square root = 12.17%, about 12.2%. Option 14.0% is the weighted average of the standard deviations, ignoring the diversification effect (it would apply only if correlation were 1... actually 0.6*10+0.4*20=14).

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