Skip to content

IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

Asset X has a standard deviation of 20% and asset Y has a standard deviation of 10%. A portfolio holds 50% in each, and the correlation between their returns is 0.5. What is the portfolio standard deviation, to the nearest 0.1%?

Portfolio variance is 100 + 25 + 50 = 175 percent squared, giving a standard deviation of about 13.2%. This is below the 15% weighted average of the two standard deviations because the correlation is less than one, which gives diversification benefit.

  1. A10.0%
  2. B12.5%
  3. C13.2%Correct
  4. D15.0%
  5. 16.5%

Explanation

Variance = 0.25*400 + 0.25*100 + 2*0.5*0.5*0.5*20*10 = 100+25+50 = 175 (percent squared). SD = sqrt(175) = 13.23%. Using 15% would assume correlation 1 (weighted average of SDs). Check: 0.25*400=100, 0.25*100=25, cross term 2*0.25*0.5*200=50.

Did you get it right without looking?

One question tells you little. A timed set on Measures of investment risk shows your real accuracy, how long you take and where you lose marks.

Practise Measures of investment riskFree diagnostic mock

More Measures of investment risk questions