Skip to content

FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

A stock's returns are described by a one-factor model with beta 1.4 on a factor whose standard deviation is 10%. The stock's idiosyncratic risk has a standard deviation of 12%, uncorrelated with the factor. What is the stock's total standard deviation?

The total standard deviation is about 18.4%. Systematic risk is 1.4 times 10%, or 14%. Because idiosyncratic risk is uncorrelated, variances add: 196 plus 144 equals 340, whose square root is roughly 18.4%. Simply adding the standard deviations would overstate risk.

  1. A18.4%Correct
  2. B26.0%
  3. C14.0%
  4. D12.0%

Explanation

Systematic standard deviation is 1.4×10% = 14%. Total variance = 14%² + 12%² = 196 + 144 = 340 (in %²), so total SD = sqrt(340) = 18.44%. Adding 14% and 12% gives 26%, which ignores that risks combine through variances.

Did you get it right without looking?

One question tells you little. A timed set on The Arbitrage Pricing Theory and Multifactor Models of Risk and Return shows your real accuracy, how long you take and where you lose marks.

Practise The Arbitrage Pricing Theory and Multifactor Models of Risk and ReturnFree diagnostic mock

More The Arbitrage Pricing Theory and Multifactor Models of Risk and Return questions