Skip to content

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

In a two-factor model, an equally weighted portfolio holds three stocks. Their betas on factor 1 are 0.8, 1.1 and 1.5, and their betas on factor 2 are -0.2, 0.4 and 0.7. What are the portfolio's betas on factors 1 and 2?

The portfolio betas are 1.133 on factor 1 and 0.300 on factor 2. Portfolio factor betas are the weighted averages of the individual betas, and with equal weights of one third each, 3.4 divided by 3 and 0.9 divided by 3 give these values.

  1. A1.133 and 0.300Correct
  2. B1.133 and 0.967
  3. C3.4 and 0.9
  4. D1.100 and 0.400

Explanation

Portfolio betas are weighted averages. Factor 1: (0.8+1.1+1.5)/3 = 3.4/3 = 1.133. Factor 2: (-0.2+0.4+0.7)/3 = 0.9/3 = 0.300. Summing without weighting gives 3.4 and 0.9, which is wrong.

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