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

A portfolio is 40% in Stock A and 60% in Stock B. Stock A has betas of 1.0 to the market factor and 0.5 to a size factor. Stock B has betas of 0.8 to the market factor and -0.2 to the size factor. What are the portfolio's betas to the market and size factors respectively?

The portfolio betas are 0.88 to the market factor and 0.08 to the size factor. Each is the weighted average of the stocks' betas: 0.4×1.0 + 0.6×0.8 for the market and 0.4×0.5 + 0.6×(−0.2) for size.

  1. A0.88 and 0.08Correct
  2. B0.90 and 0.15
  3. C0.88 and -0.08
  4. D1.80 and 0.30

Explanation

Portfolio factor betas are weighted averages. Market: 0.4×1.0 + 0.6×0.8 = 0.88. Size: 0.4×0.5 + 0.6×(−0.2) = 0.20 − 0.12 = 0.08. The 1.80 and 0.30 option sums the betas without weighting.

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