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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

In the single-index model, the excess return of stock i is written as R_i - R_f = alpha_i + beta_i (R_M - R_f) + e_i. Which statement about the residual term e_i is correct?

The residual in the single-index model is the firm-specific component of return. It has an expected value of zero and is uncorrelated with the market factor. Since it is idiosyncratic, it can be diversified away in large portfolios, unlike the systematic beta component.

  1. AIt captures firm-specific risk, which has zero expected value and is uncorrelated with the market factorCorrect
  2. BIt captures systematic risk and is perfectly correlated with the market excess return
  3. CIt equals the risk-free rate adjusted for the stock's beta
  4. DIt is the part of return that cannot be diversified away in a large portfolio

Explanation

The residual represents firm-specific (idiosyncratic) return, assumed to have mean zero and to be uncorrelated with the market factor. Because it is uncorrelated across stocks, it diversifies away in large portfolios, so the option calling it non-diversifiable is wrong.

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