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

Stock A has beta 0.8 and residual standard deviation 20%. The market's standard deviation is 10%. Using the single-index model, what is the covariance between Stock A and a Stock B with beta 1.5 (residuals uncorrelated)?

The covariance is 0.0120. In the single-index model, covariance between two stocks with uncorrelated residuals equals the product of their betas times market variance: 0.8 x 1.5 x 0.10 squared, or 0.01, giving 0.012. Residual risk does not contribute to covariance.

  1. A0.0120Correct
  2. B0.0200
  3. C0.0180
  4. D0.0150

Explanation

Under the single-index model, Cov(A,B) = beta_A x beta_B x variance of market = 0.8 x 1.5 x 0.01 = 0.0120. Including the residual variance of 0.04 would wrongly mix in idiosyncratic risk, which does not contribute to covariance.

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