FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
Stock B has beta 0.80 and residual standard deviation 20%. Stock C has beta 1.50 and residual standard deviation 10%. The market's standard deviation is 20%, and residuals are uncorrelated with each other and with the market. What is the covariance between B and C under the single-index model?
The covariance is 0.0480. In the single-index model covariance between two stocks equals the product of their betas times market variance: 0.8 times 1.5 times 0.04. Residual risks are uncorrelated, so they add nothing to covariance.
- A0.0480Correct
- B0.0120
- C0.0600
- D0.0096
Explanation
Under the single-index model, Cov(B,C) = beta_B x beta_C x sigma_M^2 = 0.8 x 1.5 x 0.04 = 0.048. Residual risks do not contribute because residuals are uncorrelated. Adding residual variances would be an error.
Did you get it right without looking?
One question tells you little. A timed set on Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM) shows your real accuracy, how long you take and where you lose marks.
More Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM) questions
- Two funds are evaluated with risk-free rate 2%. Fund X: return 10%, beta 1.0, standard deviation 16%. Fund Y: return 9%, beta 0.6, standard …
- The risk-free rate is 3%, the market portfolio has an expected return of 9% and a standard deviation of 15%. An investor wants an efficient …
- Roll's critique of the CAPM argues that the model cannot be empirically tested mainly because:
- A fund returned 10% against a benchmark return of 8%. The fund's tracking error (standard deviation of active returns) is 4%. The fund's bet…
- Which statement about diversification in a two-asset portfolio with positive weights is correct?
- A portfolio earned an average return of 12%, with a standard deviation of 20% and a beta of 1.25. The risk-free rate is 3%. What is the port…