FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
Asset P has a standard deviation of 15% and Asset Q has 25%. Which correlation between them produces the greatest diversification benefit for any fixed positive weights?
A correlation of -1.0 gives the greatest diversification benefit. Portfolio variance increases with correlation since the covariance term scales with it, so the lowest correlation minimizes risk. At a correlation of +1, portfolio risk is just the weighted average of the standard deviations.
- A-1.0Correct
- B0.0
- C0.5
- D1.0
Explanation
Portfolio variance rises with correlation because the covariance term is rho x w1 x w2 x s1 x s2. The lowest correlation, -1, gives the smallest variance. At +1, no diversification benefit exists.
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
- Roll's critique of CAPM tests argues that which of the following is true?
- A portfolio manager uses a single-factor CAPM regression on excess returns and obtains an intercept of 0.20% per month with a standard error…
- The risk-free rate is 5%, and the market portfolio has expected return 11% and standard deviation 18%. An investor wants an expected return …
- A portfolio returned 9% while its benchmark returned 7%. The tracking error (standard deviation of active return) is 4%. The risk-free rate …
- The risk-free rate is 2%. Risky asset A has an expected return of 8% and volatility of 10%. Risky asset B has an expected return of 14% and …
- An equally weighted portfolio holds N stocks, each with beta 1.0 and residual variance 0.0400. The market variance is 0.0225. Residuals are …