FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
Two assets each have a standard deviation of 12% and are held in equal weights. If the correlation between them is 0.5, what is the portfolio standard deviation?
The portfolio standard deviation is about 10.4%. With equal weights and a correlation of 0.5, the variance is 0.0108, and its square root is 10.39%. A figure of 12% would require perfect positive correlation, so diversification lowers risk here.
- A9.0%
- B10.4%Correct
- C12.0%
- D6.0%
Explanation
Variance = 0.25(0.0144)+0.25(0.0144)+2(0.25)(0.5)(0.0144) = 0.0036+0.0036+0.0036 = 0.0108. The square root is 10.39%, about 10.4%. Choosing 9.0% would assume a different correlation, and 12.0% would assume perfect correlation.
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
- 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 …
- The risk-free rate is 4%. The market portfolio has expected return 11% and volatility 14%. Portfolio X has expected return 10% and volatilit…
- In a market-model regression of a stock's returns on the market's returns, the estimated intercept is 0.5% per month and the beta is 1.1. Wh…
- In a zero-beta (Black) version of the CAPM, the risk-free asset is unavailable for unlimited borrowing and lending. The zero-beta portfolio …
- Under two-fund separation in the CAPM setting with homogeneous expectations and a risk-free asset, which statement is correct about how a ra…
- The risk-free rate is 2%, the market portfolio has an expected return of 8% and a standard deviation of 12%. An investor puts 60% of her wea…