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Basic Question 5 of 6
A risk-free asset has a return of 0.05. A risky portfolio, X, has an expected return of 0.12 and a standard deviation of 0.20. For a portfolio that is 60% X and 40% risk-free asset, the ______
II. standard deviation is 12%.
III. standard deviation is 20%.
I. expected return is 8.5%
II. standard deviation is 12%.
III. standard deviation is 20%.
User Contributed Comments 10
| User | Comment |
|---|---|
| gsuwp | Isnt the standard deviation 12% because .6*20 + .4*0 = 12% |
| aartis | Standard Deviation of Portfolio = Standard Deviation of X into wieght of X |
| soarer1 | Can someone pls explain? Where did the 9.2% go to? |
| chamad | a risk free asset has 0 standard deviation. So average weighted-----.6*20 + .4*0 = 12% |
| mariodeb | The 9.2% shows the expected return |
| VenkatB | Variance of portfolio = weight of x squared * variance of x + weight of risk free asset squared * variance of risk free asset + 2 * weight of x * weight of riskfree asset * Correlation between x and riskfree asset * sd of x * sd of riskfree asset. Because sd of rrisk free asset = 0, variance of portfolio = = (0.60^2) * (0.20^2) + 0 + 0 = 0.0144 So sd of p = square root of (0.0144) = 0.12 = 12% |
| Renaud1807 | Thanks VenkatB |
| bundy | SD formula for a combinatin of risk free asset and risky asset is (1-Wrf)sd therefore .60 X .20 = .12 |
| michlam14 | yeah calculation for E(R) is not required for this question, but I think it's a trial and error thing - we are being tested on knowing what to use for calculating E(R) and standard deviation to come at the correct answer |
| jonan203 | the 8.5% was a wrong answer intended to through you off if you calculate 9.2% correctly |
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Learning Outcome Statements
explain the selection of an optimal portfolio, given an investor's utility (or risk aversion) and the capital allocation line
CFA® 2025 Level I Curriculum, Volume 2, Module 1.