- CFA Exams
- CFA Exam: Level I 2021
- Study Session 18. Portfolio Management (1)
- Reading 52. Portfolio Risk and Return: Part I
- Subject 4. Risk Aversion and Portfolio Selection

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**CFA Practice Question**

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%.

Correct Answer: II

E(R

_{p}) = (0.6)(0.12) + (0.4)(0.05) = 0.092 or 9.2%. w_{p}σ^{2}_{X}= (0.6)(0.20) = 0.12 or 12%###
**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 |