- CFA Exams
- CFA Level I Exam
- Study Session 18. Portfolio Management (1)
- Reading 53. Portfolio Risk and Return: Part II
- Subject 3. The Capital Asset Pricing Model

###
**CFA Practice Question**

A portfolio consists of 45% of wealth invested in the market portfolio and the remaining in risk-free T-bills yielding 6.3%. The market portfolio has an expected return of 17% and a standard deviation of 19%. The beta of the portfolio is ______.

A. 0.55

B. 0.45

C. 1.0

**Explanation:**If your wealth is divided between the market portfolio and the risk-free asset, the portfolio beta equals the fraction invested in the market portfolio. It is instructive to prove this either by using the CAPM equation directly or by calculating the covariance between the portfolio and the market.

###
**User Contributed Comments**
12

User |
Comment |
---|---|

tengo |
The market portfolio has a beta of 1 the risk free asset has a beta of 0. The weights are .45 market component and .55 risk free component. Beta(portfolio) = .45*1 +.55*0 |

flobeebhead |
This is the best question I have ever seen |

whoi |
well, whoever prefers a more complicated, but easier to understand solution: E(Rp) = 0.45*17%+0.55*6.3% = 11.115% E(Rp) = 11.115% = 6.3% + Beta*(17%-6.3%) Beta = (11.115%-6.3%)/(17%-6.3%)= 0.45 |

volkovv |
The take a way from this question and the posts below is that both beta and expected return on a portfolio can be calculated by using respective weights of it components. However, this is not true for calculating portfolio's variance. |

RNAN |
Can't we just use a beta of zero for the risk free portion of the portfolio and then use the 45% remainder (all market portfolio which has a beta of 1 by definition) to get the .45 beta. Why so many formulae and numbers above? |

coolnan |
Thank you-whoi. a smart way to explain. |

steved333 |
B of (Rf) item=0, B of (Rm)=1. .55x0+.45x1= .45 Not hard. |

shival |
0,45*Rm+0,55*Rf=Rf+Beta*(Rm-Rf) Beta=(0,45*Rm-0,45Rf)/(Rm-Rf) Beta=0,45 |

Allen88 |
Thanks whoi! |

mpapwa22 |
Thanks Whoi, well explained. |

zzhumanov |
thanks Whoi |

endurance |
Whoi, Thanks |