CFA Practice Question

There are 294 practice questions for this study session.

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
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