A portfolio contains four assets.Asset 1 has a beta of .8 and comprises 30% of the portfolio.Asset 2 has a beta of 1.1 and comprises 30% of the portfolio.Asset 3 has a beta of 1.5 and comprises 20% of
The portfolio.Asset 4 has a beta of 1.6 and comprises the remaining 20% of the portfolio.If the
Riskless rate is expected to be 3% and the market risk premium is 6%, what is the beta of the
Portfolio?
A)0.80
B)1.10
C)1.19
D)1.25
E)1.40

Question

Quizplus · Accepted Answer

First, we need to calculate the weighted average beta of the portfolio using the individual betas and their weight in the portfolio:
Weighted average beta = (0.8 x 0.3) + (1.1 x 0.3) + (1.5 x 0.2) + (1.6 x 0.2) 
= 0.24 + 0.33 + 0.3 + 0.32 
= 1.19

Next, we need to use the capital asset pricing model (CAPM) to calculate the expected return and the beta of the portfolio:
Expected return = risk-free rate + (market risk premium x portfolio beta) 
= 0.03 + (0.06 x 1.19) 
= 0.1094 or 10.94%

Finally, to find the beta of the portfolio, we rearrange the CAPM formula:
Portfolio beta = (expected return - risk-free rate) / market risk premium 
= (0.1094 - 0.03) / 0.06 
= 0.124 or 1.24

Therefore, the answer is C) 1.19.

A Portfolio Contains Four Assets