Question

QUESTION 45 For the next 2 questions suppose the following holds: Suppose you are the money manager of a $10 million investment fund. The fund consists of 2 stocks with the following investment and betas. Assume that the CAPM holds, and IRF-696, rMf12%. Stock Investment $4 million $ 6 million Beta 1.0 1.5 What is beta of the investment fund? O 1.2 O 1.3 O 1.35 O 1.4 O 1.45

Answer 1

Beta of a portfolio is simply the weighted average mean of individual stock betas. So, we first need to calculate portfolio weights of stocks A and B, which is just the proportion of total money invested in each stock. Since total money invested is $10 million and the amount of money invested in stock A is $4 million, its weight in the portfolio is 0.4. Similarly, weight of stock B is 0.6. Now, portfolio beta can be calculated simply by using the formula:

$\beta _{portfolio}=w_{A}\beta _{A}+ w_{B}\beta _{B}$

where $w_{A}$ and $w_{B}$ are respective weights of stocks A and B. Substituting the values we get:

$\beta _{portfolio}=0.4(1.0)+ 0.6(1.5)$

or beta = 1.3

So, the answer is second option, 1.3

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Expected return can be calculated using CAPM. The CAPM equation is given as:

$r_{p}=r_{f}+\beta (r_{m}-r_{f})$

where,

• $r_{p}$ is the return of portfolio or security that needs to be calculated
• $r_{f}$ is the risk free rate of return
• $r_{m}$ is the market expected return
• $\beta$ is beta

Substituting values for our portfolio, we have

$r_{p}=6+1.3(12-6)$

which gives us the expected return on our portfolio as 13.8%. So the correct option is the first one.