Use the following information to answer the question(s)below.
Suppose that the market portfolio is equally likely to increase by 24% or decrease by 8%.Security "X" goes up on average by 29% when the market goes up and goes down by 11% when the market goes down.Security "Y" goes down on average by 16% when the market goes up and goes up by 16% when the market goes down.Security "Z" goes up on average by 4% when the market goes up and goes up by 4% when the market goes down.
-The expected return on a security with a beta of 1.2 is closest to:
A)4.8%.
B)8.0%.
C)8.8%.
D)9.6%.

Question

Quizplus · Accepted Answer

Using the formula for the expected return on an asset given the expected return on the market portfolio, we get:

Expected return on X = 0.5(0.29) + 0.5(-0.11) = 0.09 = 9%
Expected return on Y = 0.5(-0.16) + 0.5(0.16) = 0 = 0%
Expected return on Z = 0.5(0.04) + 0.5(0.04) = 0.04 = 4%

Next, we need to find the expected return on the market portfolio. Since it is equally likely to increase by 24% or decrease by 8%, we take the average of these two outcomes:

Expected return on market portfolio = 0.5(0.24) + 0.5(-0.08) = 0.08 = 8%

Now, we can use the formula for the expected return on an asset with beta to calculate the expected return on the security with a beta of 1.2:

Expected return on security = risk-free rate + beta*(expected return on market portfolio - risk-free rate)

Assuming a risk-free rate of 3%, we get:

Expected return on security = 0.03 + 1.2*(0.08 - 0.03) = 0.096 = 9.6%

Therefore, the expected return on a security with a beta of 1.2 is closest to 9.6%. The answer is C.

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