Question

1. The standard deviation of market portfolio returns is 15%. The beta of a mutual fund is 1.5. Can the standard deviation of mutual fund's returns be 20%?

a. Yes b. No

2.  The risk-free rate is 2%. The β of stock 1 is 0.8 while its σ is 15%. The beta of stock 2 is 1.6 while its σ is 45%. Which of the following statements is true in equilibrium?
a. The risk premium of stock 2 would be three times the risk premium of stock 1.
b. The risk premium of stock 2 would be twice as much as the risk premium of stock 1.
c. The expected return of stock 2 would be three times the risk premium of stock 1.
d. The expected return of stock 2 would be twice as much as the risk premium of stock 1.

Answer 1

Q.1 No.

Calculation

If standard deviation of the market is 15% and beta is 1.5 the stadard deviation :-

​​​​​​Fund's standard deviation​​​​​​= Market standard Deviation*beta of the fund

= 15*1.5

= 22.5%

That means the statement given above is false.

Q.2 (b)

According to CAPM model

Expected return = risk free returns + (beta* risk premium)

Here,

It is clear from the formula that there is strieght relationship with risk premium and beta as we change the beta it will directly and proportionatly impact on risk premium.

For ex. Risk premium= 7% so if the beta is 0.8 the risk premium will be = 0.8*7= 5.6%

And if beta = 1.6 than risk premium = 7*1.6 = 11.2%

So as the beta get double risk premium get double so hence we can say that as stock 2 has double beta so it has double risk premium as compared to stock 1.