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A stock has a required return of 16%; the risk-free rate is 5.0%; and the market risk premium is 3%.

a. What is the stock's beta? Round your answer to two decimal places.

b. If the market risk premium increased to 7%, what would happen to the stock's required rate of return? Assume the risk-free rate and the beta remain unchanged.
-Select--Select-IIIIIIIVVItem 2
I. If the stock's beta is equal to 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
II. If the stock's beta is equal to 1.0, then the change in required rate of return will be less than the change in the market risk premium.
III. If the stock's beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
IV. If the stock's beta is less than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
V. If the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.

c. If the beta changed to 2, what would happen to the stock's required rate of return? Assume the risk-free rate and the market risk premium remain unchanged. Round your answer to two decimal places.

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Irving Heathcote
Irving HeathcoteLv2
28 Sep 2019

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Calculating the market risk premium beta and required rate of return. CAPM. Portfolio Risk & Return.

We have a portfolio of three positively correlated but not perfectly correlated stocks.

(Correlation co-efficient between 0-1)

Stock Expected Rate of Return Standard Deviation Beta

X 10% 16% .75

Y 12% 16% 1.25

Z 13% 16% 1.50

What is the market risk premium for the portfolio ?

Required Rate of Return For the Stock = Risk Free rate of Return +

+ ( Market Risk Premium * Beta of stock )

Market Risk Premium = Market Required Rate of Return – Risk Free rate of Return

The returns on stocks X, Y and Z and their beta have been provided. Using the information provided, we will first calculate the market risk premium.

The capital asset pricing model is a model based on the proposition that any stock's required rate of return is equal to the risk free rate of return plus a risk premium that reflects only the risk remaining after diversification.

The required rate of return for a stock is calculated by adding the risk free rate of return to the product of the market risk premium and the stock's beta.

The market risk premium shows the premium that investors require for bearing the risk of average stock and is calculated by deducting the risk free rate from the market's required rate of return.

Now, using stock X or any other stock, we can calculate the market risk premium. We'll use stock X. The expected return on this stock is 10%. The risk free rate is 7& and the stock's beta is .75.

By solving the equation we determine the market risk premium to be 4%.

Next, we will calculate the beta of Fund Q.

Fund Q has 1/3 of its funds invested in each of the three stocks X, Y, and Z.

Thus, the beta of Fund Q will be the sum of one third of the beta of each stock. One third of .75 is .25. One third of 1.25 is .4167 and one third of 1.5 is .5. By adding .25, .4167 and .5, we calculate the beta of Fund Q as 1.1667.

Let’s now calculate the required return of Fund Q. The risk free rate is 7%. The market risk premium is calculated to be 4%. The beta of Fund Q is 1.1667. By adding 7% to the product of 4% and 1.1667, we determine the required return on Fund Q to be 11.67%.

Since the returns on the three stocks included in Fund Q are not positively correlated, the standard deviation of the fund will be less than 16%.

1.Which of the following statements is most correct?

Diversifiable risk is caused by events unique to a single business.
Portfolio risk is caused by events unique to a single business.
Adding similar investments to a portfolio reduces risk more than adding randomly chosen investments does
It is impossible to reduce diversifiable risk.
None of the above statements is correct.

2.Advantages of short-term financing (as compared to long-term financing) include which of the following?

Loans can be obtained faster.
The interest rate on borrowed funds is generally lower.
Interest costs are relatively stable over time.
Answers (a) and (b) are correct.
Answers (a), (b), and (c) are correct.

3.Which of the following statements about the beta coefficient is false?

A stock's beta coefficient measures its volatility relative to the market portfolio.
A stock's beta coefficient can theoretically be calculated using the capital asset pricing model.
A stock's reported beta coefficient is based on forecasted future volatility.
A stock with a beta coefficient greater than 1.0 is said to be riskier than the market portfolio.
Under the capital asset pricing model, a stock with a beta coefficient less than 1.0 would have a required rate of return that is lower than the required rate of return on the market portfolio.

4.Investors will be most likely to purchase a stock if which of the following conditions holds?

E(Re) < R(Re)
E(Re) = R(Re)
E(Re) > R(Re)
E(Re) = RF
RPe = 0

Stock X has a 10% expected return, a beta coefficient of 0.9, &a 35% standard deviation of expected returns. Stock Y has a 12.5%expected return, a beta coefficient of 1.2, and a 25% standarddeviation. The risk-free rate is 6%, & the market risk premiumis 5%.

a. Calculate each stock's coefficient of variation.

b. Which stock is riskier for a diversified investor?

c. Calculate each stock's required rate of return.

d. On the basis of the two stocks' expected and required returns,which stock would be more attractive to a diversifiedinvestor?

e. Calculate the required return of a portfolio that has $7,500invested in Stock X and $2,500 invested in Stock Y.

f. If the market risk premium increased to 6%, which of the twostocks would have the larger increase in its required return?

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