Re:Module assignment

Chapter 9, Problem 4P Bookmark Show all steps:

Problem

Consider the following information about two stocks (D and E) and two common risk factors (1

and 2):

a. Assuming that the risk-free rate is 5.0%, calculate the levels of the factor risk premia that are

consistent with the reported values for the factor betas and the expected returns for the two

stocks. b. You expect that in one year the prices for Stocks D and E will be $55 and $36,

respectively. Also, neither stock is expected to pay a dividend over the next year. What should

the price of each stock be today to be consistent with the expected return levels listed at the

beginning of the problem?

c. Suppose now that the risk premium for Factor 1 that you calculated in Part a suddenly

increases by 0.25% (i.e., from x% to (x + 0.25)%, where x is the value established in Part a.

What are the new expected returns for Stocks D and E?

d. If the increase in the Factor 1 risk premium in Part c does not cause you to change your

opinion about what the stock prices will be in one year, what adjustment will be necessary in the

current (i.e., today’s) prices?

Step-by-step solution

a. The expected return of the stock is the sum of risk-free rate and excess return. The risk

premium of the factors can be calculated by using the equation of excess return. With the risk-

free rate of 5%, the risk premiums are as follows:

Stock E(R) b 1 b 2 Risk premium

D 13.1% 1.2 3.4

E 15.4% 2.6 2.6

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Solving equation 1 and 2

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Multiply both the sides of equation (1) with 2.6 and equation (2) with 1.2. Change the signs of

equation, so the above equations becomes

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Now the variable ?b1 will be cancelled in both the equations and only ?b2 will be left out. By

solving this we can get

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The value of ?b2 will be 1.5. If we put this value in equation 1, the value of ?b1 will be 2.5.

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b. The current price of the stock is the present value of its future revenue streams. If the

company has not paid any dividend in the year and next year’s price of the stocks D and is $55

and $36 respectively, the current price of the stock D will be:

Similarly, the current price of the stock E will be:

Hence, the current year’s price of stock D and E is $48.6 and $31.2respectively.

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c. The risk premium for factor 1 calculated in part a is 2.5%. If it increases by 0.25%, then it will

become 2.75%. The expected return for stock D will be:

Similarly, the expected return for stock E will be:

Thus, the expected return for stock D and E is 13.4% and 16.05%respectively.

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d. The increase in factor 1 risk premium causes increase in the expected returns of both the

stocks. This will slightly decrease the current year’s price.

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