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Chapter 7

4. What must be the beta of a portfolio with E(rP) = 20%, if rf = 5% and E(rM) = 15%?

Answer:

Given: E(rP)=20%, rf=5% and E(rM)=15%

Formula: E(rP)=βP*(E( rM ) – rf ) + rf

0.20= βP*(0.15-0.05)+0.05

=>0.20-0.05= βP*(0.1)

=>0.15= βP*(0.1)

βP=0.15/0.1=1.5

Therefore beta of a portfolio is 1.5

5. The market price of a security is $40. Its expected rate of return is 13%. The risk-free rate is 7%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity.

Answer:

* Firstly we are using Use zero-growth Dividend Discount Model to calculate the intrinsic value, which is the market price.

* So calculating the Beta ...view middle of the document...

13 ⇒ D = 40 * 0.13 = $5.20

If the stock pays a constant dividend in perpetuity, Price = Dividend/Discount rate (New)

=>$5.20/19%=$5.20/0.19=$27.37

Increment in a stock risk has lowered the value of the Stock by 31.58%

7. Are the following statements true or false? Explain.

a. Stocks with a beta of zero offers an expected rate of return of zero.

b. The CAPM implies that investors require a higher return to hold highly volatile securities.

c. You can construct a portfolio with a beta of .75 by investing .75 of the budget in T-bills and the remainder in the market portfolio.

Answer:

a. Stocks with a beta of zero offers an expected rate of return of zero.

Answer: The Above statement is False,

Because if Beta is Zero then the ERR Er= Rf (Risk Free Rate).

b. The CAPM implies that investors require a higher return to hold highly volatile securities.

Answer: The Above Statement is False,

Only for non diversify or Market Risk investors require risk premium. Total Volatility includes diversifiable risk.

c. You can construct a portfolio with a beta of .75 by investing .75 of the budget in T-bills and the remainder in the market portfolio.

Answer: Statement is False

Porfolio should invest 75% in the market and 25% in the T-bills. Then

Beta of a Portfolio= (0.75*1) + (0.25*0) =.75

17. A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1.0. What do investors expect the stock to sell for at the end of the year?

Answer:

Dividend (D) =$9 per share at the end of the year. Beta=1.0, ERR on the market E(r) =18%=0.18

Share of Shock is now Selling, P0=$100

Let, P1 be the Stock to sell for at the end of the Year

E(r)= (D+P1-P0)/P0

0.18=(9+P1-100)/100

=>18=P1-91, =>P1=91+18

=>P1=$109

Therefore Investors expect the Stock to sell for at the end of the Year is $109.

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