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 , β=Security's risk premium/market's risk premium=6/8=0.75
Beta Doubles= 2*0.75=1.5
Then, Expected Return=7%+1.5*8%=0.07+1.5*0.08=0.07+0.12=0.19. Therefore, Expected Return=19% * The Current Risk Premium of the stock=ERR - risk free rate=13%-7%=6% * If the security of beta doubles then the risk premium is 12% * The New Discount Rate for the Security=12%+7%=19% * Given Current Market Price of a Security= $40
If the stock pays a constant dividend in perpetuity, Price = Dividend/Discount rate 40 = D/0.13 ⇒ 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