1.Suppose two factors are identified for the U.S. economy: the growth rate of in

Question

1.Suppose two factors are identified for the U.S. economy: the growth rate of industrial production, IP, and the inflation rate, IR. IP is expected to be 3% and IR 6%. A stock with a beta of 1 on IP and 0.6 on IR currently is expected to provide a rate of return of 11%. If industrial production actually grows by 4%, while the inflation rate turns out to be 7%, what is your best guess for the rate of return on the stock? (Round your answer to 1 decimal place.)

Rate of return             %

2.Assume both portfolios A and B are well diversified, that E(rA) = 15.8% and E(rB) = 18.8%. If the economy has only one factor, and A = 1 while B = 1.3,What must be the risk-free rate? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Risk-free rate             %

3.

Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 40%. Portfolios A and B are both well diversified.

What is the expected return–beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return–beta relationship E(rP) =  % +  P1 +  P2

  Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.8 2.2 30 B 2.1 -0.5 8

Explanation / Answer

Return = Alpha% + Beta1*R1 + Beta2*Rw

11% = Alpha% + 1*3% + 0.6*6%

Alpha% = 11% - 3% - 3.6% = 4.4%

New return = 4.4% + 1*4% + 0.6*7%

= 4.4% + 4% + 4.2%

= 12.6%

2)

E(Ra) = Rf + Beta * Risk premium

15.8% = Rf + 1 * Risk premium

Risk premium = 15.8% - Rf

18.8% = Rf + 1.3 * Risk premium

18.8% = Rf + 1.3 * (15.8% - Rf)

18.8% = 20.54% -0.3 Rf

Rf = 1.74% / 0.3

Rf = 5.8%

3)

30% = 5% + 1.8*R1 + 2.2*R2

8% = 5% + 2.1*R1 + -0.5*R2

Solve above 2 equations

1.8*R1 + 2.2*R2 = 25%

R1 = ( 25% - 2.2*R2 ) / 1.8, substitute R1 value in other equation

3% = 2.1*( 25% - 2.2*R2 )/1.8 + -0.5*R2

0.5*R2 + 2.57*R2 = 29.17%

R2 = 29.17% / 3.07% = 9.51%

R1 = ( 25% - 2.2*R2 ) / 1.8

   = ( 25% - 2.2*9.51% ) / 1.8 = 2.26%

Expected return–beta relationship E(rP) = 5% + Beta1*2.26% + Beta2*9.51%

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