Consider the following information about three stocks: If your portfolio is inve

Question

Consider the following information about three stocks:   

  

If your portfolio is invested 35 percent each in A and B and 30 percent in C, what is the portfolio expected return? (Round your answer to 2 decimal places. (e.g., 32.16))

  

What is the variance? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161))

  

  

What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

If the expected T-bill rate is 3.10 percent, what is the expected risk premium on the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16))

  

If the expected inflation rate is 2.70 percent, what are the approximate and exact expected real returns on the portfolio? (Round your answers to 2 decimal places. (e.g., 32.16))

  

What are the approximate and exact expected real risk premiums on the portfolio? (Round your answers to 2 decimal places. (e.g., 32.16))

Rate of Return if State Occurs   State of Probability of   Economy State of Economy Stock A Stock B Stock C   Boom 0.25 0.28 0.40 0.52   Normal 0.40 0.11 0.09 0.07   Bust 0.35 0.02 ? 0.22 ? 0.42

Explanation / Answer

a-1

If your portfolio is invested 35 percent each in A and B and 30 percent in C, what is the portfolio expected return? (Round your answer to 2 decimal places. (e.g., 32.16))

Expected return of A = 0.25*0.28 +0.40*0.11 +0.35*0.02= 12.1%

Expected return of B = 0.25*0.40 +0.40*0.09 +0.35*(-0.22)= 5.90%

Expected return of C = 0.25*0.52 +0.40*0.07 +0.35*(-0.42)= 1.10%

Portfolio expected return = 35%*12.1% + 35%*5.90% +30%*1.1%= 6.63%

  Portfolio expected return

6.63%

  

a-2

What is the variance? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161))

E(Rp) in Boom = 0.28*0.35 + 0.4*0.35 + 0.52*0.30= 39.40%

E(Rp) in Normal = 0.11*0.35 + 0.09*0.35 + 0.07*0.30= 9.10%

E(Rp) in Bust = 0.02*0.35 + (-0.22)*0.35 + (-0.42)*0.30= -19.6%

Variance of portfolio = 0.25*(39.40%-6.63%)^2 + 0.40*(9.10%-6.63%)^2 + 0.35*(-19.6%-6.63%)^2= 0.05117

  Variance    0.05117

  

a-3

What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

standard deviation = sqrt(0.05117) = 22.62%

  Standard deviation

22.62%

  

b.

If the expected T-bill rate is 3.10 percent, what is the expected risk premium on the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16))

  Expected risk premium = 6.63% -3.10% = 3.53%

  Expected risk premium

3.53%

  

c-1

If the expected inflation rate is 2.70 percent, what are the approximate and exact expected real returns on the portfolio? (Round your answers to 2 decimal places. (e.g., 32.16))

Approximate expected real return = 6.63% -2.7%= 3.93%

  Exact expected real return = (1+6.63%)/(1+2.7%) -1= 3.83%

  

  Approximate expected real return

3.93%

  Exact expected real return

3.83%

  

c-2

What are the approximate and exact expected real risk premiums on the portfolio? (Round your answers to 2 decimal places. (e.g., 32.16))

Approximate expected real risk premiums = 3.53% -2.7%= 0.83%

  Exact expected real risk premiums = (1+3.53%)/(1+2.7%) -1= 0.81%

  

  Approximate expected real risk premium

0.83%

  Exact expected real risk premium

0.81%

Finance

a-1

If your portfolio is invested 35 percent each in A and B and 30 percent in C, what is the portfolio expected return? (Round your answer to 2 decimal places. (e.g., 32.16))

Expected return of A = 0.25*0.28 +0.40*0.11 +0.35*0.02= 12.1%

Expected return of B = 0.25*0.40 +0.40*0.09 +0.35*(-0.22)= 5.90%

Expected return of C = 0.25*0.52 +0.40*0.07 +0.35*(-0.42)= 1.10%

Portfolio expected return = 35%*12.1% + 35%*5.90% +30%*1.1%= 6.63%

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