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 40 percent each in A and B and 20 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 3.80 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 3.40 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 0.20 0.20 0.32 0.54    Normal
0.45

0.18

0.16

0.14
   Bust
0.35

0.02
? 0.34
? 0.42

Explanation / Answer

a-1

Expected return of A = 0.2*0.2+ 0.45*0.18 + 0.35*0.02 = 12.8%

Variance of A = 0.2*(0.2-12.8%)^2+ 0.45*(0.18-12.8%)^2 + 0.35*(0.02-12.8%)^2=0.006

Expected return of B= 0.2*0.32+ 0.45*0.16 + 0.35*(-0.34) = 1.7%

Variance of B = 0.2*(0.32-1.7%)^2+ 0.45*(0.16-1.7%)^2 + 0.35*(-0.34-1.7%)^2 =0.072

Portfolio Variance = w2A*?2(RA) + w2B*?2(RB) + w2c*?2(Rc)

Portfolio Variance = 0.4^2*0.006^2 + 0.4^2*0.072^2 + 0.2^2*0.128^2=0.00150

a-3)Standard deviation= sqrt(0.00150) = 3.87%

b)Expected risk premium =6.28%-3.8% = 2.48%

c1

Approximate expected real return =6.28%-3.4% = 2.88%

Exact expected real return = (1+6.28%)/(1+3.4%)-1 = 2.79%

c2)Approximate expected real risk premium =2.88%-3.8%=-0.92%

Exact expected real risk premium = 2.79%-3.8% =-1.01%

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