If your portfolio is invested 40 percent each in A and B and 20 percent in C , w
ID: 2738176 • Letter: I
Question
If your portfolio is invested 40 percent each in A and B and 20 percent in C , what is the portfolio expected return? (Do not round intermediate calculations and 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? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the expected inflation rate is 3.50 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))
What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))
State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .30 .20 .25 .60 Normal .45 .15 .11 .05 Bust .25 .01 .15 .50
Explanation / Answer
A.1
Expected return of stock A = 0.3*20% + 0.45*15% + 0.2*1% = 12.95%
Expected return of stock B = 0.3*25% + 0.45*11% - 0.2*15% = 9.45%
Expected return of stock A = 0.3*60% + 0.45*5% - 0.2*50% = 10.25%
Expected return of given portfolio = 0.4*12.95% + 0.4*9.45% + 0.2*10.25% = 11.01%
A.2
State of Probability of Portfolio Return
Economy State of Economy if State Occurs Profit return if state occurs
Recession 0.30 (0.4* 0.2) + (0.4 * 0.25) + (0.2 * 0.6) = 0.3
Normal 0.45 (0.4* 0.15) + (0.4 * 0.11) + (0.2 * 0.05) = 0.114
Boom 0.25 (0.4* 0.01) - (0.4 * 0.15) - (0.2 * 0.5) = -0.156
variance of portfolio = (SD)2 = 0.3*(0.3 - 0.1101)2 + 0.45*(0.114 - 0.1101)2 +0.2*(-0.156-0.1101)2 = 0.025
A.3
Standard deviation = (0.025)1/2 = 0.158
B
Expected risk premium = Rp - Rf = 11.01% - 3.8% = 7.21%
C.1
The approximate expected real return is the expected nominal return minus the inflation rate,
Approximate expected real return = 0.1101 – 0.035 = 0. 0751
Exact real return can be obtained by the use of the Fisher equation 1 + E(Ri) = (1 + h)[1 + e(ri)]
1 + 0.1101 = (1+0.035){1+ e(ri)}
e(ri) = 0.0726
C.2
approximate real risk premium is the expected return minus the risk-free rate,
Approximate expected real risk premium = 0.1101 – 0.038 = 0.0721
exact expected real risk premium = (approximate expected real risk premium / {1+inflation rate}
Exact expected real risk premium = 0.0721 / 1.035 = 0.0696