If your portfolio is invested 25 percent each in A and B and 50 percent in C, wh
ID: 2707012 • Letter: I
Question
If your portfolio is invested 25 percent each in A and B and 50 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 3.50 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 3.10 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))
Explanation / Answer
a-1. Portfolio return in boom = 0.25*0.36+0.25*0.48+0.5*0.60 = 51%
Portfolio return in normal = 0.25*0.15+0.25*0.13+0.5*0.11 = 12.5%
Portfolio return in bust = 0.25*0.06+0.25*-0.28+0.5*-0.48 = -29.5%
Portfolio expected return = 0.3*51%+0.4*12.5%+0.3*-29.5% = 11.45%
a-2. Variance = 0.3*(51%-11.45%)^2 + 0.4*(12.5%-11.45%)^2 + 0.3*(-29.5%-11.45%)^2 = 0.09728
a-3. Standard deviation = square root of variance = (0.09728)^0.5 = 31.19%
b. Expected risk premium = expected return - return of T-bill = 11.45%-3.50% = 7.95%
c-1. Approximate expected real return = expected return-inflation rate = 11.45%-3.10% = 8.35%
Exact expected real return = (1+expected return)/(1+inflation rate)-1 = (1+11.45%)/(1+3.1%)-1 = 8.10%
c-2. Approximate expected real return = T-bill rate-inflation rate = 3.5%-3.1% = 0.4%
Exact expected real return = (1+T-bill rate)/(1+inflation rate)-1 = (1+3.5%)/(1+3.1%)-1 = 0.39%
Approximate expected real risk premium = Approximate expected real return - approximate expected real return = 8.35%-0.4% = 7.95%
Exact expected real risk premium = Exact expected real return - exact expected real return = 8.10%-0.39% = 7.71%
Hope this helped ! Let me know in case of any queries.