If your portfolio is invested 40 percent each in A and B and 20 percent in C, wh

Question

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))

Explanation / Answer

a-1. Portfolio return in boom = 0.4*0.2+0.4*0.32+0.2*0.54 = 31.6%

Portfolio return in normal = 0.4*0.18+0.4*0.16+0.2*0.14 = 16.4%

Portfolio return in bust = 0.4*0.02+0.4*-0.34+0.2*-0.42 = -21.2%

Portfolio expected return = 0.2*31.6%+0.45*16.4%+0.35*-21.2% = 6.28%

a-2. Variance = 0.2*(31.6%-6.28%)^2 + 0.45*(16.4%-6.28%)^2 + 0.35*(-21.2%-6.28%)^2 = 0.04386

a-3. Standard deviation = square root of variance = (0.04386)^0.5 = 20.94%

b. Expected risk premium = expected return - return of T-bill = 6.28%-3.80% = 2.48%

c-1. Approximate expected real return = expected return-inflation rate = 6.28%-3.40% = 2.88%

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

c-2. Approximate expected real return = T-bill rate-inflation rate = 3.8%-3.4% = 0.4%

Exact expected real return = (1+T-bill rate)/(1+inflation rate)-1 = (1+3.8%)/(1+3.4%)-1 = 0.39%

Approximate expected real risk premium = Approximate expected real return - approximate expected real return = 2.88%-0.4% = 2.48%

Exact expected real risk premium = Exact expected real return - exact expected real return = 2.79%-0.39% = 2.40%

Hope this helped ! Let me know in case of any queries.

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