Consider the following information about three stocks: Rate of Return if State O

Question

Consider the following information about three stocks: Rate of Return if State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom 0.20 0.26 0.38 0.50 Normal 0.50 0.10 0.08 0.06 Bust 0.30 0.01 0.20 0.40 a-1 If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return? (Round your answer to 2 decimal places. (e.g., 32.16)) Portfolio expected return % a-2 What is the variance? (Do not round intermediate calculations and round your final answer to 5 decimal places. (e.g., 32.16161)) Variance 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 % b. If the expected T-bill rate is 3.00 percent, what is the expected risk premium on the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16)) Expected risk premium % c-1 If the expected inflation rate is 2.60 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 % Exact expected real return % 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 premium % Exact expected real risk premium %

Explanation / Answer

a-1 If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return

We need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:

And the expected return of the portfolio is: E(Rp) = 0.20*(0.392)+0.5*(0.078)+0.3*(-0.16) = 0.1126 = 11.26%

-2 What is the variance? (Do not round intermediate calculations and round your final answer to 5 decimal places.

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is:

2p = 0.20*(0.392-0.1126)^2+0.50*(0.078-0.1126)^2+0.30*(0-.217-0.1126)^2 = 0.048802

What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places

p = (.048802)1/2 = .2209 or 22.09%

b. If the expected T-bill rate is 3.00 percent, what is the expected risk premium on the portfolio? (Round your answer to 2 decimal places

Expected Risk Premium = Expected Retun- Risk free rate = 11.62%-3% = 8.62%

c-1 If the expected inflation rate is 2.60 percent, what are the approximate and exact expected real returns on the portfolio? (Round your answers to 2 decimal places.

The approximate expected real return is the expected nominal return minus the inflation rate, so:

               Approximate expected real return = .1126 – .026 = .0866 or 8.66%

               To find the exact real return, we will use the Fisher equation. Doing so, we get:

               1 + E(Ri) = (1 + h)[1 + e(ri)]

               1.1126 = (1.030)[1 + e(ri)]

               e(ri) = (1.11260/1.03) – 1 = .0.0802 or 8.02%

c-2 What are the approximate and exact expected real risk premiums on the portfolio?

    The approximate real risk premium is the expected return minus the risk-free rate, so:

               Approximate expected real risk premium = .1126 – .03 = 8.66%

The exact expected real risk premium is the approximate expected real risk premium, divided by one plus the inflation rate, so:

              

               Exact expected real risk premium = .0866/1.026 = 8.44%

Boom E(rp) 0.3*(0.26)+0.3*(0.38)+0.4*(0.5) 0.392 39.20% Normal E(rp) 0.3*(0.1)+0.3*(0.08)+0.4*(0.06) 0.078 7.80% Bust E(rp) 0.3*(0.01)+0.3*(-0.2)+0.4*(-0.4) -0.16 -16%

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