If your portfolio is invested 30 percent each in A and B and 40 percent in C, wh
ID: 2715291 • Letter: I
Question
If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)
What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
If the expected T-bill rate is 4.40 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
If the expected inflation rate is 4.00 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded 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. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Consider the following information about three stocks:Explanation / Answer
Answer A-1 Expected return on Portfolio = 12.51% State of probability stock A Stock B Stock C Economy return p*rA return p*rB return p*rC p rA rB rC Boom 0.25 0.32 0.08 0.44 0.11 0.6 0.15 Normal 0.4 0.24 0.096 0.22 0.088 0.2 0.08 Bust 0.35 0.02 0.007 -0.24 -0.084 -0.4 -0.14 Expected return 0.183 0.114 0.09 Expected return (%) E® 18.30% 11.40% 9.00% Weight of Stock A wA 30% Weight of Stock B wB 30% Weight of Stock C wC 40% Expected return on portfolio E(P) = wA * E(rA) + wB * E(rB) + wC * E(rC) E(P) = 30% * 18.3% + 30% * 11.4% + 40% * 9% E(P) 0.1251 Expected return on portfolio = 12.51% Answer A-2 Variance of Portfolio = 0.06958 Stock A Stock B Stock C Probability rA E(rA) rA-E(rA) (rA-E(rA))^2 rB E(rB) rB-E(rB) (rB-E(rB))^2 rC E(rC) rC-E(rC) (rC-E(rC))^2 p Boom 0.32 0.183 0.137 0.018769 0.44 0.114 0.326 0.106276 0.6 0.09 0.51 0.2601 0.25 Normal 0.24 0.183 0.057 0.003249 0.22 0.114 0.106 0.011236 0.2 0.09 0.11 0.0121 0.4 Bust 0.02 0.183 -0.163 0.026569 -0.24 0.114 -0.354 0.125316 -0.4 0.09 -0.49 0.2401 0.35 Variance of Stock A = Sum(probability * (rA-E(rA)^2 = 0.25 * 0.018769+0.40*0.003249+0.35*0.026569 = 0.015291 Variance of Stock B = Sum(probability * (rB-E(rB)^2 =0.25*0.106276+0.40*0.011236+0.35*0.125316 = 0.074924 Variance of Stock C = Sum(probability * (rC-E(rC)^2 =0.25*0.2601+0.4*0.0121+0.35*0.2401 = 0.1539 Covariance of stocks A,B = sum (probability * (rA-E(rA)*(rB-E(rB)) = 0.25*0.137*0.326+0.4*0.057*0.106+0.35*-0.163*-0.354 = 0.033778 Covariance of stocks A,C = sum (probability * (rA-E(rA)*(rC-E(rC)) = 0.25*0.137*0.51+0.4*0.057*0.11+0.35*-0.163*-0.49 = 0.04793 Covariance of Stocks B, C = = sum (probability * (rB-E(rB)*(rC-E(rC)) = 0.25*0.326*0.51+0.4*0.106*0.11+0.35*-0.354*-0.49 = 0.10694 Variance of Portfolio = wA^2 * Variance of Stock A + wB^2 * Variance of Stock B + wC^2 * Variance of stock C + 2*wA*wB*Covariance A, B + 2*wA*wC*Covariance A, C + 2*wB*wC*Covariance B, C = 0.3^2 * 0.015291 + 0.3^2 * 0.074924 + 0.4^2 * 0.1539 + 2*0.3*0.3*0.033778+2*0.3*0.4*0.04793+2*0.3*0.4*0.10694 = 0.075992 Answer A-3 Standard Deviation of Portfolio = 27.57% Standard Deviation of Portfolio = Square root of Variance = =(0.075992)^(1/2) = 0.2756668 or 27.57% Answer B Expected risk premium on portfolio = 8.11% Expected return on portfolio = 12.51% Expected T-Bill rate = 4.40% Expected risk premium on portfolio = expected return on portfolio - expected T-Bill rate = 12.51%-4.40% 8.11% Answer C-1 Approximate Expected real return = 8.51% Actual Expected real return = 8.18% Inflation rate = 4% Expected rate of return = 12.51% Approximate expected real return = expected rate of return - inflation rate = 12.51%-4% = 8.51% Actuall expected real return is calculated using the below formula (1+expected rate ofreturn) = (1+ inflation rate) (1+actual expected real return) (1+0.1251) = (1+0.04)*(1+ actual expected real return) 1+ actual expected real return = 1.1251/1.04 Actual expected real return = (1.1251/1.04) -1 0.081827 or 8.18% Answer C-2 Approximate expected real risk premium = 8.11% Exact expected real risk premum = 7.80% Expected rate of return = 12.51% Expected T-Bill rate = 4.40% Inflation rate = 4.00% Approximate expected real risk premium = 12.51% - 4.40% 0.0811 or 8.11% Exact expected real risk premium = Approximate expected real risk premium /(1+inflation rate) = 0.0811/(1+0.04) = 0.0811/1.04 0.077981 or 7.80%