Question

Consider the following information about three stocks: Rate of Return If State Occurs State of Probability of State of Economy Economy Stock A .32 Stock C .56 Boom Normal Bust Stock B .44 11 -25 26 .50 24 .09 .04 -.45 a-3 a-1. 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 enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a-2. What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) If the expected T-bill rate is 3.30 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) C-1. If the expected inflation rate is 2.90 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-2. What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

C D E F State of Economy Boom Good Poor Probability | 0.26 0.50 0.24 Stock A L 0.32 0.13 0.04 15.78% 10.27% Stock B 0.44 0.11 -0.25 10.94% 24.38% Stock C | 0.56 0.09 -0.45 8.26% 35.69% Expected return Standard deviation Weight 10 40% Portfolio's Stock Stock A Stock B Stock C 12 40% 20% 13 a.1 Expected return of Portfolio 12.34% 15 16 17 18 Covariance(A,B) Covariance (A,C) Covariance (B,C) 0.024095 0.035088 0.086978 19 20 a.2 Variance of Portfolio 0.04353 a.3 Standard deviation of Portfolio 20.86% T-bill rate 3.30% 27 28 b. Expected risk premium 9.04% 29 30 Inflation rate 2.90% c.1 Approxiate expected real return Exact expected real return 9.44% 9.17% 33 34 35 36 37 c.2 Approxiate expected real risk premium Exact expected real risk premium 6.14% 5.97%

Cell reference -

E F State of Economy Probability 0.26 Boom Good 0.5 Poor Stock A 0.32 0.13 0.04 =SUMPRODUCT($C$3:$C$5,D3:05) =SQRT(SUMPRODUCT(D6-D3:05)^2,$C$3:$C$5)) Stock B Stock C 0.44 0.56 0.11 0.09 -0.25 -0.45 =SUMPRODUCT($C$3:$C$5, E3:E5) =SUMPRODUCT($C$3:$C$5,F3:F5) =SQRT(SUMPRODUCT(E6-E3:E5)^2,$C$3:$C$5)) =SQRT(SUMPRODUCT((F6-F3:F5)^2,$C$3:$C$5)) 0.24 Expected return Standard deviation Weight 0.4 Portfolio's Stock Stock A Stock B Stock C 0.4 12 0.2 =C10*D6+C11*E6+C12*F6 14 a.1 Expected return of Portfolio | 15 16 Covariance(A,B) 18 Covariance (A,C) Covariance (B,C) 20 21 a.2 Variance of Portfolio =SUMPRODUCT((D6-D3:05),(E6-E3:E5),C3:05) =SUMPRODUCT((D6-D3:05),(F6-F3:F5),C3:05) =SUMPRODUCT(E6-E3:E5),(F6-F3:F5),C3:05) 19 =(C10*D7)^2+(C11*E7)^2+(C12*F7)^2+2*C10*c11*c17+2*C10*C12*C18+2*C11*c12*c19 24 a.3 Standard deviation of Portfolio =SQRT(C21) T-bill rate 0.033 b. Expected risk premium =C14-C26 Inflation rate 0.029 32 c.1 Approxiate expected real return 33 Exact expected real return C14-C30 (1+C14)/(1+C300-1 35 c.2 Approxiate expected real risk premium 36 Exact expected real risk premium 37 =C28-C30 =(1+C28)/(1+C30)-1

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.