Consider the following information about three stocks Rate o

Consider the following information about three stocks Rate of Return If State Occurs State of Economy Boom Normal Bust Probability of State of Economy 0.20 0.55 0.25 Stock A 0.38 0.16 0.00 Stock B 0.50 0.14 0.30 Stock C 0.50 0.12 0.50 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? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Portfolio expected return a-2 What is the variance? (Do not round intermediate calculations. Round the final answer to 5 decimal places.) Variance a-3 What is the standard deviation? (Do not round intermediate calculations. Enter the answer asa percent rounded to 2 decimal places.) Standard deviation b. If the expected T-bill rate is 3.70 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) 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? (Do not round intermediate calculations. Enter the answers as a percent rounded to 2 decimal places.) Approximate expected real return Exact expected real return c-2 What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter the answers as a percent rounded to 2 decimal places.) Approximate expected real risk premium Exact expected real risk premium

Solution

a1) State of economy Probability Return of stock A Probability* Return Stock A Return of stock B Probability* Return Stock B Return of stock C Probability* Return Stock C Boom 0.2 0.38 0.08 0.5 0.1 0.5 0.1 Normal 0.55 0.16 0.09 0.14 0.08 0.12 0.07 Bust 0.25 0 0 -0.3 -0.08 -0.5 -0.13 Total .17 or 17% .10 or 10% .04 or 4% Expected return of portfolio= 17%*30% + 10%*30% + 4%*40% Expected return of portfolio=10% a2) Stock Probability Expected Return (Expected return- portfolio expected return)^2 * Probability A 30% 17% 0.30% B 40% 10% 0 C 40% 4% 0.14% Variance 0.44% a3) Standard Deviation= Square root of .44%= 6.33% b) Portfolio expected risk premium= Portfolio expected return- risk free rate= 10%-3.7%=6.3% c1) Approximate real return= Nominal rate- inflation rate= 10%- 2.6%= 7.4% Exact expected real return or real rate= (1+ nominal rate)/(1+ inflation rate) - 1 Exact expected real return or real rate= (1+10%)/(1+ 2.6%) -1 Exact expected real return or real rate= 7.21% c2) Approximate real risk premium= Real rate of portfolio- risk free rate=7.4%- 3.7%= 3.7% Exact risk premium= exact real return- exact real return of tbill Exact risk premium= 7.21%- [(1+3.7%)/(1+2.6%)-1] Exact risk premium= 7.21%- .0107= 6.14%