Question

Security Beta T-Bill= 1.4% 1.22 S& P 500 8% 0.84 2.21 0.67 Е 0.36 Based on the CAPM, what are the expected returns on the 5 stocks (A, B, C, D, E)? (12 points) If you invest 30% in the S & P 500, 20% in T-Bill, and 10 % each in the 5 stocks, what is the beta of your portfolio? (4 points) ABCD

Answer 1

Based on CAPM, Expected return on stock = R_f + Beta * (R_m - R_f)........ Equation (1)

where Risk free rate,(T-Bill), R_f = 1.4%, market return (S&P 500), R_m = 8%, Beta as given for each stock in the table.

Substituting the values in Equation (1), Expected return is calculated as shown below (using Excel)

B C А Risk free rate 1 (T-Bill), Rf Market return 2 (S&P 500), Rm 8% 3 Security Beta Required Formula 1.22 0.84 2.21 0.67 0.36 return 9.45% 6.94% 15.99% 5.82% 3.78% F$B$1+B5*($B$2-$B$1) =$B$1+B6*($B$2-$B$1) =$B$1+B7*($B$2-$B$1) =$B$1+B8*($B$2-$B$1) =$B$1+B9*($B$2-$B$1)

Required rate of return from Stock A= 9.45%, B = 6.94%, C= 15.99%, D = 5.82%, E = 3.78%

Next let us calculate Beta of portfolio as given by

Bp= wsP500* BSP500+ wi-bill * Bt-bill+WA* BA + .... +wE* BE

which is Portfolio beta = sum of (weight of each constituent of portfolio * Beta of the constituent)

Here we are taking Beta of market (S&P 500) = 1, Beta of T-Bill = 0 (As it is risk-free) & beta of stocks as given in question. Weights of the portfolio constituents are also given in question.

Calculation:

B Portfolio Portfolio Weight Beta Beta 0.30 S&P 500 1.00 T-Bill 0.20 0.00 Stock A 0.10 1.22 Stock B 0.10 0.84 0.83 Stock C 0.10 2.21 Stock D 0.67 Stock E 10.10 0.36 Portfolio Beta FB12*C12+B13*C13+B14*C14+B15*C15+B16*C16+B17*C17+B18*c18 0.10 19

Therefore Beta of Portfolio = 0.83