Suppose that the S&P 500, with a beta of 1.0, has an expected return of 12% and
ID: 2768758 • Letter: S
Question
Suppose that the S&P 500, with a beta of 1.0, has an expected return of 12% and T-bills provide a risk-free return of 5%. a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .50; (iv) .75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.)
Expected return Beta
(i) 0 % ________% ______
(ii) .25 % ________% _______
(iii) .50 % _______% _______
(iv) .75 % _______% _______
(v) 1.0 % ________% _______
Explanation / Answer
Part (i)
Ws = 0
Wr = 1-0 =1
Expected return = Ws x Rs + Wr x Rf
= 0 x 12% + 1 x 5%
= 5%
Beta = Ws x Beta s
= 0 x 1 =0
Part (ii)
Ws = 0.25
Wr = 1-0.25 =0.75
Expected return = Ws x Rs + Wr x Rf
= 0.25 x 12% + 0.75 x 5%
= 6.75%
Beta = Ws x Beta s
= 0.25 x 1 =0.25
Part (iii)
Ws = .50
Wr = 1-0.50 =.50
Expected return = Ws x Rs + Wr x Rf
= 0.50 x 12% + 0.50 x 5%
= 8.50%
Beta = Ws x Beta s
= 0.5 x 1 =0.50
Part (iv)
Ws = 0.75
Wr = 1-0.75 =0.25
Expected return = Ws x Rs + Wr x Rf
= 0.75 x 12% + 0.25 x5%
= 10.25%
Beta = Ws x Beta s
= 0.75 x 1 =0.75
Part (v)
Ws = 1
Wr = 1-1 =0
Expected return = Ws x Rs + Wr x Rf
= 1 x 12% + 0 x 5%
= 12%
Beta = Ws x Beta s
= 1 x 1 =1
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