a). Computation of the expected return on portfolio:-

Expected return on portfolio = (Weight of stock * Return of stock) + (Weight of risk free asset * Return of risk free asset)

= (50% * 13.5%) + (50% * 4.65%)

= 6.75% + 2.33%

= 9.08%

 

b). Computation of the portfolio weights:-

W = Weight of stock

Beta of portfolio = (Weight of stock * Beta of stock) + (Weight of risk free asset * Beta of risk free asset)

0.97 = (W * 1.37) + ((1 - W) * 0)

0.97 = W * 1.37

W = 0.97 / 1.37

= 0.7080

Weight of risk free asset = 1 - W

= 1 - 0.7080

= 0.2920

 

c). Computation of the beta:-

Expected return on portfolio = (Weight of stock * Return of stock) + (Weight of risk free asset * Return of risk free asset)

12.7% = (W * 13.5%) + ((1-W) * 4.65%)

12.7% = (W * 13.5%) + 4.65% - (W * 4.65%)

12.7% - 4.65% = (W * 8.85%)

W = 8.05% / 8.85%

= 0.9096

W = Weight of stock = 0.9096

Weight of risk free asset = 1 - W

= 1 - 0.9096

= 0.0904

Beta of portfolio = (Beta of stock * Weight of stock) + (Beta of risk free asset * Weight of risk free asset)

= (1.37 * 0.9096) + (0 * 0.0904)

= 1.25

 

d). Computation of the portfolio weights:-

Beta of portfolio = (Beta of stock * Weight of stock) + (Beta of risk free asset * Weight of risk free asset)

2.57 = (1.37 * W) + (0 * (1 - W))

2.57 = 1.37 * W

W = 2.57 / 1.37

= 1.8759

 

Weight of risk free asset = 1 - W

= 1 - 1.8759

= -0.8759