UBL investment management has the following portfolio: Stock Investment (millions) Beta A $ 150 1.4 B $ 50 0.8 ? $ 100 1.00 D $ 75 1.2 The investment firm plans to sell Stock A and replace it with Stock E, which has a beta of 0.75. By how much will the portfolio beta change? (a) -0.234 (b) -0.211 (C) -0.260 (d) -0.190 (e) -0.286

Calculation of weights of stocks in the portfolio:

Total value of investment in the portfolio:

$150+$50+$100+$75= $375

Hence weight of stocks is calculated below:

Stock A : 150/375 = 0.40

Stock B : 50/375 = 0.13

Stock C : 100/375 = 0.27

Stock D : 75/375 = 0.20

Beta of stocks:

Stock A : 1.4

Stock B :0.8

Stock C :1.00

Stock D: 1.2

We know that beta of the portfolio = weighted average beta of the stocks in the portfolio

Hence existing beta of the portfolio:

= 1.4 x 0.40+ 0.8 x0.13+ 1.00x 0.27+ 1.2x 0.2

=1.174

Hence beta of existing portfolio is 1.174

If stock A is replaced by stock E with stock beta = 0.75

Hence revised portfolio beta :

= 0.75x0.40+0.8x0.13+1.00x0.27+1.2x0.2

=0.914

Hence the beta of new portfolio is 0.914

Hence difference between beta of old and new portfolio = new beta - old beta

= 0.914 - 1.174

=- 0.260

Hence beta has changed by -0.260. Thus the correct answer is C.