Paul McLaren holds the following portfolio: Stock Investment Beta A $150,000 1.40 B 50,000 0.80 C 100,000 1.00 D 75,000 1.20 Total $375,000 Paul 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. −0.190 b. −0.211 c. −0.234 d. −0.286

The change in portfolio beta is -0.26.

Beta is used to measure systemic risk. The higher the value of beta, the higher systemic risk is. A portfolio's beta can be determined by adding together the weighted beta of each stock in the portfolio

Weighed beta of a stock = percentage of the stock in the portfolio x beta of the stock

Beta of the initial portfolio

[(150,000 / 375000) x 1.4] + [(50,000 / 375000) x 0.8] + [(100,000/ 375,000) x 1] + [(75,000 / 375,000) x 1.2]

= 0.56 + 0.1067 + 0.2667 + 0.24 = 1.1734

Beta of the new portfolio

[(150,000 / 375000) x 0.75] + [(50,000 / 375000) x 0.8] + [(100,000/ 375,000) x 1] + [(75,000 / 375,000) x 1.2]

0.3  + 0.1067 + 0.2667 + 0.24 =  0.9134

Change in portfolio beta = -0.26

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- 0.260

Explanation:

The computation of portfolio beta is shown below:-

Stocks     Value          Weight (a)         Beta (b)     Portfolio Beta (a × b)

Stock A    $150,000   0.4000               1.4              0.560

Stock B    $50,000     0.1333                0.8             0.107

Stock C    $100,000    0.2667              1                  0.267

Stock D     $75,000     0.2000            1.2               0.240

Total         $375,000                                                    1.173

Now the revise of beta with stock E is

Stocks     Value          Weight (a)         Beta (b)     Portfolio Beta (a × b)

Stock E    $150,000   0.4000               0.75             0.300

Stock B    $50,000     0.1333                0.8               0.107

Stock C    $100,000    0.2667              1                    0.267

Stock D     $75,000     0.2000            1.2                 0.240

Total         $375,000                                                 0.913

Now

Net Change in Beta of Portfolio is

= Beta of portfolio with Stock E - Beta of Portfolio with Stock A

= 0.913 - 1.173

= - 0.260

This is the answer but the same is not provided in the given options

a is the correct answer, tell me if im right