Tom Noel 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 Tom 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

-0.24

Explanation:

The portfolio beta is a weighted average of the betas of the individual stocks in it.

The portfolio beta before the replacement is;

= (1.4 * 150,000/375,000) + (0.8 * 50,000/375,000) + ( 1 * 100,000/375,000) + (75,000 * 75,000/375,000)

= 0.56 + 0.11 + 0.27 + 0.24

= 1.17

After the replacement, portfolio beta will be;

=  (0.75 * 150,000/375,000) + (0.8 * 50,000/375,000) + ( 1 * 100,000/375,000) + (75,000 * 75,000/375,000)

= 0.32 + 0.11 + 0.27 + 0.24

= 0.93

The change is therefore;

= 0.93 - 1.17

= -0.24

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