The investor is worried that the beta of his portfolio is too high, so he wants to sell some stock C and add stock D, which has a beta of 1.0, to his portfolio. If the investor wants his portfolio to have a beta of 1.72, how much stock C must he replace with stock D

$36,000

Explanation:

First calculate the individual weights for the different stocks as this will help with the calculation of beta.

Total amount invested = 16,000 + 48,000 + 96,000 = $160,000

Stock A weight = 16,000/160,000 = 10%

Stock B weight = 48,000/160,000 = 30%

Stock C weight = 96,000/160,000 = 60%

Stock D is to be bought by replacing some of stock C which means that the weight of stock C in the new beta calculation will be exactly less than 60% by the weight of D.

Assuming the weight of d is x, beta is;

Portfolio beta = ∑(weight of stock * beta)

1.72 = (10% * 1.3) + (30% * 1.8) + ((60% - x) * 2.2) + ( x * 1)

1.72 = 0.13 + 0.54 + 1.32 - 2.2x + x

1.72 = 1.99 - 1.2x

1.2x = 1.99 - 1.72

x = (1.99 - 1.72) / 1.2

x = 0.225

Weight of stock D will be 0.225 which is how much of stock C will have to be sold.

The amount of stock C that should be replaced by D is therefore;

= 160,000 * 0.225

= $36,000

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