Answer: $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
