Question

An investor currently holds the following portfolio:
Amount
Invested
8,000 shares of Stock A $16,000 Beta = 1.3
15,000 shares of Stock B $48,000 Beta = 1.8
25,000 shares of Stock C $96,000 Beta = 2.2
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?

Answer 1

8,000 shares of Stock A $16,000
Beta = 1.3
15,000 shares of Stock B $48,000
Beta = 1.8
25,000 shares of Stock C $96,000
Beta = 2.2
Stock D has a beta of 1.0.
If the investor wants his portfolio to have a beta of 1.72, he needs to replace Stock C with Stock D in such way:
1.72 = (1.3*16,000 + 1.8*48,000 + 2.2*(96,000 - x) + 1*x)/160,000
20,800 + 86,400 + 211,200 - 1.2x = 275,200
318,400 - 1.2x = 275,200
1.2x = 43,200
x = 36,000
So, the investor should sell 36,000*96,000/25,000 = 9,375 shares of Stock C to buy shares of Stock D