Question

You have $100,000 to invest. You can invest in stock of ABC and earn 12% return. You can also borrow at the risk-free rate of 6%. How can you invest (weight) so that you can make 15% return?

Q- How much will you invest in ABC and how much you need to borrow? (in amounts).

Q- Use the same information given in the last problem, how can you make 18% return?

Answer 1

1)

Risk free rate, Rf = 6%

Return of ABC, Ra = 12%

Let Weight of ABC be W and Weight of risk free rate is (1-W)

Required return on portfolio, Rp = 15%

Rp= Ra * W + Rf *(1-W)

15% = 12% * W + 6% *(1-W)

15% = 12% W + 6% - 6% W

9% = 6%* W

W = 9/6 = 1.5

So, (1-W) = 1-1.5 = - 0.5

So Investment in stock ABC = 1.5 * 100,000= $ 150,000

So, (150,000 - 100,000) = $ 50,000 need to be borrowed.

2)

18% = 12% W + 6% - 6% W

12% = 6% W

W = 2

Investment in stock ABC = 2* 100,000 = $ 200,000

So, 100,000 need to be borrowed.