Alternative investment hedge fund

Hi Keshav, the solution that you have generated from chatgpt is absolutely incorrect. I am providing you with a detailed solution, so please go through it.

Now let’s start with an example first.

ABC ltd, a hedge fund that has USD500 million of capital(own funds).
Suppose ABC’s underlying positions return is  8%. If it could add
leverage of USD200 million to the portfolio at a funding cost of 4.5%, what would
have been the leveraged return(rL)?

Solution: Lets summarise the data first

Own funds(Vc) = 500

Borrowed funds(Vb) = 200

Asset Return(r) = 12% (It is unleveraged return)

Borrowing Rate(rb) = 4.5%

rL = (Return on both own & Borrowed funds – Interest on Debt)/ Own funds

rL  = [r × (Vc+Vb) – (Vb × rb)]/Vc.

= [12% × (500+200) – (200 × 4.5%)]/500

= [84 – 9]/500 = 0.15 or 15%.

Explanation of the above calculation:

• Investment Total: ABC Ltd invests a total of USD 700 million by using USD 500 million of its own funds and borrowing USD 200 million.
• Portfolio Performance: The entire USD 700 million investment yields a return of 12%, which amounts to USD 84 million.
• Cost of Borrowing: The cost to borrow the USD 200 million is 4.5%, which amounts to an interest expense of USD 9 million.
• Net Gain: After paying the interest on the borrowed funds, the net gain from the investment is USD 75 million.
• Leveraged Return: This net gain of USD 75 million is then compared to the original own funds of USD 500 million to determine the return on the original capital, resulting in a 15% leveraged return.

Now lets get back to the original sum that you have provided from the core readings.

Lets summarize the data first.

Vc = 500

Vb = 200

rL = 15% (In this sum the question has provided the leveraged return i.e. return that the firm has earned from both owned and borrowed capital)

rb = 4.5%

We have to calculate r i.e. unlevered return. Lets find it out.

rL = [r × (Vc+Vb) – (Vb × rb)]/Vc.

⇒ 15% = [(r × 700) – (200 × 4.5%)]/ 500

⇒ 500 × 15% = (r × 700) – (200 × 4.5%) (200 × 4.5%)

⇒ 75 = (r × 700) – 9

⇒ (r × 700) = 75 + 9

⇒ r = 84/700 = 0.12 or 12%.

Explanation:

• We start with the given formula for the leveraged return(rL).
• We substitute the known values into the formula.
• Through basic arithmetic operations—multiplication, addition, and division—we isolate the unleveraged return (r).
• By solving the equation step-by-step, we find that the unleveraged return(r) is 12%.