High School

A hedge fund wants to take advantage of current interest rates. It projects that the euro is very likely to strengthen over the next month. Furthermore, the fund believes it is very unlikely to see anything less advantageous than the pound to dollar and euro to dollar exchange rates remaining the same, and thus, it will use no change for its projections.

Assume the current exchange rates are $1.1300 per euro, $1.3200 per pound, and 0.85606 pounds per euro. The hedge fund will pay a 0.3% annual interest rate to borrow in pounds with a bank in London. It will receive 1.2% annual interest in a bank in Paris to invest in euro. (Hint: Take the interest rate times 30/360, or approximately 0.083333333, to find the 30-day interest rate.)

At the beginning of the investment period:

1. A hedge fund converts $10,000,000 of its own money into 8,849,558 euro.
2. It borrows 100,000,000 pounds and converts them into 116,814,242 euro.
3. It then invests 125,663,800 (8,849,558 + 116,814,242) euro at 0.1% (1.2% / 12 months), ending with 125,789,464 euro.
4. The hedge fund repays its loan in pounds, needing 100,025,000 pounds (100,000,000 × 1.00025), where 1.00025 = 1 + 0.003/12.
5. Of the fund's remaining euro, it will use 116,843,446 euro to repay the pounds borrowed.

Given the current exchange rates, how many dollars in profit does the hedge fund earn in this case if exchange rates remain the same?

A. $109,000, a profit of 1.09000%
B. $10,109,000, a profit of 101.0900%
C. $96,464, a profit of 0.96464%
D. $127,327, a profit of 1.27327%

Answer :

The hedge fund earns a profit of A. $109,000, making a profit of 1.09000%.

We need to calculate the hedge fund's profit, assuming the exchange rates remain unchanged.

The initial investment of $10,000,000 is converted to euros:

[tex]10,000,000 / $1.1300 = 8,849,558 euros.[/tex]

The hedge fund borrows 100,000,000 pounds and converts them to euros:

[tex]100,000,000 / 0.85606 = 116,814,242 euros.[/tex]

Total euros invested in a Paris bank:

[tex]8,849,558 + 116,814,242 = 125,663,800 euros.[/tex]

Invest these euros at an interest rate of 0.1%:

[tex]125,663,800 * (1 + 0.001) = 125,789,464 euros.[/tex]

Repay the borrowed pounds with interest:

[tex]100,000,000 * 1.00025 = 100,025,000 pounds.[/tex]

Convert euros back to pounds to repay the loan:

[tex]100,025,000 * 0.85606 = 116,843,446 euros.[/tex]

Remaining euros after loan repayment:

[tex]125,789,464 - 116,843,446 = 8,946,018 euros.[/tex]

Convert the remaining euros back to dollars:

[tex]8,946,018 * 1.1300 = $10,109,000.[/tex]

Profit calculation:

[tex]10,109,000 - $10,000,000 = $109,000.[/tex]

The profit earned by the hedge fund in this case is $109,000, which is a profit of 1.09000%.