Question

Suppose we have the following current spot rate curve:

• 6-month spot rate: 7%.

• 12-month spot rate: 11%.

Despite the above spot rate curve, an investor firmly believes that the 6-month spot rate in 6 months will be 3%, and that she can borrow and invest $3,080 at any of the current market rates. How much profit can this investor expect to make using the entire borrowed amount if her belief turns out to be true?

Round your answer to 2 decimal places.

Answer 1

1. Borrow $3080 at 7% for 6 months and invest at 12 month spot rate

2. Future value of investment = Amount * (1 + Interest)^Years = 3080 * 1.11 = $3418.80

3. After 6 months pay off the loan taken at the beginning by taking another 6 months loan at 3% for 6 months

4. Total Loan Payment = Amount * (1 + 6 month spot rate) * (1 + forward rate)

Total Loan Payment = Amount * (1 + 7%/2) * (1 + 3%/2)

Total Loan Payment = 3080 * 1.035 * 1.015

Total Loan Payment = 3235.62

5. Profit = Future value of investment - Loan payment

Profit = 3418.80 - 3235.62

Profit = 183.18