A FRA is a contract between two parties that determines the interest rate to be paid on a future date for a certain amount of money. The interest rate is fixed at the time of the contract, but the payment is made at the end of the contract period. The payment is based on the difference between the fixed interest rate and the market interest rate on the settlement date. The amount of money is not exchanged, but is used to calculate the payment.
A futures contract is a standardized agreement to buy or sell an asset at a specified price and date in the future. The price is determined by the supply and demand in the market. The futures contract is traded on an exchange and can be bought or sold at any time before the expiration date.
A FRA can be used to hedge the risk of interest rate fluctuations in the future. For example, a borrower who expects to borrow money at a variable interest rate in the future can enter into a FRA to lock in a fixed interest rate today. This way, the borrower can avoid paying a higher interest rate if the market interest rate rises in the future. Similarly, a lender who expects to lend money at a variable interest rate in the future can enter into a FRA to lock in a fixed interest rate today. This way, the lender can avoid receiving a lower interest rate if the market interest rate falls in the future.
A FRA can also be priced and hedged using futures contracts. This is because the futures contracts have similar characteristics to the FRAs, such as the underlying asset, the contract period, and the settlement date. The futures contracts can also reflect the market expectations of the future interest rates. Therefore, a FRA can be priced by using the implied interest rate from the futures contract that matches the FRA period. For example, a 3-month FRA starting in 6 months can be priced by using the implied interest rate from the 9-month futures contract. A FRA can also be hedged by buying or selling the futures contract that matches the FRA period. For example, a borrower who sells a FRA can hedge the position by buying the futures contract, and a lender who buys a FRA can hedge the position by selling the futures contract.
Basic Theory
Forward Rate Agreements (FRAs):
A FRA is a financial derivative that allows parties to lock in an interest rate for a future period. The agreement specifies a notional amount, a reference interest rate, and the future date on which the interest rate will be determined.
Hedging with Futures:
Futures contracts can be used to offset the risk associated with FRAs. By entering into a futures contract that mirrors the underlying interest rate risk, businesses can protect themselves from adverse interest rate movements.
Procedures
- Determine FRA Cash Flow: Calculate the cash flow from the FRA using the formula:
FRA Cash Flow = Notional × (Reference Rate - FRA Rate) × (Days to Maturity / 360) - Calculate Futures Contract Notional:
Futures Contract Notional = FRA Cash Flow / Futures Rate - Execute Hedge with Futures:
Buy or sell futures contracts to offset the FRA cash flow. The number of contracts is determined by dividing the Futures Contract Notional by the size of one futures contract. - Determine the Net Cash Flow:
Net Cash Flow = FRA Cash Flow - (Futures Contract Notional × (Futures Rate - FRA Rate))
Example Scenario
Let’s consider a scenario where a company enters into a 3-month FRA to hedge against rising interest rates. The notional amount is $1,000,000, the reference rate is 5%, and the FRA rate is 4%.
Days to Maturity = 90
FRA Cash Flow = $1,000,000 × (0.05 - 0.04) × (90 / 360) = $2,500
Assuming the Futures Rate is 4.8%, the Futures Contract Notional would be:
Futures Contract Notional = $2,500 / 0.048 ≈ $52,083.33
If one futures contract covers $50,000, the company would need to buy 2 contracts.
Net Cash Flow = $2,500 - (2 × ($52,083.33 × (0.048 - 0.04))) ≈ $2,500
Excel Calculation
Here’s an Excel table demonstrating the calculations:
| A | B | C | D | E | F | G | ||
|---|---|---|---|---|---|---|---|---|
| 1 | Scenario Details | |||||||
| 2 | Notional | $1,000,000 | Reference Rate | 5% | FRA Rate | 4% | Days to Maturity | 90 |
| 3 | Calculations | |||||||
| 4 | FRA Cash Flow | =B2*(C2-D2)*E2/360 | Futures Rate | 4.8% | Futures Contract Notional | =B4/(F2*0.01) | Number of Contracts | =ROUNDUP(G4/F2,0) |
| 5 | =B2*(C2-D2)*E2/360 | =G4*F2 | Net Cash Flow | =B4-(G4*(F2-D2)) | ||||
Ensure that the formulas in cells B4, E4, and G4 are correctly referenced. The Net Cash Flow (cell E5) should match the calculated result in the example scenario.
Other Approaches
- Options Hedging: Consider using interest rate options to hedge against FRA risks.
- Dynamic Hedging: Continuously adjust the hedge ratio based on market conditions to optimize risk management.
