FRA stands for Forward Rate Agreement, which is a contract between two parties to exchange interest payments on a notional amount at a fixed rate (the FRA rate) for a specified period of time in the future. The FRA rate is agreed upon at the start of the contract, and the notional amount is never exchanged. The FRA is settled in cash at the beginning of the contract period, based on the difference between the FRA rate and the prevailing market rate (the settlement rate) at that time.
FRA Arbitrage is a strategy that exploits the difference between the FRA rate and the implied forward rate, which is the expected market rate for the contract period derived from the current spot rates. If the FRA rate is higher than the implied forward rate, the arbitrageur can sell the FRA (lend at the FRA rate) and borrow at the spot rate for the waiting period and the contract period. If the FRA rate is lower than the implied forward rate, the arbitrageur can buy the FRA (borrow at the FRA rate) and lend at the spot rate for the waiting period and the contract period. In either case, the arbitrageur can lock in a risk-free profit by receiving more interest than paying.
Basic Theory:
A Forward Rate Agreement (FRA) is a financial contract that allows parties to lock in an interest rate for a future period. It involves an agreement between two parties to exchange a fixed interest rate for a variable one at a specified future date. FRA arbitrage occurs when market conditions create an opportunity for a risk-free profit.
Procedures:
- Identify Market Discrepancies:
- Analyze the market to identify discrepancies between the implied forward rate and the expected future interest rates.
- Determine Arbitrage Opportunity:
- If the implied forward rate is lower than the expected future rate, there is a potential for FRA arbitrage.
- Execute FRA Contracts:
- Enter into FRAs to take advantage of the discrepancy. Borrow or lend funds at the current market rate.
- Cash Flow Analysis:
- Calculate the cash flows associated with the FRA contract and the borrowing/lending of funds.
- Profit Calculation:
- Determine the net profit or loss resulting from the FRA arbitrage.
Comprehensive Explanation:
Let’s consider a scenario where the current 6-month interest rate is 4%, and the 12-month interest rate is 5%. An FRA with a notional principal of $1 million and a 6×12 tenor (maturity in 6 months) is trading at an implied forward rate of 4.5%.
Scenario with Real Numbers:
- Identify Market Discrepancies:
- Implied Forward Rate (IFR) = 4.5%
- Expected 6-month rate in 6 months (EFR) = 5%
- Determine Arbitrage Opportunity:
- IFR < EFR, indicating an opportunity for FRA arbitrage.
- Execute FRA Contracts:
- Enter into a 6×12 FRA to receive the fixed rate of 4.5% and pay the variable rate (expected 6-month rate in 6 months) of 5%.
- Cash Flow Analysis:
Period Cash Flow from FRA Borrowing/Lending Net Cash Flow 0 – +$1,000,000 +$1,000,000 6 +$22,500 (FRA) – +$22,500 12 – – – - Profit Calculation:
- Net Cash Flow at maturity = -$22,500
- The investor has made a risk-free profit of $22,500.
Excel Formulas:
- For FRA Cash Flow:
=PV(EFR, n, 0, -notional) - For Borrowing/Lending Cash Flow:
=PV(IFR, n, 0, notional) - Net Cash Flow:
=SUM(FRA Cash Flow, Borrowing/Lending Cash Flow)
Other Approaches:
- Multiple FRAs: Instead of a single FRA, investors can use multiple contracts with different maturities to optimize returns.
- Adjusting Notional: Varying the notional principal in the FRA can impact the overall profitability of the arbitrage strategy.
