Interest Rate Instruments
The Interest Rate Instruments domain tests deposit mathematics, day-count conventions, FRAs, short-term interest-rate futures and swaps. The exam rewards candidates who can state the cash flow, the day count and the settlement convention without mixing them up.
Day counts and deposit maths
Interest = principal × rate × days/year. USD, EUR and JPY money markets use ACT/360; GBP uses ACT/365; most bonds use 30/360. The convention changes the answer, so check the currency and instrument before calculating.
FRA mechanics
A FRA fixes a future deposit rate. In a 3x6 FRA, the contract period runs from three months to six months. It is cash-settled at the start of the period by discounting the interest difference. The buyer, typically a borrower, gains if the fixing is above the contract rate.
Futures and swaps
Short-term interest-rate futures are quoted as 100 minus the implied rate; a rise in rates lowers the futures price. A payer swap pays fixed and receives floating; a receiver swap does the opposite. Swap rates are par rates that set the fixed leg's present value equal to the floating leg's.
Worked example
A company buys a 3x6 FRA on USD 10,000,000 at 3.50%. The fixing is 3.80% and the period is 91 days. Interest difference = 10,000,000 × (0.0380 − 0.0350) × 91/360 = USD 7,583.33. Settlement is discounted at the fixing rate for 91 days: 7,583.33 / (1 + 0.0380 × 91/360) = USD 7,511.15. The company receives about USD 7,511 because it is the buyer and rates rose.
Traps that cost marks
- Forgetting to discount the FRA settlement amount.
- Using 365 days for USD instead of 360.
- Assuming a rise in the futures price means rates rose.
- Mixing up payer and receiver in a swap.
- Ignoring the stub period in a swap.