Case 039Interest rate derivativesWarm up
Purna Finance bought a 3x6 FRA at 7.00% on Rs 50 crore. At fixing the three-month rate is 7.60%. How much is settled, when, and who pays whom?
1The situation
Purna Finance, a non-bank lender, knows it will roll Rs 50 crore of three-month borrowing in three months' time, at whatever the three-month benchmark rate is then. Worried that rates will rise, its treasurer bought a 3x6 forward rate agreementA contract that fixes today the interest rate on a notional amount for a future period. It settles in cash on the difference between the contract rate and the market rate at fixing; no loan changes hands. from a bank at 7.00% on Rs 50 crore. The FRA covers the period from month 3 to month 6.
Three months have passed. The three-month benchmark has fixed at 7.60%. Take the interest period as exactly a quarter of a year; real contracts count actual days, so confirm the convention on the confirmation.
2Your task
Compute the settlement amount, say who pays whom and on which date, and show what Purna's borrowing ends up costing.
Quick check
The FRA settles at the start of the interest period, month 3. What is the settlement?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The bank that sold the FRA pays Purna about Rs 7.36 lakh at month 3. The rate gap of 0.60% on Rs 50 crore for a quarter is Rs 7.5 lakh, and because the FRA settles at the start of the period instead of the end, it is discounted for a quarter at the 7.60% fixing. Invested to month 6, the payment offsets the extra interest on the new borrowing, so Purna's cost works out at exactly 7.00%, the rate it locked in.
Step 1What did Purna buy, and why does it gain when rates rise?
Think of paying a caterer a deposit that fixes the per-plate price of a wedding six months away. If prices rise, you are protected; if they fall, you pay the old price anyway. An FRA buyer fixes the rate it will pay on a future borrowing: if the rate at fixing is above the 7.00% contract rate, the seller pays the buyer the difference; if it is below, the buyer pays the seller. No loan passes between them. Purna still borrows Rs 50 crore in the market at 7.60%, and the FRA settles separately in cash, so the two together cost 7.00%. The 3x6 name is the period: starting in three months, ending in six.
Step 2How much is settled, and when?
The rate came in 0.60 percentage points above the contract rate. On Rs 50 crore for a quarter that is Rs 50 crore times 0.60% times 0.25, Rs 7.5 lakh, and that is the extra interest Purna will pay on its loan at month 6. The FRA pays at month 3, at the start of the period, so the Rs 7.5 lakh is discounted for a quarter at the fixing rate: divided by 1 plus 7.60% times 0.25, it is Rs 736,016, about Rs 7.36 lakh, paid by the bank to Purna. Discounting at the fixing rate is not arbitrary: it is the rate at which Purna can invest the payment for the quarter, which is what makes the hedge exact.
| N | notional, Rs 50 crore |
| L | three-month rate at fixing, 7.60% |
| K | FRA contract rate, 7.00% |
| \tau | length of the interest period, a quarter of a year |
Step 3Does the hedge actually deliver 7.00%?
Check it on the dates the money moves. At month 3 Purna borrows Rs 50 crore at 7.60% and receives Rs 7.36 lakh from the bank. It invests that for the quarter at 7.60%, and at month 6 it has Rs 7.50 lakh. Interest on the loan is Rs 95.0 lakh; less the Rs 7.50 lakh from the FRA, Purna's net cost is Rs 87.5 lakh, which is exactly 7.00% on Rs 50 crore for a quarter. Had the rate fixed at 6.50% instead, Purna would have paid the bank and the same arithmetic would still have left it at 7.00%: the FRA removes the upside along with the downside.
| Item | When | Rs lakh |
|---|---|---|
| FRA settlement received | Month 3 | +7.36 |
| Settlement invested for a quarter at 7.60% | Month 6 | +7.50 |
| Interest on the Rs 50 crore loan at 7.60% | Month 6 | -95.00 |
| Net interest cost | Month 6 | -87.50, which is 7.00% a year |
State the limits. The hedge is exact only if Purna's loan is priced off the same benchmark as the FRA; if its lenders charge the benchmark plus a margin that has also widened, the FRA does not cover the wider margin. The bank paying Rs 7.36 lakh is a counterparty, so until settlement Purna carries its credit. And the day count used here, a clean quarter, is a simplification; on the confirmation the period is counted in actual days, which moves the settlement by a few hundred rupees.
Where candidates lose it
The common loss is computing Rs 7.5 lakh and stopping, forgetting that an FRA pays at the start of the interest period. The discount is small, Rs 0.14 lakh here, but it is the one detail that shows the candidate knows when the money moves.
The second is getting the direction wrong. The buyer of an FRA is the future borrower and is paid when rates rise above the contract rate; candidates who think of buying as lending reverse the sign and have Purna paying the bank.
What the interviewer asks next
- The rate fixes at 6.40% instead. Who pays whom, and how much?
- Why is the settlement discounted at the fixing rate rather than the contract rate?
- How would Purna hedge three successive quarters of borrowing, and what single instrument does a strip of FRAs resemble?
- Purna's lenders charge the benchmark plus a margin that rises from 1.0% to 1.5%. What does the FRA not cover?
Company names and figures are illustrative.