As a hypothetical example, Company A (the buyer) and Bank B (the seller) have entered into an FRA with a notional amount of 10 billion yen and a contract rate of 2% a year. The period is 0.5 years long, and the benchmark rate set on the settlement date is 4% a year. The settlement amount is the interest difference that would be paid at the end of the period, discounted at the benchmark rate, and it is paid on the settlement date. Which payment is made on the settlement date?
Quiz: Interest Rate Forwards and Futures
Last reviewed: September 25, 2026
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5 questions to check your understanding of the chapter “Interest Rate Forwards and Futures”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: B
The buyer of an FRA is in the same position as a party that pays the contract rate and receives the benchmark rate. The benchmark rate came in above the contract rate, so the seller, Bank B, pays the buyer, Company A. The interest difference at the end of the period is 10 billion yen × (4% − 2%) × 0.5 = 100 million yen. Dividing this by 1 + 4% × 0.5 = 1.02 gives about 98.04 million yen (98,039,215.6… yen), which is paid on the settlement date. If Company A invests the 98.04 million yen at 4% a year for 0.5 years, it grows to 98.04 million yen × 1.02, or about 100 million yen. This has the same value as receiving 100 million yen at the end of the period.
If the benchmark rate is below the contract rate, the direction reverses. For example, if the benchmark rate is set at 1% a year, the interest difference is 10 billion yen × (1% − 2%) × 0.5 = −50 million yen. Dividing by 1 + 1% × 0.5 = 1.005 gives about 49.75 million yen, which Company A pays to Bank B. "Company A pays Bank B" is the direction when the benchmark rate falls. 100 million yen is the interest difference at the end of the period before discounting. About 96.15 million yen is 100 million yen divided by 1 + 4% = 1.04. It leaves out the 0.5-year period length when discounting.
Learn more: Forward Rate Agreements (FRA)
Question 2
As a hypothetical example, Company A plans to borrow 10 billion yen from Bank C for 6 months, starting 6 months from now. The loan rate will be the 6-month benchmark rate at that time. Company A has bought an FRA from Bank B covering the 6-month period that starts in 6 months, with a notional amount of 10 billion yen and a contract rate of 1% a year. Any amount paid or received on the settlement date can be invested or funded at the same benchmark rate until the maturity date. Which statement about Company A is correct?
Answer and explanation
Answer: C
With an FRA bought, the combined cost with the loan is fixed at the contract rate. If the benchmark rate rises to 2% a year, the loan interest is 10 billion yen × 2% × 0.5 = 100 million yen. At the same time, Company A receives about 49.50 million yen on the FRA on the settlement date, which grows to about 50 million yen when invested at 2% until the maturity date. The net cost is about 50 million yen (1% a year), about 50 million yen less than without the FRA. If the benchmark rate falls to 0.5% a year, the loan interest is only 25 million yen. At the same time, Company A pays about 24.94 million yen on the FRA on the settlement date, which is about 25 million yen in value at the maturity date. The net cost is again about 50 million yen (1% a year), about 25 million yen more than without the FRA.
If you assume the cost falls by as much as the loan interest does, the first option looks right. But the FRA payment rises by the same amount, so Company A gives up the benefit of lower interest payments when rates fall. An FRA settles the difference whether the benchmark rate is above or below the contract rate, and neither side is excused from paying. The notional amount is only used to calculate the difference and is not exchanged. The 10 billion yen that Company A borrows is a separate loan from Bank C, not part of the FRA.
Learn more: Forward Rate Agreements (FRA)
Question 3
As a hypothetical example, suppose you buy 4 contracts of Osaka Exchange's 3-Month TONA Futures at a price of 99.250. These interest rate futures are priced at 100 minus the annualized rate from compounding TONA (Tokyo Overnight Average Rate) over three months, and a price move of 0.01 changes the profit or loss on one contract by 2,500 yen. That rate is set at 0.950% a year, and the final settlement price is 99.050. What is the profit or loss?
Answer and explanation
Answer: A
Buying at 99.250 amounts to trading the rate for the period at 0.750% a year. When the rate rises to 0.950% a year, the price falls to 99.050 and the buyer loses. The price difference is 99.050 − 99.250 = −0.200, which is 20 times 0.01. The profit or loss on one contract is −20 × 2,500 = −50,000 yen, a loss of 200,000 yen on 4 contracts.
If the rate falls, the result reverses. For example, if the rate is set at 0.550% a year and the final settlement price is 99.450, the price difference is +0.200 and the 4 contracts make a profit of 200,000 yen. For the side that sold the same futures at 99.250, the profit or loss has the opposite sign, so it makes a profit of 200,000 yen when the rate rises to 0.950% a year. A profit of 200,000 yen is the answer you get if you think the price rises when the rate rises, and it is the seller's result. A loss of 50,000 yen is the amount for one contract, leaving out the 4 contracts. A profit of 50,000 yen gets both the direction and the number of contracts wrong.
Learn more: Interest Rate Futures
Question 4
Both interest rate futures and FRAs lock in today the rate for a future period. Which statement correctly describes a difference between them?
Answer and explanation
Answer: D
Interest rate futures are exchange-traded derivatives, and their profit or loss is calculated through daily mark-to-market. After the reference period ends and the actual rate is known, they are cash settled on the difference between the final settlement price and the traded price. FRAs are bilateral OTC derivatives. When the rate is set at the start of the period, a single payment is made, equal to the interest difference that would be paid at the end of the period, discounted to that date.
The first option describes an FRA. For interest rate futures, the size of one contract and the quarterly reference periods are set by the exchange's contract specifications. It is in an FRA that the parties agree on the notional amount and the period. The second option has it the other way around: it is interest rate futures whose specifications are set by the exchange. An FRA is a bilateral trade between the parties and fixes a rate (the contract rate). The third option describes how an FRA is settled.
Learn more: Interest Rate Futures
Question 5
As a hypothetical example, a financial institution holds 6 billion yen face value of 10-year JGBs. Their DV01 is 0.096 yen per 100 yen of face value. The institution hedges the interest rate risk on these bonds by selling 10-year JGB Futures (contract unit 100 million yen face value). The DV01 of the cheapest-to-deliver (CTD) issue is 0.06 yen per 100 yen of face value, and the CTD's conversion factor (CF) is 0.75. Using the method that matches DV01, how many contracts are sold?
Answer and explanation
Answer: B
DV01 is the change in price when the rate moves by 1bp. The futures price is roughly equal to the CTD price divided by the CF. The DV01 of the futures is therefore the DV01 of the CTD ÷ CF, or 0.06 ÷ 0.75 = 0.08 yen. The DV01 of one futures contract (100 million yen face value) is 100 million yen × 0.08 ÷ 100 = 80,000 yen. The DV01 of the bonds held is 6 billion yen × 0.096 ÷ 100 = 5.76 million yen. The number of contracts to sell is 5.76 million ÷ 80,000 = 72.
If the rates on both the bonds held and the CTD rise by 10bp, the bonds fall in value by 5.76 million yen × 10 = 57.6 million yen. The short position of 72 futures contracts makes a profit of 72 × 80,000 yen × 10 = 57.6 million yen, so the total is 0. If rates fall by 10bp, the 57.6 million yen loss on the futures offsets the 57.6 million yen gain on the bonds. The hedge limits losses, but it also gives up the gain when rates fall. Here the DV01 is assumed to be constant, and the two rates are assumed to move by the same amount. In practice, the rates on the 10-year JGBs held and on the CTD do not always move by the same amount, and the total moves away from 0 by that difference.
The 60 contracts answer matches face value instead of DV01 (6 billion yen ÷ 100 million yen). The 96 contracts answer uses the CTD's DV01 of 0.06 yen as the futures DV01 without dividing by the CF (5.76 million ÷ 60,000). The 128 contracts answer multiplies by the CF instead of dividing by it (0.06 × 0.75 = 0.045 yen, 5.76 million ÷ 45,000).
Learn more: JGB Futures