What it means
In a standard swap, the floating rate is fixed at the start of each period and the payment is made at the end. That gap gives both parties certainty about the amount they will owe long before payment day.
In an in-arrears swap, the rate is observed on the last day of the period and the payment follows straight away. The floating payer does not know the amount until it is due, which exposes it to the actual rate on that day.
Because the rate and the payment are linked to the same date, the expected payment is not equal to the simple forward rate. The relationship between interest rates and bond prices is curved rather than straight, and this curvature, called convexity, pushes the fair rate in arrears above the forward rate.
Traders use these swaps to take a view on rates, for example when they expect the curve to steepen or rates to rise. Companies seldom use them for ordinary hedging because the cash flows are harder to forecast.
Pricing models are more complex than for vanilla swaps, and dealers usually add a margin for model risk. Since LIBOR was phased out, the same structure survives under other benchmarks, although the legacy term remains in older contracts.
Regulators and auditors pay attention to these swaps because the valuation depends on assumptions about how volatile rates will be. Two banks can quote different prices for the same contract if their models treat volatility differently.
For that reason, companies that hold them should ask for independent valuations at each reporting date.
In practice
Real-world examples.
Example
A hedge fund expects short-term rates to rise sharply over a year. It enters an in-arrears swap on $15,000,000 so that each quarter it receives the higher rate observed at the end, rather than the lower rate set three months earlier.
Example
A bank structures a note for a client that pays an in-arrears coupon. The treasury team adds a convexity adjustment to the fixed rate so that the swap is fairly priced at inception.
Example
A risk manager at an insurer reviews a legacy swap and notices that its cash flows are uncertain until payment day. She asks for stress tests showing the payment if rates move 1% in the last week of each period.
Formula
Calculation
Floating payment = Notional x Rate set at period end x Days / 360
Suppose a $20,000,000 swap has a 90-day period. Under a standard swap, the rate fixed at the start is 2.00%, so the payment is 20,000,000 x 0.0200 x 90 / 360 = $100,000. Under an in-arrears swap, rates rise and the rate observed at the end is 2.40%, so the payment is 20,000,000 x 0.0240 x 90 / 360 = $120,000. The in-arrears receiver gains $20,000 for that period, while the payer owes that much more. The gain looks attractive, but the buyer paid for it through a higher fixed rate at the start. If rates had fallen to 1.60%, the in-arrears payment would have been 20,000,000 x 0.0160 x 90 / 360 = $80,000, which is $20,000 below the standard payment.Case study
Seen in the real world.
Oakmont Capital is an illustrative, fictional asset manager that entered a two-year in-arrears swap on $25,000,000. The manager expected a rate rise and received a floating payment set at each period end, while paying a fixed rate slightly above the standard swap rate to cover the convexity adjustment.
Rates rose less than expected, and the manager's gain was smaller than the extra fixed cost it paid. The story is invented, but it shows that the structure is a bet on rates and not a free improvement on a standard swap.
A reviewer from the firm's risk committee later noted that the swap's loss in a falling-rate scenario was larger than anyone had modelled. The committee now requires scenario tests with rates moving both ways before any structured swap is approved.
Watch out
Common mistakes.
- Assuming the rate in arrears is the same as the forward rate. Convexity makes the fair expected rate higher.
- Using an in-arrears swap for simple hedging. The payment is unknown until the last day, which complicates budgeting.
- Believing the change is only a matter of paperwork. The timing alters value and risk.
Questions
People also ask.
What does in arrears mean?
It means the rate is set at the end of the period instead of the start, and payment follows immediately.
Why is a convexity adjustment needed?
Because the link between rates and prices is curved, the average payment is higher than a straight-line calculation suggests.
Who uses these swaps?
Mostly banks, hedge funds and other professional traders with a view on the future path of rates.
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