Case 065Interest rate derivativesCore

A bank receives fixed 6.60% on a one-week overnight index swap on Rs 500 crore. Overnight fixings are 6.50%, 6.52%, 6.55%, 6.60% and 6.58%, the last applying to Friday, Saturday and Sunday. Compound the floating leg and compute the net settlement.

The situation

Varandha Bank's treasury entered a one-week overnight index swapA swap that exchanges a fixed rate for the compounded average of a published overnight rate over the life of the trade, settled as a single net payment at the end. on a notional of Rs 500 crore, starting on a Monday and maturing the following Monday. The bank receives a fixed 6.60% a year and pays the compounded overnight rate. Both legs use an actual over 365 day count.

The published overnight fixings for the week were 6.50% on Monday, 6.52% on Tuesday, 6.55% on Wednesday, 6.60% on Thursday and 6.58% on Friday. There is no fixing at the weekend, so Friday's rate applies for three days. The operations team must agree the settlement amount with the counterparty.

Your task

Compound the floating leg over the seven days, compute both legs and the net amount, and say who pays whom.

Quick check

Before working it: the floating leg's annualised rate for the week is closest to:

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The compounded floating rate is about 6.5616%, below the 6.60% fixed, so Varandha Bank receives a net Rs 36,823. The fixed leg is Rs 63,28,767 and the floating leg Rs 62,91,944 on Rs 500 crore for seven days. The step people get wrong is the weekend: Friday's 6.58% accrues for three days, so it carries three sevenths of the weight, and each day's interest compounds on the last.

Step 1Why does the weekend count, and how much?

A savings account pays interest every night, including Saturday and Sunday, at whatever rate was set on Friday, because no new rate is published at the weekend. An overnight index swap copies that: interest accrues for every calendar day, and a fixing applies until the next one is published, so Friday's 6.58% is used for three of the seven days. Leave the weekend out and the floating leg is short two days of interest and weighted towards the wrong fixings.

Seven days, five fixings: Friday's rate counts three times6.50%6.52%6.55%6.60%6.58%applies 3 daysweight 3/7MonTueWedThuFriSatSunFriday's fixing covers the weekendfixed 6.60%floating 6.5616%Bank receivesRs 36,823on Rs 500 crore
Over seven calendar days the five overnight fixings compound to 6.5616%, with Friday's 6.58% applying to Friday, Saturday and Sunday, which leaves the floating leg below the 6.60% fixed and the bank receiving Rs 36,823.
Step 2How is the floating leg compounded?

Each day's interest is earned on the previous day's balance including its interest, so the factors multiply. Multiply one plus each fixing times its days over 365, subtract one, and annualise over the seven days: the result is 6.5616%. The day-weighted simple average is 6.5586%; compounding adds only a sliver over one week, which is why the weekend weighting matters far more than the compounding here. Over a three-month swap the compounding term would be larger and could not be ignored.

The relationship
rfloat=[∏i(1+ridi365)−1]×3657d=(1,1,1,1,3)r_{\text{float}} = \left[\prod_{i}\left(1 + r_i \frac{d_i}{365}\right) - 1\right] \times \frac{365}{7} \qquad d = (1, 1, 1, 1, 3)
r_ithe overnight fixing for business day i
d_ithe calendar days that fixing applies to; three for Friday
7calendar days in the swap
What it says in wordsGrow one rupee night by night at each published rate for as many days as it applies, take the growth over the week, and express it as a yearly rate.
Step 3What are the two legs and the net payment?

The fixed leg is 6.60% on Rs 500 crore for seven days: Rs 63,28,767. The floating leg is 6.5616% on the same notional and days: Rs 62,91,944. Only the difference changes hands, so the counterparty pays Varandha Bank Rs 36,823. Using the plain five-fixing average of 6.550% would have produced Rs 47,945, an error of about Rs 11,122 that an operations team would see as a settlement break.

LegRateInterest on Rs 500 crore for 7 days, Rs
Fixed, received6.6000%63,28,767
Floating, paid, compounded6.5616%62,91,944
Net to Varandha Bank36,823
The fixed leg exceeds the compounded floating leg by Rs 36,823, which is the single net payment the bank receives at maturity.

Read the result as a trader would. The bank received 6.60% for a week in which the overnight rate averaged a little under that, so the trade made a small profit; had the central bank's operations pushed overnight rates up mid-week, the same trade would have paid out. The real-world conventions, including which overnight benchmark is used, the day count and any lag between a fixing and its accrual day, are set in the swap's confirmation and the market's standard documentation, and must be checked there rather than assumed.

Where candidates lose it

Candidates average the five fixings and use five days, which gets both the rate and the accrual period wrong. The swap runs seven calendar days and Friday's rate covers three of them.

The second miss is computing interest on each leg and forgetting that only the net amount settles. The answer the operations desk needs is one number and one direction.

What the interviewer asks next

  • Thursday's fixing had been 6.75% instead of 6.60%. Recompute the net and say who pays.
  • Why do banks use overnight index swaps to read the market's expectation of the policy rate?
  • If the swap had run three months, how large would the compounding effect be compared with a simple average?

Company names and figures are illustrative.