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Learning Curve: An index — the cure for Sonia calculation headaches

Bank of England fotolia

As UK loan, bond and derivative market participants work to the deadline of December 31, 2021 to stop using Libor, one of the biggest hurdles is how to calculate the new reference rate: Sonia.

François Jarrosson — director, hedging and derivatives, global advisory at Rothschild & Co

Sonia is the Sterling Overnight Index Average, first published in March 1997. Since April 23, 2018 a reformed Sonia has been computed and published by the Bank of England.

Financial markets therefore have some familiarity with Sonia as it has been used since its inception. This has been helped by Sonia being the basis for calculating overnight index swaps (OIS). It has become even more popular since the introduction of cash collateral posting, as OIS is now the market standard for discounting cash-collateralised future cash flows.

Its calculation is therefore widespread and market participants such as banks already have all the systems in place to compute it accurately.

Unfortunately for the rest of the financial world — including corporate treasurers, accountants and auditors — only a few have systems ready to use Sonia regularly and in a widespread way.

Updates will probably soon be available on commercial platforms. But many fear that the calculations may be too opaque for all participants to easily make sense of the figures they are presented with, when it is time to pay a coupon or compute accrued interest.

Calculation details

Sonia is a daily rate, which compounds day after day, including Saturdays, Sundays and bank holidays. It is based on the previous business day’s fixing.

The day count basis is the same as for sterling Libor — the Sonia rate is multiplied by 1 day and divided by 365 days (even in leap years), before being compounded on itself.

This means that to compute a rate over a six month period, one has to download about 130 Sonia fixings and compound them as shown above, while taking care not to miss any weekends and bank holidays. That will include getting the dates right, with a T-5 fixing if it becomes the norm.

This calculation is a challenge in itself and more than 100 times more complex than existing calculations, which use only one Libor fixing for a single coupon period. The formula to compute the coupon is therefore not easily approachable, and this is likely to slow down the widespread adoption of the new reference rate.

It is not difficult to imagine how many staff hours might be lost in setting up spreadsheets to compute the right numbers, all the time spent in reconciliations between parties who have arrived at different results, and the devastating effects of potential disputes arising from miscalculations.

In this light, trying to popularise the use of Sonia seems an insurmountable and potentially very costly task.

Making everyone’s life easier

However, there is a solution to reduce the Sonia calculation complexities for everyone.

At this stage we could identify two potential routes.

The first would consist of one or more market participants making available an online program or calculator (either free or for a fee) that would be accepted by users as accurate and reliable. This is the route suggested by the Sterling FRF Working Group, hosted by the Bank of England, when it suggested the following Infrastructure and Systems Work Stream: “We recommend that a calculator is built to support the adoption of Sonia-based instruments.”

Another solution would be, as we suggest, for a reputable institution to publish a Sonia index as well as as the Sonia rate.

This would solve all the issues around calculation inaccuracies, save time and bring peace of mind to thousands (millions, if this method is rolled out globally) of financiers, treasurers and accountants alike.

The way this index would be used would be very similar to what is already customary with inflation indices. To know the amount of coupon accrued or payable between two dates, one would just need to know the fixing of this Sonia index at time ‘i’ on those two dates (date ‘a’ and date ‘b’) and input them into the following, very simple formula:


Sonia Index at time ‘0’  was potentially set on April 23, 2018, when the BoE started computing the reformed Sonia. Compounding this since then at the relevant Sonia fixings would conveniently provide some past data as well.

Of course, this brings the responsibility of computing the index on to the publisher. But if the Bank of England volunteered to do so, it would not be a greater responsibility than publishing the rate itself and recommending its computation methodology.

This index-based approach not only greatly simplifies the methodology needed for the simple use and calculation of Sonia; it is also simpler than the methodology now applied for Libor, as it does not require computing the number of days for the day count convention. That said, the latter methodology will still be useful when computing the amount linked to any margin payable over Sonia.

In conclusion, with perhaps some tweaks and details, we believe this index-based methodology should be pursued and made available for the benefit of all.

With sterling leading the way on methodology standards, other currencies would follow when adopting an overnight rate to replace Libor. As this methodology would save time for everyone, finance departments could get on with the crucial business of risk management.