There’s been a lot of talk recently in the Risk Free Rates (RFR) space about conventions to use for compounding calculations, and what the "right" number is.
In an effort to help market participants understand compounded rates we launched www.RealisedRate.com back in July. Since then we’ve received lots of positive feedback, but we also often get asked "What’s the right number?" or "Why doesn't this rate match that rate?"
What lies behind these questions are disagreements within the industry about which calculation conventions to use:
- Differences in approach between asset classes (swaps v Floating Rate Notes (FRNs) loans v mortgages)
- Differences between jurisdictions (e.g. Secured Overnight Financing Rate (SOFR) v Sterling Overnight Index Average (SONIA))
There are even differences within the same asset class and jurisdiction (SOFR FRNs have seen four different models so far - see Alternative Reference Rates Committee’s (ARRC) Comparison Chart).
For those less familiar with the background to all this, a good starting point is the Financial Stability Board’s (FSB) User Guide to Risk-Free Rates (RFR). Regulators are encouraging the market to adopt daily in arrears Risk-Free Rates (RFR) as opposed to forward looking term rates. And having settled on daily in arrears rates, the question of how to calculate averages arises - simple averaging or daily compounding. Consensus seems to be building towards daily compounding as it’s a more accurate reflection of the time value of money, though that still leaves questions on how those compound averages should be calculated, the focus of this note.
UK was leading the way...
So far the UK market has led the way with adopting a standard set of conventions for SONIA compounded averages across product sets, with FRNs following swaps, and loans following FRNs. Early on the UK opted for a 5 day "observation lag" which is a lookback with the day weighting remaining against the Interest Period ("rate shift not weight shift") for both FRNs and loans.
...but the US is catching up
However the US market has become much more vocal on this topic recently. The ARRC released conventions papers in August and November, and the New York Federal Reserve has launched a consultation on publishing SOFR compound averages and an index on their website.
Most recently, an ARRC loans sub-working group is reviewing alternative compounding approaches in order to address requirements of the secondary loan trading market in relation to interest allocation and provide loan platform providers with clear methodologies to code into their systems – expect a recommendation from the working group to the ARRC early in the new year.
The latest ARRC paper lists three models for SOFR FRNs using the Daily Compounding method:
- Lookback - same as the SONIA standard for FRNs and Loans, with  day lag of the daily rate to the earlier Observation Period but with day weighting remaining against the Interest Period
- Observation Period Shift- 'Backward-shifted' model where both rate and day weighting shifts back to the earlier 'Observation Period'
- Payment Delay- in ARRC paper this option includes both a Payment Delay (eg settlement 2 days after Interest End Date) and a Lockout (daily rate 'suspended' for final  days of interest period, referred to as 'Rate Cut-off Date'); note in FSB paper these options are presented separately
The "weight" refers to the weighting in the compounding formula to account for calendar days when the RFR is not published (e.g. at weekends).
Outside of the averaging approach, other details also vary between benchmarks...SONIA and euro short-term rate (€STR) derivatives round to 4 decimal places by default, whereas SOFR rounds to 5 dps. SOFR and €STR use an Actual/360 day count convention, whereas SONIA uses Actual/365. These are well known defaults within the international swaps markets, but may not be so familiar across the wider industry. See the table below for a comparison of conventions.
Does it matter which compounding method is chosen?
In practical terms many of these alternatives don’t result in material differences in the level of interest payments. It’s more about the industry picking one answer and being consistent, to make it easier for everyone.
And we’d argue it’s probably more important to achieve consistency within an asset class across jurisdictions than to achieve alignment between asset classes. For example multi-currency loans would be simpler to implement if they shared common standards across jurisdictions & RFRs. Whether FRNs match Loans in their approach is perhaps less of an issue.
So who's the winner?
Although SONIA developed its standards earlier (#1), it looks like the US market is leaning towards backward-shift (#2), with the results of the recent International Swaps and Derivatives Association (ISDA) Fallback consultation lending further weight to that model. The Payment Delay / Lockout model (#3) seems to have less support, particularly given it could lock in an unexpected spike in daily rates for an additional period.
Whatever the answer, RealisedRate.com will continue to support the conventions as they emerge. Read on below for a brief explanation of the main models with worked examples to show how the rates differ depending upon day weighting.
And our calculator has recently been upgraded to display the most recent SONIA rate from previous business day following publication at 9:00am by Bank of England (BoE) - click through to the SONIA page and register to see the latest rate. As ever, we welcome feedback on the calculator - let us know what you think at email@example.com.
Below we list the main RFRs and conventions, though it should be noted that there is not yet consensus around the FRN and Loans space, and in many cases there are a number of different defaults already in use in different live transactions. Although not exhaustive, below gives a feel for the range of options in play.
For a detailed description of many of these terms see the ARRC Appendix to SOFR FRN Conventions Matrix. See also the original FSB RFR User Guide, the SONIA conventions paper and recent Swiss Average Rate Overnight (SARON) working group material.
Lookback v Backward Shift
The table below shows how Lookback and Backward Shift models result in different compounded rates due to different day weighting in Interest and Observation Periods.
Use our Calculator!
The good news is that our calculator at www.RealisedRate.com supports both these modes via the Advanced option "Reset Type". For Lookback (#1) select "ResetDaysPrior" and for Backward Shift (#2) select "BackwardShift":