Using Compounded Overnight Rates – a basic guide

As markets move towards overnight rates and away from LIBOR (and other IBORs) there are a variety of ways to transform theses rates into a simple interest rate that can be used for the relevant period, say 1-month. My previous blog on the alternatives for term rates in USD looked at how these could be used to replace LIBOR.

This blog addresses the ways in which the overnight rates can be turned into a rate which is applied for a period such as 1-month (or 3, 6 etc. months). and how these are accessed in the USD SOFR market example.

As many have noted previously, when you use overnight rates to calculate a ‘term’ rate (i.e. one for that period) the actual result is not known until the end of each relevant period. The final rate is not published until the day following the final rate fix and many firms need a number of days to arrange for calculation and payment resulting in a variety of methodologies to accommodate this ‘inconvenience’.

Note that the term rate is not a Term rate such as Term SOFR. A Term rate is set at the start of the period whereas the term rate is not known until the end of the period. The terminology is a little confusing but it is commonly used.

Some basic concepts

Using SOFR as an example, the basic compounding and averaging calculations for each period are:

Some common methods for allowing for payments to be arranged

As mentioned above, the final SOFR rate is not known until the day after it is set and many firms need a few days to arrange for payments. The more common variants are payment delays, lookbacks (observation shifts or ‘lag’) and observation period shifts (‘shift’).

Each variant is in current use and often one is favoured for a particular product.

The difference between the lookback and the observation period shift is important.

A lookback preserves the relevant period and simply uses the ri from a certain number of days prior. This can have the disadvantage that the ri intended for a particular number of days may not be applied to that number in the calculation. This is the main reason a 5-day lookback is often favoured because it has a better chance of alignment than a 2-day lookback.

The observation period shift avoids this problem by moving the whole calculation back a number of days thereby ensuring the ri continue to align with the correct days.

NY Fed SOFR, SOFR Averages and Index publication

The NY Fed publish the Daily SOFR and a number of other calculations each day at 0800 ET. These are excerpts of the screens.

The SOFR rate (0.05%) is per day in the first screen and the 30, 90 and 180-day averages plus the index is also provided.

The ‘Average’ is actually the simple interest rate calculated using the compounding methodology but is referred to as the average. This can be confusing but it is accepted by markets.

The index is the discount factor calculated each day using the SOFR rates and measures the cumulative value since 2 April 2018. The index can be used for the observation period shift methodology by finding the dates and using the formula below. Note the index cannot be used for a lookback because the dates are no longer aligned to the appropriate SOFR rates.

The following tables are snapshots of the NY Fed pages for SOFR and then the Averages and Index.

Does this matter?

The simple answer is ‘not at this time and with these rates’.

In this table I have used 8 decimal places to show there is little difference in the rates. Most product and contracts round to 5 decimal places so there would be no difference. But be aware that the NY Fed Averages are actually the compounded 90-day and do differ from the more commonly used 3-month period.

It is also worth noting that the compounded and averaged calculations of the rate are different.

Read the fine print

It is clearly important to know if the methodology is compounded or averaged because this will almost always lead to different rates. Both calculations are used in USD products.

Likewise, it is important to use the correct dates: 90-day or 3-month as this also matters to the final rate.

So, read the contractual terms very carefully, it does matter!

The next blog will look more into how the methodologies can impact the rates when rates are SOFR higher and/or have greater volatility. In these cases, the choice of lookback or observation period shift can matter.