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July 2, 2022

How Is SOFR Calculated? Birth Of A New Era

LIBOR’s Alternative: SOFR

               With the publishing of LIBOR set to come to an end at the end of June 2023, financial entities are creating and looking for alternatives. These alternatives, listed in table one below, are selected risk-free rates (RFRs) for each of the currencies that were a part of LIBOR. If you are unsure what LIBOR is or just need a refresher, click (HERE) for a post on LIBOR including how it is calculated and some of its history. So how is SOFR calculated? It’s time to dive in.

               As you can tell from the table below, there are two different funding markets that the RFRs are used to price, overnight unsecured transactions, and overnight secured transactions. The unsecured funding market rates reflect the same market as LIBOR was used for. This is where there is no collateral used for the lending process, therefore, these transactions reflect the perceived risk of the lending counterparties as it is their credit that is the basis for the decision on the interest rate at which they can borrow. The overnight secured rate is for repo transactions (secured funding markets). This means that these transactions are collateralized, typically with US treasuries. The RFR for the US Dollar is the Secured overnight funding rate (SOFR), which being rather self-explanatory, is for the secured funding market. To be explicit, SOFR is a measure of the cost of borrowing cash overnight that is collateralized by US Treasuries (this includes various sectors of the repo market).

U.S. DollarSOFROvernight secured repo rate
SterlingSONIAOvernight unsecured rate
Japanese YenTONAOvernight Unsecured rate
EuroESTEROvernight unsecured rate
Swiss FrancSARONOvernight secured repo rate
Table one: Selected RFRs for the five currencies used to report LIBOR as well as the funding market in which they measure[1]

               Originally published in April of 2018, SOFR is administered by the Federal Reserve Bank of New York and is one of the three reference rates that the FRBNY produces in cooperation with the Office of Financial Research. These three reference rates include TGCR (tri-party general collateral rate which is based on trade-level tri-party repo data), the BGCR (Broad general collateral rate which is based on the TGCR and GCF repo), and finally SOFR  (secured overnight financing rate which is based on BGCR and FICC-cleared bilateral repo data)[2].

               SOFR itself is published at 8 AM Eastern Standard Time reflecting the previous business day and is the preferred benchmark of the Alternative Reference Rate Committee (ARRC) for the transition of US dollar risk-free rates away from LIBOR 

SOFR vs. LIBOR

               Since the transactions used to calculate SOFR are repo transactions, typically secured with U.S. Treasuries, they are considered to be risk-free. This assessment is due to the fact that the short-term T-bills that are used as collateral for the transactions are considered to be free of risk on their own. However, remember that LIBOR is for the unsecured funding markets, meaning there is no collateral for the transactions. Now, this isn’t necessarily a bad thing because this means that the counterparty risk of each entity is an active factor in the calculation of LIBOR. So, LIBOR is not risk-free, but it can be used as a measure of the relative counterparty risk within the market.

               Another difference between SOFR and LIBOR is that the primary SOFR rate is calculated in arrears (meaning is it calculated from data that has already been collected, looking into the past) so the interest rate paid on SOFR transactions is what actually accrued during the previous interest period. LIBOR on the other hand is more forward looking and is published at the beginning of the interest period rather than the end. Now, with SOFR, there are various ways SOFR can be calculated depending on the financial contract, meaning there are different ways for the interest to accrue. However, this nuance will be saved for later as it can be subject to an entire post on its own.

Characteristics of SOFR

               Another characteristic of SOFR is that it is fully-transaction based, so there is no expert judgement incorporated into its calculation like it is for LIBOR. Actually, the data provided for the three repo market segments that comprise SOFR is by the Bank of New York Mellon (BNYM and the Depository Trust and Clearing Corporation (DTCC).

               For a comparison to LIBOR, recall the proportion of panel bank submissions for the three levels of the waterfall methodology bar graph that was used in the LIBOR post which is below as well. Take note that the light blue (bottommost) is level one transactions (transaction-based), the black (middle) is level two submissions (transaction-derived) and the dark blue (topmost) is level three submissions (based on expert-judgement). The Below bar graph is for the USD, which is actually the one with the least amount of submissions based off of expert judgement, however, with SOFR, this need for these submissions disappears because of the process in which the rate is calculated. LIBOR is for unsecured lending, which banks are no longer incentivized to utilize as much and the secured repo market.

USD LIBOR panel submission distribution
Report of the proportion of Panel bank submissions used to calculate the test LIBOR rates during the test of the waterfall methodology September 15th, 2017, to December 15th, 2017[3]

               Two other important characteristics of SOFR is that it one, correlates closely to other money market rates and two, covers multiple repo market segments. The latter allows for ease of future market evolution because even as incentives change within the market that change the proportion of market participation in each segment, it is still incorporated into SOFR. Whereas if only one segment of the market is used for calculation, it may run into a similar problem as LIBOR did with not having enough transaction data to base the benchmark rate calculation off of transaction data alone. In other words, if market participants pivot to using a different market segment, it is more likely that the new market segment is already incorporated in SOFR, so the transactions are still used in the calculation of the RFR.

How is Correlates with other Money Market Benchmarks

how is SOFR calculated? overnight money market rates
Overnight money market rate comparison for OBFR (dark blue), TGCR (red), SOFR (light blue) and USD LIBOR (green)[4]

               Above is a chart of four different overnight money market rates for the year of 2017 to show how SOFR correlates with similar rates over the short term. As can be seen, SOFR moves almost identically with TGCR which should be expected, since the market that TGCR measures is also incorporated into the calculation of SOFR. The other two rates OBFR and USD LIBOR are similar to one another in the same way as TGCR and SOFR.

               The Overnight Bank Funding Rate (OBFR) is a measure of wholesale, unsecured funding for overnight bank transactions. OBFR is calculated by a volume-weighted median of transactions in overnight fed funds and eligible Eurodollar and domestic deposit transactions. This is why it closely resembles overnight USD LIBOR; they both reflect overnight bank funding with unsecured transactions.

               On the other hand, the Tri-party General Collateral Rate (TGCR) is a rate for a specific type of repo transaction. General collateral repos are ones where the specific security is not identified until after the terms of the trade are agreed upon. Tri-party repo is where there is a third party that essentially acts as a clearing house for the buyer and seller of the repo. This third-party agent is responsible for selection, custody, and management of the collateral throughout the transaction. As similar to SOFR, the TGCR measures transactions that are secured by U.S. treasury securities. More on the repo market and how it works can be found in the posts linked below if more clarification is necessary.

how is SOFR calculated? rolling 3 month averages
Rolling 3-moth geometric average of overnight money market rates with OBFR (dark blue), TGCR (red), SOFR (light blue), USD LIBOR (green)[5]

               In order to filter out the noise that can happen from day to day throughout markets, we look at a comparison of the same four rates but where we take a rolling 3-month geometric average to see how they correlate on a more long-term basis. As can be seen above, by looking at this longer-term average, the correlation between the rate is much closer, and it is much easier to see the similar rate group together. This closer correlation is due to the day-to-day volatility in the individual rates being averaged out over the rolling three month period.

Money Market Segments Covered By SOFR

how is SOFR calculated? repo market segments
Money Market segments covered by SOFR where SOFR covered segments are surrounded by green rounded box. [6]

               SOFR itself covers multiple sections of the repo market. In each section the nuances of the repo transactions are different and have different incentive structures, therefore, it can be argued that if general incentives change in the future (say legislation passed that changes where banks would like to go for funding, similar to how Dodd-Frank and other GFC related legislation pushed banks away from unsecured markets), then SOFR would incorporate these flows, accordingly, leading to a more robust benchmark.

General Tri-Party (BNYM)

               In the General Tri-party segment for SOFR, data is collected from the Bank of New York Mellon and transactions with the Fed are removed. Meaning the transactions governed by ON RRP (Overnight Reverse Repos) are not included in SOFR. Again, if more clarification on the repo market is necessary, links to repo market posts are in the above sections.

Inter-dealer (GCF Repo)

               The GCF (General Collateral Finance) repo was created to reduce transaction costs and increase liquidity in the inter-dealer repo market. The costs for repo transactions between dealers had a lot to do with their settlement process as the starting legs of the inter-dealer repos had to be settled on an individual, trade-by-trade basis. In brief, GCF repos allowed for the netting of multiple legs in the settlement process within given criteria. More information of GCF specific repos and how it works can be found in the link below are the FRBNY’s website.

https://www.newyorkfed.org/medialibrary/media/research/current_issues/ci9-6.pdf

               With respect to SOFR, duplicate transactions with FICC (Fixed Income Clearing Corporation) as the central counterparty are treated as a single transaction as to not double count transactions. [7]

FICC-cleared

               Contrary to the Inter-dealer repos, transactions between affiliated entities for the FICC-cleared market segment are not removed because counter party names are not available to be calculated into SOFR. This means this market segment can be subject to double counting. However, any transaction with rates below the 25th percentile on a volume weighted basis is removed from the data set in order to reduce the impact that activities in specials could have of the calculation of SOFR.[8] Specials are securities in the repo market that have such high demand relative to other securities that it drives the rates down significantly (high demand bids up price, which lowers yields).

How Is SOFR Calculated?

               SOFR is calculated by taking a volume weighted median of repo transactions over the course of a particular business day. The rate is published at around 8 AM Eastern Standard Time on the following day. For example, the rate published on a Tuesday morning was calculated based off of the transaction data of Monday. This means that SOFR reflects data that has already happened instead of something that is believed to happen in the future.

Payment Structure: In arrears vs. In advance

               When calculating interest, there are two main ways to structure its payment: in arrears and in advance. A combination of the two is also a possibility, however, the two basic ones must be understood first. For an in advance payment structure that is based on an overnight rate, like SOFR, some type of average of the overnight rates observed before the current period would be used to calculate the interest rate for the current period. This is because the interest is calculated at the beginning of the current interest period so that the party paying the interest knows their payment in advance.

An in arrears payment structure, on the other hand, would reference a rate over the current interest period. This way, the overnight rate would reflect what actually happened to the interest rate over the period[9]. A downside to an in arrears payment structure is that the payment amount in not known until the end of the payment period. However, since the interest itself is calculated based off of what has actually happened, it can be argued that interest rate risk is fully hedged because there would be no spread between the interest rate paid and the actual behavior of interest rates throughout the given period.

Averages of SOFR

               One of the main goals of the Federal Reserve is price stability. Along with the fact that SOFR is published by the Federal Reserve Bank of New York, it makes sense the averages of SOFR would be published as well in order to smooth over any daily volatility that would reflect market conditions on a specific day. For this reason, the FRBNY also publishes 30-day, 90-day, and 180-day averages of SOFR as well as a SOFR index on its website. This is important to mention because it is normally one of these averages that are referenced in financial contracts as they are smoother (less volatile) than the daily SOFR rates. An obvious manifestation of this is when SOFR and other overnight repo rates spiked in the fall of 2019 which can be seen in the figure below[10]. Since the spike was short-lived, the averages were not really affected by it on a relative basis.

How is SOFR Calculated? SOFR versus SOFR averages

How is SOFR Used?

               Since SOFR was created to be an alternative to USD LIBOR, the list of financial products in which SOFR is used for are very similar to that of LIBOR. Below is a table[11] of the various financial products using SOFR along with the ARRC conventions and term sheet documentation names for the specific products. Specific ones that should pop out are student loans and adjustable-rate mortgages as these were major ones for LIBOR as well.

                A final thing to note on how SOFR is used in financial contracts is the number of different characteristics that can be modified for a specific purpose. Referencing the table below again, you can see that the SOFR rates differ on their duration, type of averaging, payment structure, and various other attributes that are used (Lookback, observation shifts, payment delays, etc.). If nothing else, this should show to versatility or the amount of financial engineering that can be introduced to a metric or interest rate to fine tune it for a specific purpose.

ARRC conventions and term sheet documentation
Links in image do not work, please go to reference (“An Updated User’s Guide to SOFR”, The Alternative Reference Rates Committee, February 2021, Pg. 24) and see documents from there if you are interested

Final Words

               In a constantly changing financial environment, it is important to keep up, or at least maintain a decent understanding of recent developments. The transition away from LIBOR into SOFR is one of these developments and one where the vast majority of people who will be affected have probably never heard of these rates that could effect their financial well-being. This is most applicable to the products of adjustable-rate mortgages and student loans as those seem to be the most likely to have participants who would not be as well verse in the topic as participants in the other products. This is why financial education is a must and something that a person must take into their own hands.

To your wealth and future,

James Forsythe

References

[1] “An Updated User’s Guide to SOFR”, The Alternative Reference Rates Committee, February 2021

[2] J. Frost, “Introducing the Secured Overnight Financing Rate (SOFR)”, FRBNY ARRC Roundtable (presentation). LINK

[3] Intercontinental Exchange, “ICE LIBOR Evolution” April 25th, 2018. Pg. 19. Link

[4] J. Frost, “Introducing the Secured Overnight Financing Rate (SOFR)”, FRBNY ARRC Roundtable (presentation)

[5] Ibid.

[6] Ibid.

[7] Ibid.

[8] Ibid.

[9] “An Updated User’s Guide to SOFR”, The Alternative Reference Rates Committee, February 2021, Pg. 10

[10] Ibid. Pg. 7

[11] Ibid. Pg. 24

Studied but not directly referenced

“Secured Overnight Financing rate (SOFR) Benchmark Factsheet”, Bank of Scotland LINK

“Secured Overnight Financing Rate (SOFR) frequently asked questions” TRUIST LINK

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James Forsythe


While finishing up my physics degree I became obsessed with learning about macroeconomics and investing. Unfortunately, this is a topic not many people I knew were also interested in, so I decided to create a web-presence that would develop into a community for people with like interests. Through my study, I noticed that a lot of people do not dive into the nuances of the monetary system and do not understand how our system actually works. Not only do I deepen my understanding by creating content about it, but hopefully I will help others understand the monetary system better as well. Please feel free to contact me, I am most active on Instagram and Twitter, both usernames are ( jamesdforsythe )

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