CME Group is frequently asked the question, “What is the notional value of the Three-Month SOFR futures contracts?" The answer is somewhat more complex than the question. In purely technical terms, the answer would be that the Three-Month SOFR futures contract is not defined by a notional amount, rather it is defined by its IMM index value, which is $2,500 per index point. However, the nuance of the original question pertains to the equivalent notional rather than the definitions laid out in CME rulebook chapter 460.

For many years, short-term interest rate (STIR) market practitioners have been familiar with an understanding that the notional of three-month USD STIR contacts can be approximated to $1 million per contract, and that the basis point value per contract is $25. In this guide, we will review how both these parameters derive from the contract specifications in CME rulebook chapter 460. We will also review an alternative representation for notional or contract equity that derives both from the contract specifications and the reporting practice in other futures contracts.

## Historical context

Three-Month SOFR futures (SR3) have replaced Three-Month Eurodollar futures contracts, which debuted in the early 1980s and were a cornerstone of the U.S. interest rates market though the LIBOR cessation that occurred in the summer of 2023. To provide familiarity for users, many of the features of Eurodollars were carried over to SOFR, including the following characteristics:

**Cash settlement:** An expiring contract is fulfilled by cash settlement, through a mark-to-market to the contract final settlement price. The calculation of final settlement price is based on realized SOFR overnight benchmark rates compounded over the contract reference period. A detailed explanation can be found here.

**Futures based on index numbers:** The price basis for the SR3 futures contract is an index number, known as the IMM Index, which is equal to 100 minus the contract grade market rate of interest per annum. At final settlement, the price of an expiring SR3 contract is 100 minus the compounded SOFR rate over the contract reference period. For example, if the realized, compounded SOFR rate for the contract reference period is 3.748%, the contract’s final settlement will be 96.252.

**Value of the IMM Index:** For SR3 contracts, the value of the IMM Index is defined at $2,500 per index point. From above, we have that the Index number is 100 minus the interest rate; it thus follows that each Index point is equal to 1% of interest. This recognition brings us neatly to our understanding that the value of one basis point (1/100^{th} of 1%) is $25 ($2,500/100).

**Heuristic notional of $1 million:** Many participants have relied upon a heuristic description of the contract mechanism that links to an imaginary notional amount. Based on the understanding of $25 per contract per basis point and the observation that each contract covers three months or a quarter of one year, the $1 million value is derived:

$25 = $1,000,000 x 0.01 pct per year x ¼ (one quarter of one year)

It should be noted that $1 million is not a defined attribute of SR3 contracts per any CME rules.

## Index futures and contract equity

Maintaining consistency with Equity futures contracts, the notional contract size of SR3 futures is:

($ per price point per contract) x (contract price, in points)

Where interest rates are above zero, this results in a contract size less than $250,000.

**SR3 example:** For one SR3 contract priced at 95.670 points (implying a contract interest rate of 4.33 percent per annum), the contract equity would be $239,175 per contract, equal to:

($2,500 per price point per contract) x (93.670 price points).

**ES example:** For one E-mini S&P 500 (ES) futures contract priced at 4,150, the contract equity would be $207,500 per contract, equal to:

($50 per price point per contract) x (4,150 price points).

## Contract Risk

We have noted that the risk of a SR3 contract is defined by the IMM Index in terms of DV01 as $25 per basis point per contract. The heuristic notional of $1 million is also directly inferred from this risk definition. Each contract covers approximately a three-month period, whereby exact specific dates are defined by the IMM calendar (i.e., third Wednesday of contract named month to third Wednesday of month, three months after the contract named month). Each three-month contract therefore can be approximated to one quarter of one year. One basis point of risk for one quarter of one year is defined to represent $25 of risk, which is aligned with the SR3 contract definition, and furthermore, one basis point of risk for one whole year would represent $100, implying a representative notional of $1 million, thus the heuristic notional of $1 million is explained.

However, potential notional calculations for SR3 contracts are further complicated when considering two additional factors:

- First, U.S. money market convention uses a day count basis of Actual/360 -- the consequence of which is that the only time a contract would have an exact heuristic notional of $1 million is if the contract length is 90 days (90/360 = ¼ of one year), which it never is.
- Second, the reference period of Three-Month SOFR contracts can vary in length. Contracts run from the third Wednesday of the named month to the third Wednesday of the month that is three months later. As a result, most commonly the contract length is 13 weeks or 91 days. However, contract dates vary such that the start or end date using the third Wednesday rule can vary between the 15th of the month and the 21st of the month. Therefore, occasionally contract length is either 12 weeks (84 days) or 14 weeks (98 days). In all cases, the exact heuristic notional is not exactly $1 million, despite that approximation being in general use throughout the lifespan of Three-Month Eurodollar futures and carried over to Three-Month SOFR futures.

When calculating risk exposure, readers are reminded that the contract is defined by the IMM Index, not the heuristic notional.

## Comparing DV0^{1} vs. contract equity vs. heuristic notional

Comparison of a $10 million one-year time deposit hedged with futures over similar contract dates. A time deposit or loan at a fixed rate can be hedged by the lender by selling interest rate futures at the time of the deposit. Consider lending money at 4.68% for one year in the amount of $10 million beginning on the third Wednesday of March 2023. Hedged by selling 10 contracts in each of the Three-Month SR3 contracts covering the same one-year period – namely, March 23, June 23, September 23, and December 23. We will use hypothetical contract prices of 95.14, 95.125, 95.37, and 95.645, respectively.

In the case of the loan or time deposit, the notional is $10 million and the DV01 is approximately $1,000.

The contract equity in the futures is calculated as the number of contracts x $2,500 x price:

10 x 2500 x 95.14 + 10 x 2500 x 95.125 + 10 x 2500 x 95.37 + 10 x 2500 x 95.645 = $9.532 million

The resulting calculation here has similar notional to the time deposit that the futures are hedging.

Using the heuristic $1 million notional would yield:

10 contracts x 4 expiries x $ 1 million = $40 million

The observation that the notional is four times larger using the heuristic is a simple function of each contract representing only one quarter of a year rather than the full year, as in the case of the time deposit. The equity notional calculation yields a closer representation of the time deposit notional since that calculation compensates for the length of the futures contract.

In both cases, the DV01 risk of the strip of 40 futures is exactly $1,000, the same as the time deposit.

## Reference

*DV01 is the dollar value of one basis point, where one basis point is equal to 1/100*^{th}of 1%. It measures the change in value of a security or portfolio due to the change in interest rate of one basis point.

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*All examples in this report are hypothetical interpretations of situations and are used for explanation purposes only. The views in this report reflect solely those of the author and not necessarily those of CME Group or its affiliated institutions. This report and the information herein should not be considered investment advice or the results of actual market experience. *