Our SOFR futures are ‌Short-Term Interest Rate (STIR) futures. They are financially settled to an index that is calculated from the realized SOFR overnight benchmark rates compounded over the contract’s 3-month reference period. 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. 

The market price of a SOFR futures contract represents the market’s aggregated expectations for overnight interest rates over the reference period covered by the contract’s reference period dates. Like the final settlement price, the live market price is represented as 100 - R, where R represents the expected settlement interest rate. Hence, the price of STIR futures moves up when expectations for interest rates fall and vice versa. Critical dates for each contract run from and including the third Wednesday of the contract’s named month up to, but not including the third Wednesday of the month 3 months after the contract’s name. For example, the March 2025 contract, known as H5, has a reference period running from March 19, 2025, up to but not including June 18, 2025. 

Using the prices of each SOFR futures contract, market participants can derive a projected value of overnight SOFR for each overnight period that the futures represents. For example, if the price of the aforementioned March 2025 (SFRH5) contract is observed at 95.705, that would imply an expected 3-month compounded rate of 4.295%. By using a simplifying assumption that overnight rates remain constant during the reference period, we can decompound the futures-implied 3-month rate to an overnight rate, which would imply day-to-day SOFR overnight benchmark is in the region of 4.2725%. Daily compounding accounts for the difference between 4.2725% and final settlement rate of 4.295%.

Market participants derive a projection curve for overnight SOFR interest rates by observing the market prices of SOFR futures contracts spanning different points along that curve. Using said curve, traders can “price” a range of other interest rate derivative and cash products. Beyond that, should market makers transact in alternative products, they may be able to hedge using the same SOFR futures at prices that are equivalent to their projection curve.

Quarterly IMM SOFR futures are listed on the March cycle, meaning that contract months are March, June, September and December, in a contiguous way.  They span across time without gaps. Such a series of futures is often referred to as a strip. These quarterly IMM contracts are complemented by serial contracts that also cover three-monthly periods though these contracts cover intermediate months at the front end of the curve to add granularity.

SOFR futures are traded on an electronic all-to-all central limit order book (CLOB); they are considered by many to be the primary market for short-term interest rate (STIR) risk transfer and thus the origin of price discovery, making SOFR futures a compelling hedge instrument.

A vanilla interest rate swap (IRS) is an agreement to exchange a set of fixed (known) cash flows for a set of (as yet unknown) floating cash flows. The transaction is defined by its notional amount, value dates (start, end and settlement), the fixed interest rate‌ and the floating interest rate benchmark, complemented by a number of additional conventions regarding payment frequency, day count fraction and holiday calendar. There are acknowledged market conventions for many of these parameters, usually determined by the currency used in the swap.

In the U.S., most IRS that are traded are based on overnight index floating rates and are called overnight index swaps (OIS). We use the terms OIS and IRS synonymously in this paper. Floating leg cash flows are calculated based on money market convention, meaning the interest rate is multiplied by the number of days in the period and divided by the standard number of days in the year, which for USD is rounded by convention to 360. Fixed leg cash flows can also vary by convention. For longer-dated swaps, the USD Semi-Annual Bond basis is common (cash flows paid every 6 months using the 30/360 day count fraction). Shorter swaps commonly use Annual or Quarterly Money Market convention, where cash flows are paid either once per year in the annual case or 4 times for quarterly payments. The money market convention is as for the float leg above, where the day count fraction use is actual/360.

The price of an IRS is usually expressed in terms of the fixed rate. The fixed rate is calculated by the participant pricing the swap as the equilibrium rate where discounted fixed cash flows are equal to discounted floating cash flows. 

Individual Three-Month SOFR (SR3) futures can be thought of as single period interest rate swaps over the value dates that are defined in the specific contract. As we discussed above, the price of a SOFR future is 100 - R, where R is the annualized, implied compounded overnight interest rate over the reference period. Each SR3 has a three-month reference period and the rate R for each future represents the swap rate for that reference period. Here we have an interest rate swap where the fixed and floating legs are 3 months in length and their cash flows are paid out at the end of that period. 

The rate R implied by the future is the equilibrium market price for that contract’s reference period. In other words, it is the market’s current expectation for the aggregated and compounded value of all the overnight SOFR rates during that reference period. Moreover, it is the rate at which market participants can lend or borrow money (or replicate/hedge the cost of lending or borrowing) for that reference period.

This feature makes SOFR futures ideal building blocks for creating a forecast of the yield curve, often known as the projection curve. SOFR futures are very liquid, meaning that the price of each contract is highly representative of the equilibrium market consensus interest rate for each contract’s reference period. Also, consecutive contracts concatenate without gaps so that a strip of futures can provide a very useful view of the projection curve.

Let us compare the market price of a 2-year IMM-dated IRS with quarterly payments on both fixed and floating legs with the array of futures that would be used to build a projection curve over that same period. For example, assume it is April 2025 and we have a set of prices for the following eight quarterly futures, beginning with June 2025 and ending with March 2027 as follows: 

Based on the futures price in the above table, we can envisage a forward yield curve:

Note that each horizontal line represents the aggregated compounded overnight SOFR rates for the contract's reference period. Within the reference period, overnight rates may fluctuate. In this example, we will reference the average rate only. 

Based on these rates, we can relatively simply create a table of discount factors for the end dates of each contract period. For example, the implied interest rate for June 2025 is 4.105%, thus, the discount factor for the end date of the contract is:

Similarly, we can calculate the discrete discount factor for each subsequent contract and thus the cumulative discount factor for the end date of each contract.

Remember our definition of the fixed price from above, where the fixed rate is the equilibrium rate where discounted fixed cash flows are equal to discounted floating cash flows. Also, we recognize that the rates observed for each individual futures contract are the floating rates used to calculate the floating cash flows, which are then discounted. Hence, by utilizing a principal amount of 1 we can aggregate the discounted floating cash flows by summing:

where

i = index of floating period
n = number of floating periods (i.e. 8)
CDF = Cumulative Discount Factor

This sum is shown in the table below as 0.0647505. Armed with the sum of discounted floating cash flows, we now move to solve for the fixed coupon that equates to the same value as the sum of the discounted fixed cash flows.

Similar to the equation for floating, we can see that for fixed cash flows we have:

We can factorize the Fixed Coupon and the daycount fraction denominator, thus:

Leading to:

With numbers from the table:

In our example above, the daycount for each period is identical for both floating and fixed cash flows. In other IRS, this may not be true. In such a case, once the sum of discounted float cash flows has been found, the above calculation can be used, but one would specifically need to use the sum of the discounted fixed days per period.  

Given the prices of futures in the tables above, the market price for an interest rate swap spanning the same contract critical dates as futures, known as IMM dates, is 3.3304%. We can also say that if we were to buy one of each future in the strip, that would be equivalent to receiving fixed on an interest rate swap at 3.3304% and, conversely, if we were to sell one of each future that would be equivalent to paying fixed at 3.3304%

A market maker in this situation might make a price in such an interest rate swap with a bid/ask spread of half a basis point, hence 3.3275/3.3325 could be the quoted price. Should the customer receive fixed (at the market maker’s bid price 3.3275) the market maker could buy futures at the prices in the table to lock-in a receive fixed hedge at 3.3304, thus making a hypothetical profit of 0.29 basis points, predicated on being able to buy each future at the price shown in the table. 

Note that the prices of futures in this example are all valid tradeable prices – those could either be bids in some contracts or offers in others. In reality, market makers will likely spend some effort determining with the greatest degree of certainty where the mid-market is on the futures prices and use those as their inputs to the calculation of the equivalent swap price. It is very likely that the futures prices used to model the projection curve will be at a finer level of granularity than tradeable values. When hedging the swap, the market maker may use some of the captured bid/ask spread in the swap to pay for the bid/ask of the futures hedge.

Further adjustment to pricing is required to account for the convexity bias inherent in pricing interest rate swaps from futures prices. This is due primarily to the fixed value of a basis point when trading standardized futures products versus the variable value of a basis point in an OTC IRS, where the value changes with the outright level of interest rates. This convexity effect will be discussed in more depth in a later section.

Packs and bundles are trade execution strategies. A pack or bundle are not distinct products, rather they are combinations of multiple consecutive futures that are transacted via a single order. Packs are comprised of four consecutive quarterly contracts, covering one-year of curve exposure, while bundles span longer time periods in integer multiples of four contracts, covering between two and five years of exposure.

The price of a SOFR pack or bundle is quoted as the arithmetic average of the price levels of its constituent contracts. We will see how the use of packs or bundles can provide effective hedges for or alternatives to OTC interest rates swaps. 

In our example of interest rate swap pricing above, we consider a 2 year IRS and price that using 8 futures. Those futures could be used to hedge the risk of the swap and can be executed as a strategy, in this case it would be a 2-year bundle. We can easily calculate the arithmetic average of the 8 futures contract prices: 96.675625.

Other swaps of differing maturity can be hedged with different combinations of futures many of which are represented by a standard pack or bundle product depending on the start date and maturity. 

Note that based on product specifications, packs and bundles of SOFR futures are eligible to trade in minimum price increments of 0.25bp. Given the average price noted above, we might expect the market to have bid/ask pricing of 96.675 - 96.6775 (i.e., around the calculated average). In this case, a market maker may elect to buy the bundle at 96.6775 as a hedge against the customer who received fixed in the swap. In such a case, the market maker would spend some of the hypothetical profit from the swap on the hedge. In this case, 96.6775 - 96.675625 = 0.001875 or 0.1875bp. As a result, the net profit from hedging the swap with a bundle of futures is ~0.1bp (0.29 less 0.1875).

In order to hedge our hypothetical 2-year SOFR swap with futures contracts we will want to determine the value sensitivity of the swap to changes in prices of each of the futures contracts. 

This is more commonly known as calculating the DV01. DV01 or dollar value of a basis point is a measure of risk. It is defined as the change in value of a security or instrument for a 1 basis point movement in interest rates. A positive DV01 for a position in a security or instrument is realized for a one basis point movement lower in rates. Hence being long of a bond or receive fixed on a swap would be a positive DV01 position. This is also called being “long the market.”

To accurately determine the DV01 sensitivity, we can independently move the futures prices, calculating the value change of the original swap each time, thus determining the sensitivity to movements in price of each contract.

Using the same example as above, we move the price of the first contract up by 0.01, which represents a fall in the interest rate by 1 basis point.

Note that the projection of ‌ fixed cash flows uses the original swap coupon. As a result of the price change in the futures contract, we see a corresponding change in the value of the sum of the discounted floating cash flows (different float rate and different discounting rate) and a different change in the sum of the discounted fixed cash flows (only a different discounting rate).

The calculated change in value of the swap for $100 million notional is determined by: 

Given that each SFR contract represents $25 per basis point of price movement we can simply divide the change in value of the swap by 25 to arrive at the hedge amount for that in. 

In this case, the swap has risen in value for the movement of the futures hence the hedge in the SFRM5 would be to sell 100 contracts.

We repeat this process, resetting the first contract to its original price and bumping the second contract by 1 basis point:

It is notable that the number of futures required for hedging movement in the second contract is 99 rather than 100 seen earlier in relation to the nearby contract. This is because the effect of discounting on the swap reduces the change in value as we move along the curve, whereas the value of 1 basis point move in futures remains the same at $25 per basis in all contracts near or far-dated. This characteristic is what leads to the convexity bias that we will discuss later.

Continuing the process of bumping each future along the curve independently, we arrive at hedge values for each contract as shown here:

Note that having bumped each futures contract by 0.01 upwards, the calculated coupon rate is 1 basis point lower as we would expect. We also note that the change in value for $100M notional of this swap is $19,480 and the total of the hedges comes out to 779 3-month SOFR futures. Again, this is as expected given that each futures contract is worth $25 per basis point and 779 x 25 = 19,475. Had we received fixed at the original coupon of 3.3304%, our swap would be in profit of $19,480, and if we had hedged by selling the prescribed number of each futures contract at the original prices, our futures hedge would show a loss of $19,475, almost perfectly hedged. As we noted above, a trader would like to receive higher than the calculated mid-market rate and thus in this case the profit from the offer to mid spread would be preserved.

Let’s see what happens if rates move by larger increments.

The table below shows the total profit or loss from holding the following “hedged” position: 

Received fixed on a USD 100m notional of a 2y Jun 25 IMM dated OIS at 3.3304%
Short 779 3-month SOFR futures across 8 consecutive contracts as per above

We assume that all futures move by the same amount for this example thus the P&L from futures can be calculated by simply multiplying 779 x movement in bp x 25. It also follows that a 10bp movement upwards in rates (down in futures prices) will result in a loss of value in the futures position that is equal but opposite to the effect of a 10bp downward movement in rates.

From the table you will note, first, that the value of the swap is opposite in sign while similar but not equal in magnitude. This is due to the effect of compounding being non-linear at different rate levels. Secondly, the change in value of the swap becomes increasingly less equal (although opposite) to the change in value of the futures at each different price level.  

At all price levels, the hypothetical position we created will be profitable as we move away from the original prices, and as we move farther away from those original prices, the deviation becomes exponentially larger. It also follows that a participant who pays fixed on a swap and hedges with the requisite number of futures will lose money as the original transactions move away from their starting point.

The effect that we have just described is known as convexity. More specifically, it is that listed futures contracts do not have convexity while OTC IRS do. Practically, this comes down to the simple observation that the value of 1 basis point movement for a Short-Term Interest Rate (STIR) contract is fixed and constant, (in the case of 3-month SOFR futures it is $25 per contract per basis point) while the value of a 1 basis point movement in an OTC IRS is variable depending on the level of interest rate.

The consequence of this observation is that the DV01 of an OTC IRS changes over different rate levels. If we rerun our hedge analysis over the original swap but varying individual contract price at +100 bp vs. +101bp to the original, we can determine the DV01 of the swap (with the original coupon) at interest rates that are 100bp lower. We see that the DV01 has risen from $19,480 to $19,921 and the futures hedge has risen from originally 779 contracts to 797 contracts.

Earlier, we noted that the effect of convexity is non-linear, increasing exponentially as we move away from original rate levels. This means that the gradual change in the futures hedge as rates move away from their original levels is also non-linear. That said, that change is small relative to the total hedge, such that if we model simple linear change of hedge by taking the difference in hedges, 797 - 779 = 18 half that and then multiply the change of rates and the tick value - 18 x 0.5 x 100 x 25  = 22,500 it should be no surprise that we calculate a number almost identical to the total P&L from “hedged” position at -100bp. Note that this is a linear approximation despite the phenomenon being non-linear. The reason we half the position is to represent the increasing size of the difference in hedges over the movement in rates. That is to say we don’t have an additional short position of 18 contracts for all of the 100bp rate move, but on average we have half that.

This hypothetical position of received fixed in IRS versus short STIR futures, which as we see above generates profit from any move in rates, is considered to be a “long convexity” position. Conversely, the opposite position of paid fixed in IRS versus long STIR futures is considered “short convexity.” Clearly there is benefit from being long of convexity. Invoking the traditional economic maxim of no free lunch, we will not be surprised to learn that one must pay for the benefit of being long convexity. What that means in practical terms is that a receiver of fixed rates would have to receive at a rate that is lower than implied by the original futures prices because the payer of fixed rates would be unwilling to give away the benefit for free. 

The magnitude of the difference between the fixed rate implied by futures prices and the equilibrium price for the swap is a function of volatility. Following any price change, a profit will be created but also a risk position will emerge as the hedge amounts change based on the price changes. After each price change, the long convexity holder can rehedge their position. In the case of price rises (rates going down) the holder of long convexity will increase their short position in futures. If rates then retrace the move back to original levels, the holder will again realize profit on the new hedge ratio. Let’s exemplify this with the extreme movement of 100bp in the example above. 

The long convexity holder realizes ~$22,500 from the movement down in rates by 100bp. At this point, the trader sells an additional 18 futures to re-hedge. If rates fully retrace their move, the swap’s value will return to its original state, i.e., zero PV, and the futures prices will also revert to their original levels, resulting in zero profit – except for the additional sale of 18 contracts. 

If this seems to be very similar to hedging the change of delta in an option, that is precisely what it is. The more volatility there is, the more probability that additional value can be realized and hedged, hence it follows that the value of convexity is a function of volatility as we stated earlier. 

The difference in the price of a swap and the price implied by futures prices is essentially the cost of the premium for buying the embedded option in the convexity position. 

Initial margin (IM) is collateral that is collected by a clearing house when a trade is centrally cleared. The purpose of the collateral is to provide the clearing house with sufficient funds to allow for unwinding and replacing or novation of the original trade in the event of default by the original counterparty. In listed futures and options IM is sometimes referred to as performance bond.

The initial margin of a transaction is typically a function of the volatility of the underlying risk. Clearing houses such as CME Group will publish the current margin costs of the products they clear. We provide an online tool called CME CORE, which can be used to calculate the IM of any of our cleared products, either standalone or in a portfolio.

We can review the results for the convexity transactions that we covered previously. First we will look at futures and IRS independently, then we will review the impact of combining the risk of both positions, which will accrue the benefits of Portfolio Margining. 

Portfolio Margining at CME for rates derivatives is achieved by moving exchange traded derivative (ETD) products out of their normal clearing waterfall and putting them into the same waterfall as over the counter (OTC) traded products. By regulation the treatment of these products is different and as we will see below OTC products tend to have a more conservative treatment due to greater complexity. While moving futures to the more conservative treatment is allowed it does not negatively impact when the futures are offsetting existing risk in the OTC waterfall. 

We will continue to use the example transaction as previously: 

Received fixed on a USD 100m notional of a 2y Jun 25 IMM dated OIS at 3.3304%
Short 779 3-month SOFR futures across 8 consecutive contracts

Let us now break the futures out by contract as follows: 

Similarly, we can review the hypothetical margin of the swap in the CME CORE system:

Our first observation is that the total cost of the initial margin in the futures hedges ($569,910) is approximately 36% of the total cost of the IM in the interest rate swap ($1,568,352). This is mainly because of the standardized nature of futures and the readily available liquidity provided by the central limit order book (CLOB), which supports futures trading, compared to the bespoke nature of IRS and the nature of transaction execution. As a result, futures are afforded a margin period of risk (MPOR) of 1 day under U.S. regulations. In practical terms, this means that a U.S. clearing house is expected to replace the transaction of a defaulted participant 1 day after the last margin collection when a default has been confirmed. By comparison, the more complex nature of IRS means that they are designated to have a 5 day margin period of risk, and in their case a clearing house would have 5 days in which to facilitate the replacement of risk resulting from a defaulted counterparty.

Clearly there is greater risk associated in managing the default of an IRS that can take 5 trading days compared to futures that will take just 1 day.

At this point, we can conclude that if a participant needs to take or manage risk using a directional interest rate derivative, it may be more cost-efficient to use listed futures rather than an OTC IRS. 

We observe that very few participants have simple, one-directional risk management needs. Many of our clients manage interest rate risk using a variety of products, including futures, IRS, options and cash products.

For these clients, the concept of Portfolio Margining becomes relevant and important. Portfolio margining enables a clearing house to combine transactions with offsetting risk profiles and then request IM based on the net risk of the entire profile. If we consider the transactions discussed above in the convexity section, we note that the risk is almost entirely offsetting, in fact, only the convexity risk remains. As such, a portfolio of this nature would attract significantly less IM when considered together than when looking at ‌futures and the IRS separately. 

CME CORE is our go-to resource for modeling both the swap and the futures, allowing us to calculate the IM of the portfolio: 

We can see that the margin is significantly less than if the positions were margined separately. In our example, the total initial margin of the portfolio is $46,161 versus the margin that would be required if Portfolio Margining was not available at $2,138,262. The power of Portfolio Margining is evident, as it can result in nearly a 98% reduction in the margin required compared to considering the trades separately. 

It is worth highlighting that in order to accrue the benefits of portfolio margin at CME Group, a number of criteria need to be satisfied, including:

1. Both the futures and the IRS need to be cleared at CME Group.
2. The participant needs to use the same FCM (Futures Commission Merchant) for both the futures and the IRS.
3. The legal entities of the counterparties to the transactions need to demonstrate the same beneficial ownership. 

CME CORE is able to provide calculations of sample or real portfolios of client transactions to help assess the benefits of Portfolio Margining. Contact your CME Group client representative for further information. 

Margin and capital efficiencies are a frequent topic of conversation among our clients. It is notable that the total savings accruing to clients who benefit from Portfolio Margining in interest rates has risen from just over $2 billion in 2018 to a peak of over $9 billion in early 2025.