The price of any CME Three-Month SOFR (SR3) futures contract is quoted and dealt in terms of the familiar IMM Index -- 100 minus R – where R is the contract interest rate. After trading terminates in an expiring contract, the final settlement price is determined by the exchange as 100 minus R, with R set equal to compounded daily Secured Overnight Financing Rate (SOFR) interest during the contract reference quarter, expressed as a money market interest rate per annum.1
Example: For June 2018 SR3 futures (SR3M8), the contract reference quarter spans 91 days, starting on (and including) the third Wednesday of June, 20 June 2018, and ending on (and not including) the third Wednesday of September, 19 September 2018.
The contract interest rate conveys information about expected future values of SOFR --
In what follows, three examples illustrate why this is so and how it works.
The Federal Reserve Bank of New York (FRBNY) produces a SOFR value for every weekday, excluding those days flagged by the Securities Industry and Financial Markets Association (SIFMA) as US government securities market holidays.2 The final settlement price of an expiring SR3 contract is based on SOFR values for all US government securities market business days (business days) occurring within the contract reference quarter. The compounding scheme employed in determining the final settlement price adheres to broadly accepted industry conventions,3 according to which:
Example: For any standard weekend, the SOFR value for Friday, r, applies as simple interest to the ensuing Saturday and Sunday. Thus, the interest amount that accrues over the weekend is assumed to equal Principle Amount x (r/100) x (3/360).
The link between the contract interest rate and expected future values of SOFR is rooted, in turn, in the method for setting the SR3 contract final settlement price.
To see how, consider the composition of the contract reference quarter for SR3M8. It comprises:
The resultant relationship between the contract interest rate R and the hypothetical constant daily SOFR value during the contract reference quarter, r, is:
(1+(4/360)(r/100)) x (1+(3/360)(r/100))12 x (1+(2/360)(r/100)) x (1+(1/360)(r/100))49
On the day before its reference quarter begins, SR3M8 is priced at 98.075 points, making a contract interest rate of 1.925 pct (equal to 100 minus 98.075). Setting R = 1.925, the solution of the polynomial above is r = 1.92043 pct, the implied constant daily SOFR during the reference quarter.
FRBNY has published SOFR values for each of the first two days of SR3M8’s reference quarter:
Wed, 20 Jun = 1.87 pct
Thurs, 21 Jun = 1.87 pct
Assume SR3M8’s daily settlement price is 98.065 points on Thursday, 21 June, making a contract interest rate of 1.935 pct (equal to 100 minus 98.065). Each of the two published SOFR values applies to a true overnight interval (with no intervening weekend days or holidays), leaving 47 true overnight intervals in the remainder of the reference quarter. Thus, the relationship between the contract interest rate and hypothetical constant daily SOFR for the remaining 89 days in the reference quarter (r89) is:
x (1+(4/360)(r89 /100)) x (1+(3/360)(r89 /100))12 x (1+(2/360)(r89 /100)) x (1+(1/360)(r89 /100))47
where entries in red font indicate known information (either the SR3M8 contract interest rate or published daily SOFR values). Solving the polynomial – the entries in black font – produces the implied expected constant daily SOFR for the rest of the reference quarter, r89 = 1.93174 pct.
If, as before, we partition the general polynomial relationship to reflect those intervals for which we possess information (in red font) and those for which we do not (in black font), we can estimate the implied constant daily SOFR value (r79) that market participants collectively expect to prevail during the remaining 79 days of the reference quarter:
(1+(1/360)(1.87/100))2 x (1+(3/360)(1.92/100)) x (1+(1/360)(1.91/100)) x
x (1+(1/360)(1.90/100))2 x (1+(1/360)(1.93/100)) x (1+(3/360)(2.12/100)) x
x (1+(4/360)(r79 /100)) x (1+(3/360)(r79 /100))10 x (1+(2/360)(r79 /100)) x (1+(1/360)(r79 /100))43
The solution is r79 = 1.914675 pct. Exhibit 1 illustrates.
For SR3 futures for a given contract month, the final settlement price is the contract-grade IMM Index, 100 minus R, with R evaluated on the basis of realized SOFR values during contract reference quarter:4
|R||=||[ Πi=1…n ( 1+(di /360)(ri /100) ) – 1 ] x (360/D) x 100|
|n||=||Number of US government securities market business days in the reference quarter|
|i||~||Running variable indexing US government securities market business days during reference quarter|
|Πi=1…n||denotes the product of values indexed by the running variable, i = 1,2,…,n.|
|ri||=||SOFR value for ith US government securities market business day|
|di||=||Number of calendar days to which ri applies|
|D||=||Σi di (ie, number of calendar days in reference quarter)|
Recast in the form we’ve used in the preceding examples, this becomes:
1 + (D/360)(R/100) = Πi=1…n ( 1+(di /360)(ri /100) )
For any instance in which we know the contract interest rate R and the values of ri for the first k business days of the contract reference quarter, we can obtain the implied expected constant value of daily SOFR for the reference quarter’s remaining n-k business days by solving the following equality for r:
( 1 + (D/360)(R/100) ) = Πi=1…k ( 1+(di /360)(ri /100) ) x Πi=k+1…n ( 1+(di /360)(r /100) )
( 1 + (D/360)(R/100) ) / Πi=1…k ( 1+(di /360)(ri /100) ) = Πi=k+1…n ( 1+(di /360)(r /100) )
where, as before, entries in red font indicate information we know, and entries in black font impound the variable r for which we solve.
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