Estimating SOFR Futures Sensitivity to a Post-Meeting Rate Change

Summary

This note explains how the sensitivity of a three-month SOFR rate to an overnight-rate change after an FOMC meeting can be estimated. It compares the days in the post-meeting portion of the contract period with the full contract period. That fraction gives a simple approximation to the contract’s exposure to the changed rate.

The answer then gives a compounding relationship for the three-month rate, using separate overnight rates before and after the meeting, and differentiates it with respect to the post-meeting rate. The derivative consists of the calendar-day fraction and a compounding factor. In the example described, the contract period spans 92 days and the post-meeting period 42 days, producing a fraction of about 0.4565 that is close to the spreadsheet’s value. The approximation ignores weekends, and the response does not show the sensitivities of the one-month contracts or a full portfolio hedge.

Key ideas

• A three-month contract’s sensitivity to a rate change is approximately proportional to the share of its accrual period affected.
• The simple day-count fraction provides a quick estimate of post-meeting rate exposure.
• Compounding adds a factor to the derivative of the contract rate with respect to the post-meeting overnight rate.
• The example ignores weekends, so the day-count approximation has limits.

Tags

# Sensitivity of SOFR Contracts


# Sensitivity of SOFR Contracts












I am reading SOFR Futures and Options by Huggins and Schaller . In chapter 2 , they described a portfolio of 3m and 1m sofr contracts as a hedge from FOMC meeting . The accompanying spreadsheet calculates sensitivity to level and jump but the values are hardcoded. Can anyone help me with the method to calculate such sensitivities ? Thank you !

## Answer by Attack68 (score 2, accepted)

https://quant.stackexchange.com/a/77964

You will observe that your 3month period runs from 16/mar/22 to 16/jun/22 (92 calendar days) and the FOMC period under consideration runs from 5/may/22 to 16/jun/22 (which is the relevant end point in this analysis) (42 calendar days).

42/92 = 0.4565

This already gets very close to the value in the spreadsheet.

It is also quite easy to demonstrate this is very close mathematically. Suppose that $d=1/360$ is a 1-day day count fraction and the overnight rate before the meeting is $r_0$ and the rate after is $r_1$ then the 3M rate, $r_{3m}$ is very closely related (ignoring weekends) by:

$$(m+n)dr_{3m}=(1+dr_0)^m(1+dr_1)^n - 1$$

where n is 42 and (m+n) is 92. Thus,

$$\frac{\partial r_{3m}}{\partial r_1} = \underbrace{\frac{nd}{(m+n)d}}_{\text{fraction}} \underbrace{(1+dr_0)^m(1+dr_1)^{n-1}}_{\text{compounding}} $$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.