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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 !

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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,

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

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  • $\begingroup$ Thank you for sharing the analysis.. I appreciate it $\endgroup$ Mar 27 at 11:39

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