Assume 3-month term SOFR on March 31, 2023 is quoted at 4.90%. On that date you observe the following closing prices on actively-traded CME 3-month term SOFR futures contracts:

Contract Closing Price

June 2023 95.10

September 2023 95.40

December 2023 95.70

a. Based on the above, what should the quoted fixed rate in a standard 1-year (4 quarterly payment) SOFR-based interest rate swap with payments in arrears be? Do this by hand and show your work.

b. Assume you took a long position in the swap as the fixed rate payer/floating rate receiver on $100,000,000 of notional principal, at the fixed rate you calculated above, and the forward term structure has remained unchanged. 3 months into the swap, after the first exchange is made, is the value of your position, if you were to mark it to market, positive, zero or negative? Why?

Hint: consider the amount of the first net payment, which is known at inception, and the present value of the remaining payments after the first payment has already been received.