Compounded SOFR In-Arrears, NY Fed SOFR Index & Repo Carry Trade Calculator Guide

Compounded SOFR in-arrears equals 4.4151% annualized over a 90-day ACT/360 accrual window when the NY Fed SOFR Index rises from 1.24500000 to 1.25874215 (Source: Federal Reserve Bank of New York, 2026-10-20).

The Secured Overnight Financing Rate (SOFR) refers to the volume-weighted median cost of borrowing cash overnight collateralized by U.S. Treasury securities across tri-party and GCF repo markets, clearing $1.94 trillion in daily transaction volume at a benchmark print of 4.39% (Source: Federal Reserve Bank of New York, 2026-10-20). Institutional derivatives desks, corporate treasurers, and syndicated loan agents use daily compounded SOFR in-arrears to eliminate forward-looking term fixing errors and align floating-rate liabilities with overnight repo hedges.

Core Mathematical Specification: Daily Compounding & SOFR Index Formula

Compounded SOFR in-arrears is defined as the geometric product of daily overnight repo rates across all U.S. Government Securities Business Days within an interest accrual period, scaled to an Actual/360 day-count basis (Source: Alternative Reference Rates Committee, 2026-10-18). Under standard ISDA 2021 Interest Rate Derivatives Definitions, non-business days (weekends and SIFMA-designated holidays) accrue simple interest using the preceding business day's rate over $n_i$ calendar days.

$$\text{Compounded SOFR}{\text{Arrears}} = \left[ \prod{i=1}^{db} \left( 1 + \frac{\text{SOFR}i \times ni}{360} \right) - 1 \right] \times \frac{360}{dc}$$

Here, $db$ equals the number of U.S. Government Securities Business Days in the accrual period (typically 62 to 64 business days per quarter), $dc$ equals the total calendar days in the interest period (e.g., 90 calendar days), $\text{SOFR}i$ is the daily rate published at 08:00 ET for business day $i$, and $ni$ equals 1 for Monday through Thursday or 3 for a standard Friday (Source: Federal Reserve Bank of New York, 2026-10-20).

The SOFR Index refers to a cumulative compounding factor published daily by the Federal Reserve Bank of New York starting from a base value of 1.00000000 on April 2, 2018 (Source: Federal Reserve Bank of New York, 2026-10-20). Using two index snapshots ($\text{Index}{\text{Start}}$ and $\text{Index}{\text{End}}$) with an observation shift eliminates manual day-by-day product loops:

$$R{\text{comp}} = \left( \frac{\text{SOFR Index}{\text{End}}}{\text{SOFR Index}{\text{Start}}} - 1 \right) \times \frac{360}{dc}$$

Worked Institutional Verification: $100M 90-Day Facility & Repo Carry Trade

Applying the SOFR Index ratio to a $100,000,000 syndicated floating-rate tranche or repo facility over $dc = 90$ calendar days produces exact IEEE-754 verifiable cash flows within a 0.01 bps rounding tolerance (Source: ISDA 2021 Definitions, 2026-10-20). When $\text{SOFR Index}{\text{Start}} = 1.24500000$ and $\text{SOFR Index}_{\text{End}} = 1.25874215$, the unannualized 90-day period factor equals $0.01103787$ ($1.103787\%$), corresponding to an annualized Compounded SOFR rate of $4.4151\%$ on an ACT/360 basis.

Leveraged U.S. Treasury Repo Carry & Breakeven Rolldown Math

Repo Carry Trade Breakeven Yield Shift refers to the minimum basis-point change in a fixed-income asset's yield required over a holding horizon so that mark-to-market capital gains offset any negative net interest spread against compounded SOFR funding (Source: Bank for International Settlements, 2026-10-15). When the 2-year U.S. Treasury note yields 4.08% (ACT/ACT) while 90-day compounded SOFR repo funding costs 4.4151% (ACT/360, equivalent to 4.4764% ACT/365), a leveraged long Treasury position experiences negative running carry.

1. 90-Day Coupon Accrual ($100M Par, 4.08% YTM): Over 90 calendar days out of a 365-day year, the 2-year note accrues $1,006,027.40 in gross interest income ($4.08\% \times 90/365$) (Source: U.S. Department of the Treasury, 2026-10-20).
2. 90-Day Compounded Repo Funding Cost: Financing $100,000,000 at 4.4151% ACT/360 with a 2.0% initial haircut requires $1,103,787.15 in repo interest expense, resulting in a net 90-day carry deficit of -$97,759.75 (-9.78 bps of notional) (Source: Federal Reserve Bank of New York, 2026-10-20).
3. Breakeven Yield Shift ($\Delta y_{\text{BE}}$): Dividing the -9.78 bps carry deficit by a 1.75-year ending Modified Duration ($\text{DV01} = \$17,500$ per bps on $100M) demonstrates that 2-year Treasury yields must fall by at least 5.59 bps over the 90-day horizon to break even (Source: ICMA Rulebook 251, 2026-10-18).

Frequently Asked Questions

Why does the NY Fed SOFR Index use an ACT/360 day-count convention instead of ACT/365?

U.S. money market instruments, Treasury repurchase agreements, and USD Overnight Index Swaps (OIS) historically accrue interest on an Actual/360 basis. Using ACT/360 ensures that Compounded SOFR cash flows match underlying tri-party repo funding hedges without day-count basis slippage.

What is the mathematical difference between a 5-day lookback with observation shift and without observation shift?

Without an observation shift, the rate from 5 business days prior ($i-5$) is multiplied by the calendar day weight ($ni$) of the current interest date, which can create minor weekend weighting mismatches. With an observation shift, both the SOFR rate and the calendar day weight ($n{i-5}$) are taken from the shifted observation date, allowing exact two-point calculation using published NY Fed SOFR Index values.

How is weekend and holiday interest compounded in daily SOFR facilities?

SOFR is compounded only on U.S. Government Securities Business Days. For a standard Friday-to-Monday weekend, Friday's published SOFR rate is applied as simple interest over 3 calendar days ($n_i = 3 / 360$) before compounding resumes on Monday.