Understanding Investing

Designing SOFR Floating‑Rate Notes: Pass the Calculator Test

We believe a floating-rate note tied to SOFR (Secured Overnight Financing Rate) should employ the right mix of technical features to permit investors to independently verify the interest calculations.

Just over two years ago, the Secured Overnight Financing Rate (SOFR) came into being. Designed as a broad measure of the cost of borrowing cash overnight collateralized by U.S. Treasury securities, SOFR is published daily by the Federal Reserve Bank of New York. Securities linked to SOFR, such as floating-rate notes (FRNs), initially appeared in 2018. In 2020, the U.S. Department of the Treasury is exploring development of U.S. Treasury FRN linked to SOFR.

The concept of a SOFR FRN seems fairly simple – the investor earns interest at the SOFR rate plus a spread that was set at issuance. In reality, however, interest calculation conventions combined with SOFR’s 1-day publishing delay tend to significantly complicate the process of calculating the precise amount of interest payment. Issuers have attempted to improve SOFR FRN cash flow certainty by combining a variety of technical features such as lookback, lockout, and payment delay, but each of these calculation tweaks comes with pros and cons.

The Treasury Department recently issued a request for comments on possibly developing a SOFR FRN. At a high level, we believe a Treasury SOFR FRN should employ the right mix of technical features to permit investors to independently verify the interest calculations. We suggest a “calculator test” to help determine which technical conventions are appropriate, useful, and not overly complex.

  • Calculator test: If an investor can calculate the precise amount of interest payment using only a hand-held calculator and a reasonable amount of effort (i.e., without resorting to a spreadsheet or programming), then the calculation is deemed sufficiently simple.

After reviewing developments in the existing SOFR FRN market and the calculation conventions available, we suggest three technical preferences for a potential Treasury SOFR FRN issuance.

Preference #1: Utilize daily compounding calculation rather than simple average

The first SOFR FRN was issued in July 2018, and since then U.S. agencies (e.g., Federal Home Loan Bank System, Fannie Mae, and Freddie Mac) have issued about 86% of all SOFR FRNs by volume, according to PIMCO estimates. Most of these issuances used simple average compounding of SOFR + spread. This means that to calculate the interest payment, an investor tracks the all-in rate for each day and the accrual day weights (e.g., 3 days for Friday’s rate to cover the weekend), then calculates the simple average rate and uses appropriate annualization to calculate the final interest payment. Issuers likely favored the simple average method, at least initially, because SOFR FRNs were a relatively new product and not all back office infrastructure supported the more complex (at the time) daily compounding calculation. However, despite the straightforward concept, simple average compounding almost always required customized (and cumbersome) calculations due to a combination of SOFR’s publishing delay, the “lockout” feature (more on this below), and market holidays. For these reasons, we think simple average calculation fails the calculator test.

Daily compounding is the other method, and when the New York Fed began publishing a SOFR Index in March 2020, daily compounding immediately became much simpler. The SOFR Index is a total return index, precise to 8 decimal places, that reflects the daily compounded returns from investing at the SOFR rate overnight. The initial value was indexed to 1.00000000 on 2 April 2018 (the first day SOFR was published), and the SOFR Index was 1.04145556 on 15 June 2020, implying a rounded 4.15% cumulative return over the roughly two-year period. To calculate the precise interest payment using the daily compounding method and the SOFR Index, an investor first finds the percentage difference of the interest period start and end dates for the SOFR Index, and then annualizes the rate to obtain the compounded SOFR rate (see formula below).

The SOFR Index level as of end date is divided by the SOFR Index level as of start date, and then 1 is subtracted from the result. This result is then multiplied by the result of 360 divided by the number of days that interest accrues. Please see text above for further explanation of this formula.

After obtaining the annualized SOFR rate for the interest accrual period, the investor adds the spread before calculating the final coupon payment, with appropriate annualization. Thanks to the SOFR Index, there is no longer any need to track every daily SOFR rate, and the index takes account of holiday adjustments, compounding day weights, and rounding daily interest precise to the nearest 0.000001%. We believe that daily compounding, only if using the SOFR Index and only if utilizing lookback and backshifted observation period (more on these below), simplifies FRN interest calculation – and definitely passes the calculator test.

Preference #2: Avoid the lockout feature

When assessing the relative advantages (and disadvantages) of simple average versus daily compounding, the devil is in the details. Because the SOFR rate is published with a 1 business day delay, issuers cannot determine the precise amount of interest payment until the very same day of cash transfer. Traders often cannot determine the precise amount of accrued interest at the time of trade, since the SOFR rate for settlement date is not yet available. To cope with these quirks, many SOFR FRN issuers adopted both 2-day lockout and 1-day lookback conventions, along with simple average interest accrual. The 2-day lockout feature “locks” the rate on the third business day before interest payment, and duplicates this rate for the next 2 business days. Hence, issuers can prepare the precise amount of interest payment 3 days in advance.

However, a clear drawback is that the lockout date may fall on month-end, when SOFR tends to spike (typically due to volatility in repo markets), and thus accrue interest for several days based on an unusually high rate. Compared with other conventions, we believe the lockout feature may cause the largest economic distortion, even if it is often negligible. Furthermore, lockout is incompatible with daily compounding – because lockout uses duplicated dates, the investor cannot use the SOFR Index to calculate interest accrual, but must instead perform customized calculations for each interest period. Based on our earlier preference for daily compounding using the SOFR Index, the lockout feature fails our calculator test.

Preference #3: Utilize the lookback feature, combining a 5-day lookback and a 5-day backshifted observation period

We believe that the lookback feature, when combined with a backshifted observation period, helps simplify interest calculations and minimizes economic distortion. The basic version of 2-day lookback is that Friday’s interest accrual uses Wednesday’s SOFR rate. Economic mismatch arises because FRNs accrue 3 days of interest on Fridays, but Wednesday’s SOFR rate only accrues interest for 1 day in the SOFR Index.

In our view, the lookback feature alone is not compatible with the SOFR Index. Recently, a handful of financial SOFR FRN issuances featured 2-day lookback with a 2-day backshifted observation period, meaning Friday’s interest accrual period will still use Wednesday’s SOFR rate but will only accrue interest for 1 day instead of 3 days. The backshifted observation period feature aligns the FRN’s compounding day weights with those used in the SOFR Index. For daily compounding to pass our calculator test, it must be combined with lookback and a backshifted observation period.

Additionally, we believe 5-day lookback and 5-day backshifted observation are better than the 2-day versions. A longer lookback period 1) allows for T+3 and T+4 trades to pre-determine accrued interest at time of trade, 2) allows projection of precise interest amounts 5 days before payment, and 3) allows international investors additional time to determine cash flow and settlement. Although at face value the 5-day mismatch between lookback period and interest accrual date seems like a long time, consecutive and continuous SOFR rates are used in the calculation: Shifting the entire observation period ahead by 5 days in a stepwise manner causes a relatively small distortion compared with other conventions.


In our view, an optimal U.S. Treasury SOFR FRN is one that passes the calculator test, so investors can independently verify the rigorous interest calculations with relative ease. We think the most desirable set of features would encompass daily compounding by referencing the SOFR Index and incorporate 5-day lookback with a 5-day backshifted observation period. Better transparency behind the inner workings of the Treasury SOFR FRN should help reduce illiquidity premium, and could ultimately lower the cost of funding for the Treasury. We believe the Treasury can help increase liquidity in the SOFR cash and derivatives markets by issuing the first Treasury SOFR FRN near the “Big Bang” scheduled for October 2020, when clearinghouses such as the Chicago Mercantile Exchange (CME) plan to shift derivative discounting from Libor to SOFR. This Treasury issue could set the stage and offer helpful guidance for more new SOFR FRN issuances from agencies, supranationals, and corporates.


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