Quantifying and Hedging Equity Financing Risk
Introduction
The Alternative Reference Rate Committee (ARRC) was formed in 2014 in response to recommendations from the Financial Stability Board (FSB) to address weaknesses in USD LIBOR. Following consultation in 2017, the ARRC selected the Secured Overnight Financing Rate (SOFR) as its recommended alternative to Libor. In 2020 a formal end date for the publication of USD LIBOR was announced and regulatory guidance encouraged the transition away from LIBOR. USD LIBOR ceased to be published after the end of June 2023, by which time all products had transitioned to the new benchmark.Since then, the equity derivative marketplace has been split in using CME Fed Fund futures and CME SOFR futures in hedging interest rate risk within equity derivatives with varying results.
By defining rate attributions, rate risk derived from equity derivatives can be better quantified and hedged. An October 2023 research piece by the New York Fed highlighted the interest rate derived from option box spreads trades, known as the box rate, as an alternative reference rate. Index Options Box Spreads as a Financing Tool from April 2024 explains the E-mini S&P 500 option box spread structure, liquidity and market trends. Similar to the work by Binsbergen et al (2023), this paper finds the convenience yield, the spread between the box rate from E-mini S&P 500 option box spreads and the SOFR forward curve, to be persistent and quantifiable.
During the time period analyzed, E-mini S&P 500 total equity roll cost is shown to have a stronger relationship to the box rate from E-mini S&P 500 option spreads than the 3m SOFR forward curve alone. This paper decomposes total equity roll costs into three buckets: 3m SOFR forward curve, the convenience yield and equity repo premium. Similarly, Adjusted Interest Rate S&P Total Return future calendar spreads are shown to capture both the convenience yield and equity repo premium in hedging the implied E-mini S&P 500 equity roll premium over the 3m SOFR forward curve. This paper concludes with an empirical example showing that the Adjusted Interest Rate S&P 500 Total Return (EFFR) calendar spreads can be used in conjunction with interest rate hedges to reduce equity financing risk. For more information, read the FAQ on AIR TRF Globex calendar spreads. This strategy can be useful to index arbitrage traders, relative value and multi-strategy hedge funds, traditional asset managers, managed futures (CTAs) and real money accounts.
The importance of a reference rate
The ideal reference rate is liquid and transparent in capturing risks associated with the currency, term, collateral, credit and market risks. SOFR is an ideal benchmark rate because it looks at actual U.S. Treasury repo transactions, accounting for collateralized lending. CME 3-month SOFR futures are used by many market participants to build their forward SOFR curve.
Despite having similar economics, Index option box spread structures have a different risk profile to SOFR. Index Option Box Spreads as a Financing Tool gives a detailed analysis of how a box spread is similar to a discount bond. By simultaneously buying and selling two synthetic forwards with the same expiration but different strikes, the payout at expiration is defined by the difference in strikes. Index option box spreads are guaranteed by a systematically important financial institution (SIFI) with a strong credit rating, but the underlying derivative financial instrument valuation can vary from theoretical levels day to day, thus necessitating variation in margin to be posted to CME Clearing.
CME Clearing’s risk management framework encompasses a broad spectrum of risks to be managed, including but not limited to, collateral, credit, market risk, model risk, stress testing and default management. These different characteristics create the existence of a “convenience yield,” a premium lost in holding cash-like instruments over a more complex derivative instrument.
Index option box spreads as an investment
Index option box spreads also benefit from the liquidity of the E-mini S&P 500 market (sometimes abbreviated using the Globex code, “ES”). E-mini S&P 500 option box spreads are actively blocked in accordance to Rule 526 and traded electronically through a central limit order book (CLOB) on Globex, as highlighted in Index Options Box Spreads as a Financing Tool.
The two-year historic box rate from E-mini S&P 500 option box spreads is visualized in Figure 1. The total implied E-mini S&P 500 box rate is broken down between the underlying benchmark interest rate (3-M SOFR forward curve) and the convenience yield. This demonstrates Index option box spread buyers receive a premium over the SOFR forward curve in carrying derivative risk. Achievability of option box spread financing rates as an investment strengthens the case for using this as a reference rate.
Figure 1: Two-year average E-mini S&P 500 box rate broken down into convenience yield and SOFR
Rate Attribution
Chart 1 shows that the 3-M convenience yield generated from E-mini S&P 500 option box spreads over 3-M SOFR forward curve from February 2024 through March 2025 ranged between zero and 110 bps, averaging 35.5 bps. This premium aligns with the long-term average found by Binsbergen et al (2023). Interestingly, December 2024 funding pressures drove the convenience yield to levels not seen since the 2008 financial crisis.
Chart 1: 3-M E-mini S&P 500 option box spread rate, 3-M SOFR forward curve and convenience yield
Chart 2 compares 3-M SOFR forward curve, E-mini S&P 500 futures implied roll costs and the 3-M box rate from E-mini S&P 500 option box spreads. It is intriguing that in December 2024 both the implied financing costs from E-mini S&P 500 futures rolls and the box rate from E-mini S&P 500 option box spreads both initially increased as the Federal Reserve cut interest rates and 3-M SOFR forward curve fell. This phenomena will be discussed further in the next section.
Chart 2: E-mini S&P 500 futures roll, 3-M SOFR forward curve, 3-M E-mini S&P 500 option box spread rate
In Table 1 we compare the quarterly changes of E-mini S&P 500 futures implied rolls, 3-M box rates from E-mini S&P 500 option box spreads and 3-M SOFR forward curve. As the visual in Chart 3 indicates, changes in E-mini S&P 500 implied roll costs may be better explained by changes from the box rate from E-mini S&P 500 option box spreads (89% correlation) relative to changes in 3-M SOFR forward curve (57% correlation).
Table 1: E-mini S&P500 futures roll, 3-M SOFR forward curve, 3-M E-mini S&P 500 option box implied correlation of quarterly changes
| 90d ES Box rate | 3m Term SOFR | Total ES Roll Cost | Δ 90d ES Box Rate | Δ 3m Term SOFR | Δ ES Roll implied rate | |
|---|---|---|---|---|---|---|
| Dec-22 | 4.77% | 4.507% | 4.95% | |||
| Mar-23 | 4.91% | 4.942% | 5.14% | 0.14% | 0.44% | 0.19% |
| Jun-23 | 5.54% | 5.243% | 5.60% | 0.64% | 0.30% | 0.45% |
| Sep-23 | 5.70% | 5.408% | 5.86% | 0.16% | 0.17% | 0.27% |
| Dec-23 | 5.68% | 5.377% | 5.99% | -0.02% | -0.03% | 0.13% |
| Mar-24 | 5.60% | 5.321% | 5.95% | -0.08% | -0.06% | -0.04% |
| Jun-24 | 5.80% | 5.343% | 6.06% | 0.20% | 0.02% | 0.11% |
| Sep-24 | 5.08% | 4.880% | 5.61% | -0.72% | -0.46% | -0.45% |
| Dec-24 | 5.15% | 4.353% | 5.96% | 0.07% | -0.53% | 0.36% |
| Mar-25 | 4.48% | 4.299% | 4.94% | -0.67% | -0.05% | -1.02% |
|
Δ 90d Box Rate Correlation |
57% | 89% |
Equity financing risks can be greater than the sum of its parts
To further delve into equity financing we will decompose the total cost of equity financing visualized in Chart 2 of the last section. We define the implied equity financing over 3m SOFR forward curve as the total equity roll premium. The total equity roll premium represents the convenience yield and the equity repo premium. This is visualized in Figure 2 with the E-mini S&P 500 total equity roll cost split into the components of 3-M SOFR forward curve, the 3-M convenience yield from E-mini S&P 500 option box spreads and the E-mini S&P 500 equity repo premium.
Figure 2 Two-year average E-mini S&P 500 implied roll cost broken down into equity repo premium, convenience yield and SOFR
To analyze funding pressures, Chart 3 compares the financing spread of the Adjusted Interest Rate S&P 500 Total Return Dec 2027 futures to the 3-M convenience yield from E-mini S&P 500 option box spreads. Both spreads experienced a similar trend into 2024 year end. The year-end phenomena of capital supply scarcity compounded by strong upside demand is described in detail in Equity Financing Demand Dynamics for AIR TRFs.
Chart 3: 3-M E-mini S&P 500 convenience yield vs. AIR SPTR Dec 2027 funding spread
Zooming in on December 2024, Chart 4 shows the term structure of both the convenience yield and equity repo financing costs, measured using the financing spread from the Adjusted Interest Rate S&P 500 Total Return (EFFR). The term structure premium for both spreads exhibit similar behavior out the curve, signaling stickiness of both premiums in the long run.
Chart 4 – Equity repo and convenience yield term structure from December 20, 2024
Hedging
This section will further explore an empirical example in using AIR S&P 500 Total Return (EFFR) futures calendar spreads as a hedge for the total equity roll premium. AIR Supply is a good first resource in exploring financing spread adjustment (FSA) trading by way of AIR TRF calendar spreads. Table 2 compares two years of E-mini S&P 500 roll cost to an AIR S&P 500 TRF Sep ‘25 / June ‘25 calendar spread. The June 2025 AIR TRF S&P 500 Total Return futures (EFFR) and September 2025 AIR TRF S&P 500 Total Return futures (EFFR) legs are chosen to both align with E-mini S&P 500 futures quarterly roll and the 916 day data period.
Table 2: E-mini S&P 500 total equity roll cost, 3-M SOFR forward curve and AIR S&P 500 Total Return futures
| Day Count | Total ES Roll Cost | 3m Term SOFR | Total Equity Roll Premium | ES FUTURES Price | SPTR Price | Jun 2025 AIR S&P500 TRF | Sep 2025 AIR S&P500 TRF | AIR S&P500 TRF Calendar Spread Cumulative Pnl | Jun 2025 BTIC on AIR TRF S&P 500 TRF (EFFR) | Sep 2025 BTIC on AIR TRF S&P 500 TRF (EFFR) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Dec-22 | 91.00 | 4.95% | 4.507% | 0.445% | 3,852.36 | 8,200.90 | 8,163.23 | 8,170.68 | – | 47.00 | 46.00 |
| Mar-23 | 91.00 | 5.14% | 4.942% | 0.201% | 3,916.64 | 8,375.21 | 8,234.39 | 8,242.21 | 9.25 | 47.00 | 46.00 |
| Jun-23 | 91.00 | 5.60% | 5.243% | 0.355% | 4,409.59 | 9,468.81 | 9,196.29 | 9,205.02 | 32.00 | 36.50 | 36.50 |
| Sep-23 | 91.00 | 5.86% | 5.408% | 0.457% | 4,450.32 | 9,592.86 | 9,187.24 | 9,196.09 | 35.00 | 36.50 | 36.50 |
| Dec-23 | 91.00 | 5.99% | 5.377% | 0.616% | 4,719.19 | 10,213.49 | 9,690.86 | 9,703.00 | 117.25 | 47.00 | 47.00 |
| Mar-24 | 97.00 | 5.95% | 5.321% | 0.633% | 5,117.09 | 11,115.69 | 10,460.83 | 10,475.84 | 189.00 | 59.50 | 58.50 |
| Jun-24 | 91.00 | 6.06% | 5.343% | 0.717% | 5,431.60 | 11,839.27 | 11,037.67 | 11,057.23 | 302.75 | 73.00 | 71.50 |
| Sep-24 | 91.00 | 5.61% | 4.880% | 0.726% | 5,702.55 | 12,474.44 | 11,482.89 | 11,505.44 | 377.50 | 77.50 | 76.00 |
| Dec-24 | 91.00 | 5.77% | 4.353% | 1.419% | 6,051.09 | 13,276.56 | 12,148.50 | 12,182.29 | 658.50 | 113.00 | 109.00 |
| Mar-25 | 91.00 | 4.94% | 4.299% | 0.642% | 5,638.94 | 12,414.28 | 11,086.08 | 11,106.96 | 335.75 | 65.50 | 66.00 |
| Average | 5.59% | 4.97% | 0.62% | 4,928.94 | 10,697.15 | 60 | 59 |
The E-mini S&P 500 implied equity financing cost over 3m SOFR forward curve since the December 2022 roll has averaged 62bps rich or totaled $3,895.08 (Multiplier * ES Futures Price * Total Equity Roll Premium * Day count / 360 or 50 * 4,928.94 * 62bps * 916 days / 360). Table 2 represents ten E-mini S&P 500 quarterly rolls (916 days) and the 91 day AIR S&P 500 TRF Sep ‘25 / Jun ‘25 calendar spread.
The duration hedge ratio of the 91 day AIR S&P 500 TRF Sep ‘25 / June ‘25 calendar spread is ~10x (916 days for total period / 91 days for the calendar spread duration). Being long ten AIR S&P 500 TRF Sep ‘25 / Jun ‘25 calendar spreads as a hedge against rolling ES over the same period would have recouped $3,357.50 (10 * AIR S&P 500 TRF calendar spread cumulative Pnl from Table 2 of $335.75). During this period, the S&P 500 TRF Sep ‘25 / Jun ‘25 calendar spread proved to be a good hedge in reducing total equity roll risk in conjunction with 3-M SOFR forward curve.
With the recent announcement to list of Adjusted Interest Rate S&P 500 Total Return (EFFR) futures calendar spreads on Globex, traders can now access calendar spreads electronically as well as through ClearPort blocks in accordance to Rule 526. The Globex AIR TRF calendar spread methodology is highlighted in this FAQ.
Conclusion
This paper explores different reference rates and a hedging strategy for equity financing risk. Changes in the box rate generated from E-mini S&P 500 option box spreads can have a stronger correlation to changes in E-mini S&P 500 roll costs than SOFR alone. Adjusted Interest Rate S&P Total Return futures calendar spreads capture both the convenience yield and equity repo premium, which equates to the total equity roll premium. This paper concludes that AIR TRF calendar spreads can be used in conjunction with an interest rate hedge to reduce E-mini S&P 500 futures roll risk. This strategy can be helpful to index arbitrage traders, relative value and multi-strategy hedge funds, traditional asset managers, managed futures (CTAs) and real money accounts.
References
Jules van Binsbergen, William Diamond, and Peter Van Tassel, “Options for Calculating Risk-Free Rates,” Federal Reserve Bank of New York Liberty Street Economics, October 2, 2023
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