Broadly speaking, the switch from LIBOR to SOFR has two fundamental consequences:

• A switch from a term-rate to an overnight rate, from which term lending needs to be constructed as discussed in Chapter 3.
• A switch from an unsecured to a secured rate, which will be analyzed in this chapter.

This chapter begins with a classification of the STIR contracts and the forces driving the spreads between them. Together with the differences between 1M and 3M contracts discussed in Chapter 2, the basis is key to understanding and modeling spreads between STIR futures.

In a second part, this chapter describes the factors influencing the basis and presents a model linking the basis between secured and unsecured lending to other bases, such as the CCBS (cross-currency basis swap).

This model and its link are then applied in three ways:

• It derives a fair value¹ for the spread contracts affected by the secured–unsecured basis from other market parameters.
• Vice versa, since the SOFR versus ED/FF spread contracts depend almost exclusively on the secured–unsecured basis, the model shows how they can be used as a cheap replacement of the expensive CCBS in many relative value (RV) trades.
• Finally, it establishes a new RV relationship between some STIR future spreads and the CCBS.

From a general perspective, the analysis and trades possible for the unsecured curve and ED contracts can be transferred to and repeated with SOFR futures for the secured curve. Chapters 2 and 5 provide a few examples of this. But in addition, the spread between the two provides the basis for new analyses and trades, including a new source for alpha. This chapter presents the first steps in this direction.

In a third and final part, this chapter provides an overview of the implications of the switch from LIBOR to SOFR as floating legs in asset swaps. Using the terms of the two fundamental consequences again, these implications can be classified into

• Technical adjustments required to deal with the floating payment being determined in arrears.
• The elimination of the unsecured–secured basis in asset swaps of government bonds and the introduction of this basis in asset swaps of corporate (bank) bonds.

SOFR FUTURES IN THE STIR UNIVERSE

Figure 4.1 illustrates the fundamental feature of the introduction of the basis between secured and unsecured lending rates via SOFR futures. Before SOFR futures existed, STIR contracts were based on unsecured lending rates, such as LIBOR and Fed Funds (FF). Hence their spreads were only a function of different time periods covered (and hence of the expectations of Fed policy for these time periods) and of different specifications, such as simple averaging and daily compounding. In other words, the situation between 1M and 3M SOFR futures described in Chapter 2 was enough to understand the spreads in the STIR universe, such as between FF and ED futures.

With SOFR futures based on secured lending, a new dimension has been added to the STIR universe, reflected in the two dimensions of Figure 4.1. In addition to the horizontal relationship between contracts on the same type of lending rate (secured or unsecured) covering different time periods and with different specifications, there is now also the vertical relationship between contracts covering (almost) the same time periods and with almost the same specifications for different types of lending rates.

DRIVING FORCES OF SPREADS IN THE STIR UNIVERSE

Hence, one can classify the driving forces of spreads between STIR futures by looking at Figure 4.1:

• The spread between futures in different columns is driven by the expectations about the interest rates (Fed policy) in different time periods, and the difference between simple averaging and daily compounding, which also depends on the general level of yields.

  This applies to the 1M–3M SOFR future spread discussed in Chapter 2 and to the FF–ED futures spread.

• The spread between futures in different rows is driven by expectations about the basis between secured and unsecured interest rates for the same time period.

  This applies to the SR1–FF and SR3–ED future spreads analyzed in this chapter.

• The spread between futures in different columns and rows is driven by both factors.

  This applies to the SR3–FF futures spread.

A few details need to be added to this broad conceptual perspective:

• While Fed Funds and LIBOR are different rates (unlike the same SOFR used for both SR1 and SR3 contracts), with very few exceptions they trade closely to each other. This is due to the fact that both represent unsecured lending rates – and validates our approach to classification based on secured vs unsecured lending.
• While SOFR futures have been constructed to mirror both the time period covered by FF and ED futures and their specifications, due to the different underlying rates and their conventions, there can occur slight differences from time to time. In particular, depending on the calendar situation, the underlying 3M LIBOR of an ED contract can deviate from the reference quarter of a 3M SOFR contract. And different holiday schedules apply.²

  In most cases, however, these differences are negligible from a practical perspective.³ Hence, the spreads between SOFR and FF/ED contracts can be considered to represent a “pure” market price for the secured–unsecured basis. This is the advantage of mirroring the specifications of FF and ED futures in 1M and 3M SOFR contracts. And this is also the foundation of using spread contracts as proxies for the secured–unsecured basis (and its links to other bases through the model) in RV trades. Specifically, it allows replacing CCBS in some RV relationships directly with SR3–ED spread contracts, without further adjustments.

CME'S SPREAD CONTRACTS

All “edges” of the square and the “diagonal” between SR3 and FF (not between SR1 and ED, though) shown in Figure 4.1 can be traded as inter-commodity spreads (ICS) on CME's Globex platform. Table 4.1 summarizes the specifications of these ICS. Given the margin offsets, this is a cheap and easy way to hedge against or gain exposure to the driving forces of these spreads, particularly to the secured–unsecured basis.

Figure 4.2 depicts the volume for the ICS involving SOFR contracts. We observe a clear correlation between the exposure of an ICS to the unsecured–secured basis and its liquidity: SR3:ED, which is exposed to a 3M basis, is most liquid, SR1:FF with exposure to a 1M basis less so. The SR1:SR3 spread, without any basis exposure, is currently without any liquidity. This suggests market demand for trading the basis via spread contracts.⁴

In fact, after switching from LIBOR to SOFR, banks cannot pass on their credit risk directly via LIBOR-based lending rates anymore.⁵ In other words, banks engaging in SOFR-based lending face exposure to a secured–unsecured basis. And the need to hedge this basis explains the demand for ICS covering the basis.

As our model links the basis covered by ICS with other bases, like the CCBS, it could become the foundation for replacing the CCBS with ICS in some RV trades, thereby further increasing demand and liquidity in the relevant ICS, especially the SR3:ED spread.

As mentioned in Chapter 2, ED futures settling after the end of LIBOR on June 30, 2023, trade on a fallback rate calculated as a spread over SOFR compounded in-arrears.⁶ Hence ED futures expiring after this date are basically 3M SOFR contracts plus a fixed spread. This means that only SR3:ED spread contracts until June 2023 incorporate the secured–unsecured basis; afterward, only SR1:FF and SR3:FF spread contracts will be suitable to trade this basis and to analyze it through the model developed below. Due to the currently higher liquidity, we present the analysis for SR3:ED spread contracts and encourage the reader to repeat the same analysis for SR1:FF and SR3:FF spread contracts after liquidity will have shifted (and in case the legs of the CCBS change, as discussed at the end of this chapter).

DRIVING FACTORS OF THE SECURED–UNSECURED BASIS

As a start, we summarize a simple model for the spread between the secured repo rate R (for any term, not just overnight) and the unsecured LIBOR L presented in Huggins and Schaller (2013, p. 149):

where

• p is the probability of default and c the recovery rate for the unsecured loan.
• q is the BIS risk weighting for the unsecured loan, d the BIS capital ratio, g the cost of equity, and b the marginal cost of funds (such as deposits).

Conceptually speaking, the higher cost of capital for unsecured loans should translate into a higher rate for unsecured loans. Assuming no default risk (p = 0) and L = b (i.e., the bank using the LIBOR market rather than deposits as low-cost funds) and using the usual BIS risk weighting q = 20% and d = 8%, the equation simplifies to:

This means that an increase in the cost of equity g by 5% versus LIBOR should result in a widening of the LIBOR-Repo spread by 8 bp, since unsecured loans become more costly to fund relative to secured ones. This relationship can explain the increase in (LIBOR-based) asset swap spreads of government bonds in times of stress in the banking sector and the fact that asset swap spreads tend to be higher in those markets when the cost of equity is higher. Moreover, it can be used to predict the effect of changes to BIS rules on LIBOR-repo spreads and hence on swap spreads. For example, a doubling of the capital ratio d should also result in a doubling of the LIBOR-repo spread.

In qualitative terms, the key results of this equation are that the LIBOR-repo spread is an increasing function of

• Level of interest rates
• Cost of equity (core capital) (relative to low-cost sources of funds, such as deposits)
• Capital ratio and risk weighting

A LIBOR-based asset swap can conceptually be considered as a LIBOR-repo basis swap over the life of the bond. Buying the bond, financing it in the repo market, and entering into a hypothetical LIBOR (minus X) – repo basis swap achieves the same cash flows as an asset swap of that bond versus LIBOR (minus the same X) (Huggins and Schaller 2013, p. 160). With the introduction of SOFR-based futures, the LIBOR–repo basis swap, which was a theoretical construct before, can now be traded, for instance, via SR3:ED strips.⁷ On the other hand, at the same time that the theoretical modeling of LIBOR-based asset swaps via LIBOR–repo basis swaps became practically tradable, the switch from LIBOR to SOFR as reference rate has diminished the importance of LIBOR-based swap spread models.

While at the time of publication (Huggins and Schaller 2013) this model was able to explain most of the dynamics in the LIBOR–repo spread, a number of developments since then require additions. In general, the influencing factors described above remain important driving factors of the basis. Accordingly, the following model has the level of interest rates as one input variable. But unlike before, they explain only one part of the driving forces of LIBOR–repo spreads.

The increasing regulations in the aftermath of the financial crisis require banks to carefully assess the regulatory costs of each position relative to those of other possible positions. While without these constraints, each trade could be analysed separately, most market participants nowadays need to optimize their balance sheets under numerous capital and regulatory constraints.⁸ This makes life difficult for analysts, as we will see in a moment, and also explains the occurrence and even persistence of market situations that would appear to present arbitrage opportunities in the absence of those constraints.

In the absence of balance sheet constraints, the LIBOR–repo spread can be modeled quantitatively via the formula above. Accordingly, unsecured rates trading below secured rates appear to be an anomaly and an arbitrage opportunity. However, as described in Chapter 1, in the presence of balance sheet constraints, there are costs associated with executing this arbitrage. For example, in some cases this may require the issuance of additional equity in order to maintain regulatory capital requirements. In this case, the advantage of repo versus LIBOR loans due to the different BIS treatment, which the formula captures, recedes.

The formula above models the secured–unsecured basis when the costs of balance sheet constraints are low. But when the costs of balance sheet constraints are relatively high, we observe situations that run contrary to the intuition captured by this simple model. In fact, we sometimes observe situations in which relations that had been viewed as inequalities (e.g., SOFR ≤ EFFR) are violated. Thus, high costs of balance sheet constraints are the reason that repo rates exceeded Fed Funds, as depicted in Figure 4.3. Negative values in this graph correspond to repo rates trading above Fed Funds.

And as discussed in Chapter 1, the reaction of the Fed to SOFR spikes – the introduction of the standing repo facility – has resulted in the additional constraint that the overnight SOFR value should be less than or equal to the Fed's SRF rate.

It would be nice if the costs of balance sheet constraints in the banking sector could be modeled via a simple equation of the sort used above to characterize the relations between these various money market rates. But in practice, each bank has a unique balance sheet, which presents its own set of regulatory costs, and there's no way to build an industrywide model by aggregating these costs across the banking industry.

However, while it isn't possible to develop a quantitative financial model of these spreads from first principles, it may be possible to develop a quantitative statistical model. The insights into the financial reasons for the statistical relationships will not directly enter the quantitative equations anymore, but we at least can consider whether the statistical relations are consistent with our intuition, thereby minimizing the risk of relying on spurious correlations.

A MODEL FOR THE SECURED–UNSECURED BASIS, LINKING IT WITH OTHER BASES (CCBS)

Building on the previous considerations, we can ask which consequences are to be expected from stress in the banking sector, a broad term that may encompass higher cost of equity for banks, repatriation of funds from abroad to the US banking sector, etc. One would expect to observe this stress in several market segments, specifically:

• In a greater preference for secured lending (as given by the formula above for a higher g) and hence in a richening of SR3 versus ED futures.
• The model above has linked a higher secured–unsecured spread to a higher overall yield level and one would therefore generally expect increasing rates, though there have been historical instances when the basis has widened in an environment of decreasing yields.
• In greater volatility, both realized and implied.
• In wider (i.e., more negative) CCBS (Cross-Currency Basis Swaps) spreads,⁹ since market participants tend to prefer keeping their funds in the US banking sector rather than in foreign countries in times of uncertainty.¹⁰
• In wider bank CDS (Credit Default Swap) spreads.

Given the causal links between these variables, it is reasonable to look at their correlations.¹¹ And indeed, the signs are as expected by the relationships already described. A higher spread of unsecured versus secured lending (as expressed by the SR3:ED future spread) is linked to a higher level of rates, a higher implied swaption volatility, a richening of the USD versus the EUR, higher (more negative) CCBS, and higher CDS for banks.

Especially high correlations exist with the level of interest rates as measured by SOFR (0.64) and to the CCBS. While the correlation with all maturities of both the JPY and EUR CCBS is significant, it is most pronounced for the 2Y JPY CCBS (–0.71), which is also relatively liquid. Figure 4.4 shows this specific regression.

A multiple regression of the SR3:ED futures spread versus the candidates for explaining variables listed above suggests that the rate level (SOFR) and the 2Y JPY CCBS have most explanatory power, as summarized in Table 4.2. Adding more explanatory variables does not lead to a significant improvement of the R-squared value. We therefore decide to use the regression from Table 4.2, i.e., to model the SR3:ED future spread via SOFR and the 2Y JPY CCBS.

FIRST APPLICATION OF THIS MODEL: PRICING SPREAD FUTURES

This statistical model allows pricing the SR3:ED future spread¹² as a function of SOFR and the 2Y JPY CCBS. Figure 4.5 illustrates the proximity of the model prediction to the actual value of the SR3:ED future spread in the past. Assuming the correlations will be stable in future as well,¹³ one can predict the likely level of the SR3:ED future spread for a number of scenarios. Table 4.3 shows these predictions: The left side assumes a constant CCBS and calculates the effect of changes in the yield level on the futures spread, corresponding to a scenario in which Fed policy rather than stress in the banking sector drives market pricing. The right side assesses the opposite scenario of constant (low) interest rates for different CCBS levels, reflecting different levels of stress in the banking sector.

Of course, as statistically reflected in an R-squared below 1, there are other driving factors as well, which can at times overpower the ones captured by the model. Analysts are therefore well-advised to complement the model with other considerations. Unfortunately, as noted in Chapter 1, the missing accessibility of raw data makes some analyses impossible. For example, it would be interesting to know whether there are additional factors driving the secured–unsecured basis from the distribution of trades during the day.¹⁴

Returning to the classification at the beginning of this chapter, one can analyze the “horizontal” spread between 1M and 3M contracts via the method outlined in Chapter 2 for the SR1:SR3 futures spread and the “vertical” spread via the model for the basis described here. Combining both helps understand and predict most of the spreads in the STIR universe. For example, a trader expecting the yield curve to steepen 25 bp during the reference quarter could use the spreadsheet “3M versus 1M” of Chapter 2 to assess the effect on the SR1:SR3 futures spread. He can then go on and apply the model to analyze the effect of a repetition of the subprime crisis with a 2Y JPY CCBS at –80 bp on the SR3:ED future spread. And he can combine both to see what might happen to the SR3:FF futures spread if the yield curve steepening occurs together with a banking crisis.

SECOND APPLICATION OF THIS MODEL: REPLACING THE CCBS WITH SPREAD FUTURES IN SOME RV TRADES

The CCBS plays a vital role in many RV relationships: As it allows swapping cash flows in different currencies, it provides the foundation for comparing and trading global swap spreads against each other. It links all global bond markets and enables comparing all bonds via a single number, i.e., the spread of the basis-swapped bond over USD LIBOR¹⁵ and exploiting different swap spread levels for investing and funding, for instance, by issuing Samurai bonds.

Unfortunately, precisely due to its function of exchanging cash flows in different currencies, the CCBS suffers from high capital costs, regulatory burdens, margins, and transactions costs, which limit its practical use. Analysts often find themselves in a situation in which an RV relationship between global bonds seems out of line but cannot be exploited because the required CCBS is too costly to transact.

As our statistical model links the CCBS to the secured–unsecured basis, which has been introduced to the STIR universe (Figure 4.1) and can therefore be traded easily and cheaply (with margin offset), a major consequence could be the replacement of CCBS by SR3:ED spread positions. After ED futures trade on fallback rates, only SOFR–FF spread contracts remain as a possible replacement, which will then probably enjoy higher liquidity due to the migration from ED futures.

While the R-squared value of the regression shown in Figure 4.4 is only 0.51, significant moves in the CCBS seem to be well reflected in the futures spread. Moreover, the time series of the residual of this regression depicted in Figure 4.6 suggests that deviations are usually short-lived. Calibrating a simple mean-reverting process to this time series gives an estimated half-life of 3.7 weeks (Table 4.4). For comparison, a similar regression versus the CDS of Bank of America exhibits a trend and a slower speed of mean reversion, implying the SR3:ED spread is less suitable as a replacement for CDS than for the CCBS.

It appears therefore attractive to replace the expensive CCBS with cheaper SR3:ED spread futures whenever possible. This relationship allows execution of some of the arbitrage positions between global bond markets, which have been impractical due to prohibitively high costs of CCBS until now. Vice versa, the suitability of SR3:ED spreads to replace the CCBS in some RV trades should result in improved liquidity in the spread contracts covering the basis (Figure 4.2).

The question is, thus, in which trades can the CCBS be replaced by SR3:ED spread futures? In those trades which require the function of the CCBS to actually swap different currencies, it cannot be replaced by a financial product, which mirrors the behavior of the CCBS, but does not provide its cash flows. For example, a USD-based investor wanting to invest into a JGB without taking FX exposure requires the currency exchanges of an actual CCBS, particularly the exchange of the principal between USD and JPY at the beginning and at expiration of the CCBS.¹⁶

On the other hand, as the CCBS is the link between global bond markets, it is influenced by different valuations in different countries. For example, if basis-swapped 10Y Bunds trade at USD LIBOR-20 bp and 10Y USTs at USD LIBOR-50 bp, a USD-based investor judging both to be of the same credit quality may want to use the CCBS to invest his USD without FX exposure into basis-swapped Bunds. These flows support a narrowing (less negative) of the EUR CCBS. Hence, analysts of global bond markets seeing such a mismatch may want to position for the likely moves in the CCBS – without needing the cash flows from its FX swaps. They can therefore replace a CCBS position with a financial instrument that exhibits similar behavior without providing the cash flows. In summary, the CCBS can be replaced if the goal is to exploit its moves only, but not if it is important to obtain the CCBS cash flows.

From a conceptual perspective, the effects of introducing futures on secured rates to the STIR universe can be summarized as follows:

• They provide a market price for the LIBOR-GC basis swap, which is an important part of (LIBOR-based) swap spread models.
• They provide a cheap substitute for trading the moves of CCBS.
• Their link to the CCBS and rate level via the model is a new RV relationship and hence a new source for generating alpha, which is discussed in the next application.

THIRD APPLICATION OF THIS MODEL: NEW RV RELATIONSHIP

Figure 4.7 shows the residual of the regression from Table 4.2, i.e., of the SR3:ED spread future versus SOFR and the 2Y JPY CCBS. Table 4.4 exhibits the mean reversion characteristics of this regression residual and of the regression versus the CCBS only (shown in Figure 4.6) when modeled through a simple mean-reverting model (the Ornstein-Uhlenbeck process).

The new RV relationship of the model seems both optically and numerically attractive. For example, the Sharpe ratio of trading the residual of these two regressions at a level of 10 bp is expected to be 7.68 and 5.37 over the first week.¹⁷

However, due to the capital and transaction costs involved in trading the CCBS mentioned above, the residual may seldom be high enough to allow executing this RV relationship as a stand-alone trade. But it could still be incorporated as an additional and uncorrelated source of alpha in CCBS trading. Specifically, Figure 4.6 can be used as a guide, at which point in time replacements of CCBS with SR3:ED spread future positions are particularly attractive.

THE CCBS AND THE MODEL AFTER THE END OF LIBOR

The transition from unsecured to secured reference rates is a major event for financial products and their analysis. We have seen that the switch from LIBOR to SOFR as reference rate eliminates the basis inherent in LIBOR-based swaps. Following the final transition in June 2023, ED futures will trade on a fallback rate and therefore only FF–SOFR spread contracts will remain¹⁸ to trade the “vertical” dimension of the basis and as objective of the model.

However, one should keep in mind that the unsecured–secured basis affects the CCBS due to exchanging different currencies. Hence, independent of the type of rate used in the basis swap (unsecured or secured), the CCBS should remain influenced by the unsecured–secured spread and therefore continue being usable in the model even after transitioning to SOFR as reference rate. One could say that the basis in the CCBS is between the two legs, not in the two legs. Actually, in case both legs switch from secured to unsecured rates simultaneously, it is possible that the effect on CCBS would be minimal – though it is of course advisable to re-run the regressions of the model in this case. If only one leg transitions from secured to unsecured, for instance, due to uncoordinated global regulations, the CCBS is likely to become more or less correlated to the unsecured–secured basis, depending on whether the transition occurs only in the US or only abroad.

In summary, while it is possible that the correlations of the model are affected by the transition of CCBS to secured rates, we are optimistic that the CCBS will remain correlated to the unsecured–secured basis and that the model built on it can still be used – though for the spread between SOFR futures and FF contracts only.

REMAINING PRODUCTS WITH EXPOSURE TO THE BASIS AFTER THE END OF LIBOR

In the course of the book, we have come across a few reasons for the reluctance of end users to embrace the transition to SOFR. In Chapter 1, we mentioned concerns about the lack of a level playing field with big banks. In Chapter 3, we described the tension between the reality of cash loan markets and the ideal SOFR arrangements envisioned by regulators. Here, we can add another reason for this reluctance: while loans on a LIBOR basis enable lenders to profit from a banking crisis as the widening unsecured–secured spread results in a higher reference rate, the switch to SOFR as reference rate eliminates this source of return. This may be another reason behind the perception that SOFR is a project forced on the market by regulators for the benefit of big banks by immunizing their funding rates (of the already outstanding loans with a fixed spread above SOFR) against increasing unsecured–secured spreads. Of course, one can counter this perception by arguing that banks as lenders face the other side of the coin, i.e., that they are unable to pass on their higher unsecured lending costs during a crisis via the reference rate.

But this argument also leads to the interesting question: Which instruments remain for a lender to profit from a widening of unsecured–secured spreads after the transition eliminates many products?

• Before the transition, lenders enjoyed a widening of the basis automatically via increasing LIBOR.
• After the transition to SOFR, lenders need to add a product to maintain exposure to a widening basis after entering into a SOFR-based loan. (If the basis widens before entering the loan, it should be reflected in higher spreads the bank offers over SOFR.)
• However, due to the transition to SOFR, most products providing this basis will disappear together with LIBOR. Asset swap spreads of government bonds, which incorporated the basis as long as they had LIBOR as floating rate, will no longer express the basis once they use SOFR as floating leg.

Hence, given these consequences of switching to a secured reference rate, products allowing to trade the unsecured–secured basis are likely to become rare. In this environment, CCBS could turn out to be a valuable exception. As we mentioned above, one can think of CCBS as incorporating the unsecured–secured basis between its two legs rather than in one of the two legs and hence to remain a proxy for the unsecured–secured basis even if both legs reference secured rates. And after the migration of ED futures to the fallback, when they become 3M SOFR contracts plus a spread, SR1:FF and SR3:FF spread contracts will be the only STIR positions covering the “vertical” dimension of the basis. Actually, these spread contracts could turn out to be the cheapest way to gain exposure to the secured–unsecured basis, which is likely to result in high demand from end users looking for a method to continue profiting from banking crises and thus increased liquidity.

SWAPS WITH SOFR AS FLOATING LEG AND ASSET SWAPS AFTER THE END OF LIBOR

Historically, swaps started with LIBOR as floating leg, i.e., an unsecured term rate, usually 3M. Under the impression of the financial crisis, the risk of an unsecured term rate was deemed to be unacceptably high and was mitigated by using OIS (overnight index swaps) with FF as floating leg, i.e., an unsecured overnight rate. Thereby, the unsecured exposure to banks was reduced from a (3M) term to overnight. In Figure 4.8, this corresponds to the horizontal dimension.¹⁹

The introduction of SOFR, i.e., a secured overnight rate, can be considered as further reduction of the risk to the lowest possible level. Conceptually, it adds the vertical dimension of secured rates as floating leg. Thus, a swap can now be based on overnight or term rates (horizontal dimension) and on unsecured or secured rates (vertical dimension). Whether SOFR term rates will someday be used as floating leg in swaps will depend on the evolution of the regulatory tension described at the end of Chapter 3. In that case, the full matrix of Figure 4.8 would become available. Currently, there are only the three choices: secured overnight (SOFR), unsecured overnight (FF), and unsecured term (LIBOR).

The adjustments required for switching from LIBOR to SOFR as floating leg in a swap can therefore be classified along the two dimensions:

• The move from term to overnight requires the technical adjustment of moving from a rate determined in advance to a rate determined in arrears – and is familiar from the move from LIBOR to FF as the floating leg of OIS.
• The move from unsecured to secured has the fundamental effect of eliminating the secured–unsecured basis in asset swaps of government bonds.

In a swap with LIBOR as floating leg, the payment is determined at the beginning of each interest rate period but takes place at the end. In a swap with SOFR as the floating leg, the payment is determined at the end of each interest rate period, which could be the same time it takes place, depending on the specifications.²⁰ As a consequence, unlike in LIBOR-based swaps, when using SOFR as floating leg, the first payment is not known at the time of entering into the swap agreement. Moreover, the move from “in advance” to “in arrears” results in the problems discussed in Chapter 3, specifically, the issue of a short notice period. And the remedies outlined for cash loans, such as lookbacks, can also be applied in swaps. While OTC swaps allow the counterparties full flexibility to agree on a specification, clearinghouses may determine a particular remedy. For example, CME-cleared SOFR swaps use daily compounding with a two-day payment offset (CME Q4 2018, p. 7). The problems and possible solutions to adjusting swaps to an overnight floating rate are well known from the switch from LIBOR to FF and can be directly replicated for SOFR.

By contrast, the switch from LIBOR to SOFR also contains the fundamental new feature of a secured rate as floating leg. Unlike the mere reduction of unsecured exposure by reducing the term from 3M to overnight (FF) in OIS, it eliminates the unsecured exposure and can therefore be considered as the final stage of the search for the least risky floating rate. It also eliminates the basis in asset swaps of government bonds. We have mentioned that a LIBOR-based asset swap of government bonds is conceptually the same as a LIBOR-repo basis swap over the life of the bond; replacing LIBOR with SOFR as floating leg, an asset swap of a government bond becomes conceptually the same as a SOFR-repo basis swap over the life of the bond. In other words, asset swapping a government bond with SOFR as floating leg results in exposure to the spread between SOFR and the specific repo rate of this government bond. If the repo rate of the bond were always the same as SOFR, the SOFR-repo basis swap and hence the swap spread of the bond should be zero. And the expected specialness of a government bond is (theoretically²¹) the only driving factor of SOFR-based asset swap spreads.

Repeating this argument in formal terms, LIBOR-based asset swaps of government bonds can be priced as LIBOR-repo basis swaps, which can be decomposed in a LIBOR-SOFR and a SOFR-repo basis swap, with SOFR usually being close to GC, as discussed in Chapter 1. The first part is driven by the unsecured–secured basis, while the second part is driven by the specialness of the specific bond. If the bond is not expected to become special – for example, because it is no benchmark anymore and has no chance of being the cheapest-to-deliver (CTD) of a bond futures contract, the SOFR-repo basis swap can be assumed to be close to zero. In this case – which is true for most bonds – all of the LIBOR-based asset swap is driven by the first part – and disappears when using SOFR as floating leg instead. Hence, while LIBOR-based asset swaps were mostly driven by the unsecured–secured basis (which we have suggested to assess through the model described above), SOFR-based asset swaps eliminate this basis and leave only the specialness (SOFR-repo basis swap) as driving factor. Except for benchmarks and CTD candidates, the expected specialness is typically small, resulting in a theoretical fair value of close to zero of the SOFR-based asset swaps of most government bonds.

As explained in Chapter 1, this theoretical consideration is likely to be influenced by regulation as well. If holding a government bond requires less capital than engaging in a SOFR-based swap, the prediction of SOFR-based asset swaps for government bonds to reflect their expected specialness (and hence to be close to zero for most of them) will only materialize in times of little constraints from regulation, e.g., at a distance from leverage limits. If, on the other hand, the regulatory restrictions play an important role, for example, due to already high leverage, SOFR-based asset swap spreads of government bonds can deviate quite significantly from zero.

Vice versa, while the switch from LIBOR to SOFR eliminates the unsecured–secured basis in asset swaps for government bonds (funding at the secured repo rate), it introduces this basis in asset swaps for corporate issues, such as bank bonds. Combining the floating rates shown in Figure 4.8 with the different types (secured and unsecured) of fixed rates in asset swaps, one can therefore

• Asset swap government bonds without a basis by using SOFR-based swaps (and with a basis by using FF-based OIS).
• Asset swap corporate bonds without a basis by using FF-based OIS (and with a basis by using SOFR-based OIS).

Additionally, the horizontal dimension allows choosing a different term than overnight, currently for unsecured only.

It seems therefore likely that the asset swap market could evolve to a situation where SOFR is used for asset swaps of government bonds and FF for asset swaps of corporate bonds, allowing to exclude basis risk in both.

Both (asset) swaps and OIS using SOFR and FF in general are connected through the SOFR–FF basis, which can be hedged with future spreads as described above. Hence, one could foresee a future swap universe in which SOFR- and FF-based OIS take center stage for asset swapping government and corporate bonds respectively, and the spread between the two is actively traded via SR1:FF spread contracts.

HEDGING SOFR-BASED SWAPS AND GOVERNMENT BONDS WITH SOFR FUTURES

In broad conceptual terms, the transition from LIBOR to SOFR as a reference rate has led to SOFR future strips, SOFR-based swaps, and government bonds becoming very similar. All three can be considered as slightly different ways to compound a secured overnight rate into a term rate. (See Figure 9.1 for an illustration of this statement.) This fundamental link between the three markets, futures, swaps, and bonds, makes it possible to replicate and hedge each one with each other. And that is the conceptual foundation on which Chapter 9 will construct the hedges of swaps with SOFR as floating leg and of Treasuries with SOFR futures.