Measuring synthetic leverage in interest rate swaps

by Annalaura Ianiro, Agnese Leonello and Dario Ruzzi^[1]

Published as part of the Macroprudential Bulletin, 15 January 2025.

Synthetic leverage is a key source of vulnerability for the non-bank financial intermediation (NBFI) sector. Yet there is lack of consensus on how to measure it. In this article, we propose a novel methodological framework to measure synthetic leverage and apply it to interest rate swaps using data gathered under the European Market Infrastructure Regulation (EMIR). Our contribution is threefold. First, compared with notional-based measures of synthetic leverage, our formula is sensitive to changes in the underlying risk factor and thus reflects different degrees of resilience to interest rate shocks. Second, thanks to its duration-based approach, our methodology is particularly suitable as a policy tool for scenario analysis. Finally, by providing an estimate of the leverage risk that an institution faces through its derivatives positions, our framework makes it possible to investigate the potential implications for an NBFI entity’s overall exposure to liquidity and solvency risk.

1 Introduction

Leverage is a source of vulnerability for the financial system, significantly contributing to the fragility of the non-bank financial intermediation (NBFI) sector, as recent episodes have shown.^[2] High leverage tends to compound with other sources of risk, leading to increased fragility and detrimental aggregate dynamics. As described in detail in the overview article, it plays a key role in amplifying return volatility, exacerbating liquidity stress and driving dangerous contagion effects.^[3]

Like other financial intermediaries, NBFI entities can build up leverage both through secured and unsecured borrowing (financial leverage) and through derivatives contracts (synthetic leverage). Financial leverage can be obtained through a diverse set of instruments, such as repurchase agreements and margin lending. Analyses of these market segments show that financial leverage is low on average, but pockets of high leverage exist in some segments, particularly among hedge funds (see Box 2).^[4] However, NBFI entities can also accumulate leverage via derivatives contracts, and this is usually referred to as synthetic leverage (SL). Irrespective of the reason why NBFI entities enter such contracts – whether it is to increase their financial exposure to underlying assets or to hedge existing positions – these instruments allow investors to take on exposure to an underlying asset at significantly lower cost (in terms of capital) than investing directly in that asset.

Despite its importance, providing an accurate measurement of SL remains challenging. First, there is a lack of consensus on how to conceptually measure the market exposure embedded in a derivatives contract and its committed capital.^[5] Second, information on derivatives exposures often suffers from limitations due to (i) data reporting requirements varying across jurisdictions and market segments and (ii) data quality issues. To overcome these constraints, the practice is often to use proxies that only reflect partial information about SL and the risks it entails. As a result, those metrics frequently provide a partial and biased representation of the risks to which high levels of SL expose NBFI entities.^[6]

This article proposes and empirically tests a new methodological framework to measure SL in interest rate swaps (IRSs). Our approach builds on the classical definition of leverage and on the commonly used replica portfolio approach to convert a derivatives position into cash-equivalent balance sheet items.^[7] The analysis yields novel predictions about the interpretation of leverage values as a measure of risk, as well as about leverage dynamics. Our contribution lies in explicitly accounting for the effect of interest rate movements on leverage by introducing the concept of bond duration into the leverage formula.^[8]

2 The framework: a replica portfolio approach applied to IRSs

Leverage measures how changes in the value of assets translate into changes in the value of capital.^[9] Using this definition, we can formally express leverageL as the elasticity of the value of capital (E) with respect to the value of assets (A) as follows:^[10]

L=∂E∂AAE. (1)

Leverage values are indicators of risk, given their role in amplifying portfolio risk. When leverage is high, even small asset depreciations have a large impact on capital, potentially threatening the solvency of the financial intermediary. To apply this same logic in the context of IRSs, it is necessary to calculate a formula in which all the losses (gains) a counterparty suffers (obtains) map onto changes in the value of its own resources committed to enter and maintain the position in the contract.

An IRS is essentially an exchange of cash flows between two counterparties. In an IRS contract, two counterparties agree to exchange a stream of cash flows for a predetermined number of years. Specifically, in a plain vanilla, fixed-for-floating IRS, one counterparty (swap seller) receives cash flows equal to interest at a predetermined fixed rate on a given notional. The other counterparty (swap buyer) meanwhile receives cash flows equal to interest at a floating market rate on the same notional amount.^[11]

In addition to cash flows, the counterparties may also have to exchange margins during the lifetime of the contract. Margins may cover potential changes in the value of each participant’s position (initial margins) or actual changes in the market value of the contract (variation margins).^[12] Interest rate movements affect the market value of the IRS and have implications for the margins that are exchanged. The swap seller loses (gains) when interest rates rise (fall), while the opposite is true for the swap buyer. Specifically, the swap seller is required to post additional variation margins when interest rates rise, while the swap buyer does so when interest rates fall.^[13]

Figure 1

Using the replica portfolio, a seller’s position in an IRS can be replicated with a long position in a fixed-rate bond, financed with collateralised short-term borrowing

IRS seller’s cash flows: IRS and cash-equivalent position

From the perspective of a swap seller, changes in the value of an IRS are akin to changes in the value of a fixed-rate bond, with the margin calls mirroring the depreciation of the capital committed so far.^[14] Using the replica portfolio approach, the position of a swap seller can then be replicated by a fixed-rate bond with the same maturity and notional value as the swap, financed through short-term borrowing collateralised by the initial margins (Chart 1). Formally, this implies that the present value of the synthetic fixed-rate bondcaptures the value of the asset (A in (1)). The sum of the stocks of posted initial margin and net received variation margins^[15]gives a measure of the own resources committed by the swap seller to its position in the contract (E in (1)). For the sake of simplicity, we refer to this replica-portfolio-based formula as static SL.^[16] A depreciation of the synthetic fixed-rate bond translates into a decrease in the own capital committed to the positions (via changes in margins), which in turns leads to an increase in the level of SL. Consistently with other SL measures, higher levels of static SL imply higher risk.

Measures of SL based on derivative notional exposures can be misleading. In practice, SL is often measured as the ratio of gross notional value to either posted initial margin or net asset value (the standard measure of capital for funds). The numerator in both ratios tends to overestimate the actual market exposure and is not risk-sensitive (Chart 2, panel a). Static SL better reflects market exposure and the effects that interest rate movements have on leverage (Chart 2, panel b). Specifically, it responds to price changes in the synthetic bond, with the magnitude of the price changes depending on the bond’s duration. However, caution is needed when using snapshots of leverage levels as risk indicators.

Chart 2

Measures of SL based on gross notional exposure fail to capture risk sensitivity and overestimate market exposure

a) Distribution of SL, computed as GNV/IM	b) Distribution of SL, computed using the replica portfolio approach (static SL)
(Jan.- Dec. 2022, ratio)	(Jan.- Dec. 2022, ratio)

Static SL does not provide a comprehensive picture of entities’ resilience to shocks. Two swap sellers that share the same level of SL at a specific point in time may significantly diverge following an interest rate shock (Chart 3, panel a). Through the value of the synthetic asset and margins, movements in the interest rate affect the level of SL. The impact of these changes depends crucially on the duration of the synthetic fixed-rate bond.^[17] Hence, even small interest rate shocks can have a large impact on SL when the swap duration is high. Static SL does not provide a full representation of the riskiness associated with a particular IRS position, as it does not explicitly account for the sensitivity to interest rate risk captured by the duration. In other words, the level of SL at a given point in time does not provide information about how it reacts to an interest rate shock. Importantly, this limitation is even more severe for notional-based metrics of SL. First, the risk insensitivity of the gross notional exposure implies only limited changes in response to interest rate movements. Second, entities with high exposure to interest rate risk, as captured by high swap duration, and small gross notional values may appear less risky than entities with large notional exposures characterised by low duration (Chart 3, panel b).

Chart 3

Different sensitivities to interest rate risk imply diverging SL paths

a) Static SL distributions for entities with high and low interest rate risk exposure	b) SL distributions, computed as GNV/IM, for entities with high and low interest rate risk exposure
(Jan.- Dec. 2022, ratio)	(Jan.- Dec. 2022, ratio)

A dynamic formula of SL, with an explicit duration component, provides a more comprehensive measure of the risk associated with the IRS. Using duration to approximate the values of the asset and equity after a rate change, we rearrange static SL into a dynamic version, dynamic SL.^[18] For a given interest rate shock, the level of SL at a specific point in time depends on the level of leverage in the previous period and the modified duration of the underlying portfolio of fixed-rate bonds.^[19] This feature makes dynamic SL particularly suitable for scenario analysis. Specifically, it can be used to assess how a change in the interest rate affects the riskiness associated with a specific IRS position, as measured by the associated level of SL.

3 The framework in action

We estimate our formula using trade repository data collected under the European Market Infrastructure Regulation (EMIR).^[20] Our sample includes the IRS trades reported by euro area non-bank entities (investment funds, insurance companies and pension funds). We focus on a subsample restricted to euro-denominated fixed-for-floating IRSs. For those trades, we collect data at all month-end dates between January and December 2022.^[21] We work with a controlled environment so that the only source of variability in the asset and margin of our SL measure comes from changes in the value of bonds underlying the existing swaps.^[22] For each entity in our sample, we compute the value of its assets at any given time as the difference between its short and long swap positions.^[23] In addition to bond present values, we also compute bond yields to maturity and modified durations, which are used to approximate the future value of assets.

Dynamic SL gives a good estimation of the realised level of synthetic leverage (static SL). In our controlled environment, we compute the realised and estimated level of SL by setting the interest rate shock ∆y equal to the observed bond yield changes. Dynamic SL captures the sensitivity of leverage to interest rate risk and provides a good approximation of the future level of SL (Chart 4). As expected, the higher the interest rate shock, the lower the duration’s predictive power, as observed during the beginning of the 2022 hiking cycle.

Chart 4

Dynamic SL has good predictive power for the realised level of static SL

a) Realised (static) and estimated (dynamic) synthetic leverage distributions for entities with high interest rate risk exposure	b) Realised (static) and estimated (dynamic) SL distributions for entities with medium interest rate risk exposure	c) Realised (static) and estimated (dynamic) SL distributions for entities with low interest rate risk exposure
(Jan.- Dec. 2022, ratio)	(Jan.- Dec. 2022, ratio)	(Jan.- Dec. 2022, ratio)

Dynamic SL can be used as a policy tool to assess potential SL levels in stress scenarios. Depending on the level of duration, SL may react very differently to the same interest rate shock. Entities with high swap duration will exhibit a marked increase in their SL when interest rates move. The changes may be smaller for lower duration entities (Chart 5). Dynamic SL therefore emerges as a useful policy tool in stress-testing exercises to predict the potential evolution of SL over time.

Chart 5

The effect of an LDI-like shock (130 basis points) on SL varies significantly across interest rate risk groups

Dynamic SL distributions after a 130 basis point shock, by interest rate risk group

(Jan. 2022, ratio)

4 From activity-based SL to entity balance sheet: preliminary insights

High levels of SL are a source of risk because of the effect that valuation changes and margin calls have on the entity’s balance sheet. Honouring margin calls requires the counterparty concerned to obtain liquidity at short notice either with available cash, increased borrowing (leveraging) or asset sales (deleveraging). The revaluation of derivatives contracts thus directly affects an entity’s net worth, its leverage and risk exposure. The structure of the balance sheet (e.g., the liquidity of the assets) and whether the entity decides to invest in IRS for hedging purposes or speculation determine the magnitude and the direction of the impact.

The effect of an interest rate shock can be broken down into three parts. First, a change in the interest rate affects the value of both the asset and liability side of the entity’s balance sheet. Second, it has an impact on the value of the entity’s position in the IRS contract. Third, it may trigger the payment of margins. While the first two effects may offset each other, the third is always present and generates a short-notice liquidity need for the entity. All of these effects contribute to the entity’s overall leverage.

When an IRS is used for hedging, an increase in SL exposes the entity to higher liquidity risk, affecting the entity’s leverage through the margin call. When an entity hedges with a swap, its derivatives position and its balance sheet items are negatively correlated.^[24] An increase in SL may not immediately translate into a deterioration in net worth and higher balance sheet leverage, as it only requires the entity to obtain liquidity at short notice. However, this liquidity need, if sufficiently large, may lead to forced asset liquidations, potentially increasing the entity’s balance sheet leverage. When IRS portfolios are held for speculation, an increase in SL, on top of liquidity risk, could also lead to net worth deterioration and even higher balance sheet leverage.

It is crucial to account for the interactions between leverage and liquidity risk in the design of policy instruments addressing these sources of vulnerability. If derivatives are used for generating leverage, there is a particularly strong link between leverage and liquidity risk via margining.^[25] Addressing vulnerabilities related to one aspect would therefore help mitigate the risks associated with the other.^[26] For instance, leverage constraints would limit valuation losses, thus reducing the size of margin calls and, in turn, the associated liquidity risk. Similarly, enhanced liquidity preparedness would mitigate liquidity risk directly and avoid fire sale spirals that could trigger large fluctuations in net worth and leverage. Therefore, the two regulatory instruments complement each other by reducing the need for deleveraging to raise liquidity in a stress scenario.

5 Conclusions

Developing adequate metrics of synthetic leverage is key from a policy perspective, in terms of both risk identification and assessment of regulatory measures. Our framework highlights the importance of relying on measures of SL that fully reflect the degree of exposure to underlying risk factors. Failing to do so, as in the case of risk-insensitive notional-based measures, can lead to levels of leverage and exposure to risk being overestimated or underestimated. By highlighting the different response of SL to the same interest rate shock, our analysis sheds light on the importance of developing a duration-based approach for IRS. Such an approach overcomes the limitations of existing metrics and provides a measure of SL to use as a policy tool for scenario analysis. This is particularly relevant to designing a regulatory framework that will be effective in preventing the materialisation of fragilities associated with otherwise hidden pockets of risk. In addition, by providing an estimate of the leverage risk that an institution faces through its derivatives positions, our framework makes it possible to investigate the potential implications for the institution’s overall exposure to liquidity and solvency risk. Developing such measures may not always be straightforward, especially if more complex instruments are used or several instruments are combined at the portfolio level. Our analysis is intended as a first step in this direction.

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