LASH risk and Interest Rates9
Laura Alfaro

Saleem Bahaj

Robert Czech

Harvard Business School

University College London& Bank of England

Bank of England

Jonathon Hazell

Ioana Neamt, uLondon School of Economics

Bank of England

May 10, 2024

Abstract
We introduce a framework to understand and quantify a form of liquidity risk that
we dub Liquidity After Solvency Hedging or “LASH” risk. Financial institutions take
LASH risk when they hedge against losses, using strategies that lead to liquidity needs
when the value of the hedge falls, even as solvency improves. We focus on LASH risk relating to interest rate movements. Our framework implies that institutions with longer
duration liabilities than assets—e.g. pension funds and insurers—take more LASH risk
as interest rates fall, because solvency concerns rise in a low rate environment. Using
UK regulatory data from 2019-22 on the universe of sterling repo and swap transactions, we measure, in real time and at the institution level, LASH risk for the non-banksector. We find that at peak LASH risk, a 100bps increase in interest rates would have
led to liquidity needs close to the cash holdings of the pension fund and insurance
sector. Using a cross-sectional identification strategy, we find that low interest rates
caused increases in LASH risk. We then find that the pre-crisis LASH risk of nonbanks predicts their bond sales during the September 2022 LDI crisis, contributing to
the yield spike in the bond market.
Keywords: Liquidity, Monetary policy, Non-Bank Financial Intermediaries, Hedging
JEL Codes: E44, G10, G22, G23
9
Email contacts: lalfaro@hbs.edu, s.bahaj@ucl.ac.uk, robert.czech@bankofengland.co.uk, j.hazell@lse.ac.uk, andioana.neamtu@bankofengland.co.uk. We would like to thank Claudio Borio, Marco Bardoscia, Victoria Ivashina, Huw Pill,
Matthew Pritsker, Matt Roberts-Sklar, Adi Sunderam, Fabricius Somogyi (discussant), Misa Tanaka, Quynh-Anh Vo andseminar participants at the Bank of England, Bank of International Settlements, Federal Reserve Board, Federal Reserve Bankof Boston, IMF Research Department for their useful comments. We thank Anna Pilipentseva, Seyed Hosseini and Younghun
Lee for excellent research assistance. Part of this work was conducted when Alfaro was visiting the Bank of England and she
thanks them for their hospitality. The views expressed in this paper are those of the authors and not necessarily those of the
Bank of England or its committees.

1

Introduction

Liquidity crises have become increasingly common in the non-bank financial sector. Recent
examples include the pandemic-era “Dash for Cash” in Spring 2020, the 2022 commodity
market turmoil following Russia’s invasion of Ukraine, and the UK LDI crisis in September
2022.1 and These liquidity crises are linked to the surge in the use of hedging instruments inthe past decade — by pension funds, insurance companies, and alternative investment funds
employing tools like interest rate swaps and repos.2 These crises have also been accompanied
by distinctive trends in interest rates. While government bond yields have been low andfalling in recent decades, they have often risen sharply around these crises.
This paper argues that falling interest rates lead to a less examined form of liquidity risk,
which relates to the recent rise in hedging instruments, and applies to non-banks and banks
alike. We label this risk Liquidity After Solvency Hedging or “LASH” risk. Institutions take
LASH risk when they hedge against losses, using strategies that lead to liquidity needs whenthe value of the hedge falls and the solvency of the institution improves. As such, LASH isdifferent from other forms of liquidity risk that materialize when solvency deteriorates. We
argue that lower interest rates lead non-bank financial institutions, with longer term liabilities
than assets, to increase LASH risk, which then materializes when rates rise sharply.
We start with a simple framework to define LASH risk, differentiate it from other formsof liquidity risk, and link LASH risk to falling interest rates. As an example, consider a fund,best thought of as a life insurer or a pension fund, with long-duration liabilities, arising fromits commitments to its members. These commitments stretch beyond the duration of mostbonds and so the fund has a portfolio of shorter-duration assets. A fall in interest rates
lowers solvency, since the value of its liabilities rises more than the value of its assets. The
fund has different strategies to hedge this solvency risk. In particular, the fund can use aninterest rate swap, which pays out when rates fall. However, this hedging strategy exposes
the fund to liquidity risk when rates rise, because the value of the swap falls and the fundmust pay margin to their counterparty (Froot, Scharfstein and Stein, 1993). That is, thefund must pay liquid assets equal to the fall in the value of the swap. This requirement to
pay margin is LASH risk materializing.
1

The disruption in global sovereign bond markets during the Dash for Cash has inspired a volume ofacademic research, see e.g. Duffie (2022); He, Nagel and Song (2022) or Czech, Huang, Lou and Wang
(2023). Other recent studies examine the dynamics during the 2022 commodity market turmoil (Avalos andHuang, 2022) or the UK LDI crisis in the same year (Pinter, 2023).
2
For example, the outstanding gross notional in interest rate derivatives has increased from $426 trillion
in 2017 to $574 trillion in 2023. Similarly, FX gross notionals have risen by 38% to $120 trillion over thesame period (BIS, 2023).

1

We formalize these ideas using a simple model of a fund with short duration assets
and long duration liabilities. The fund hedges the duration mismatch using interest rates
derivatives to avoid the costs of insolvency. The derivative in our model is best interpreted
as a swap, but we also discuss how LASH risk applies to other hedging strategies for financial
institutions, such as repo (i.e. short term collateralized debt). A loss on the swap generates
the need for liquidity, which can be costly because holding liquid assets requires paying a
convenience premium, and selling longer term assets requires paying liquidation costs. The
optimal hedging strategy trades off the loss of solvency when rates fall with illiquidity whenrates rise.
LASH risk is different from some other common forms of liquidity risk. In our example,
the fund is exposed to LASH risk precisely when their solvency improves, due to risingrates. Therefore, LASH risk differs from the feedback between funding and market liquidity(Brunnermeier and Pedersen, 2009), which arises when solvency deteriorates. In the example
LASH risk applies to institutions who borrow long duration and invest in short duration
assets, the opposite of the maturity mismatch of a typical bank.3 As such, LASH risk is
associated neither with maturity transformation and callable claims (Diamond and Dybvig,
1983), nor with rollover risk (Calvo, 1988).
We show that incentives to take on LASH risk increase in a low interest rate environment.
Unless the fund is fully hedged against interest rate risk, falling rates reduce net worth andbring the fund closer to costly insolvency. Funds can avoid insolvency by further hedging—at
the expense of further LASH risk. This idea is again formalized using the trade off in oursimple model.
With our conceptual framework in hand, we make three contributions. First, we measure
LASH risk for pound sterling interest rate contracts held by UK non-banks, and find thatLASH risk is large. In this context, LASH risk measures how many liquid assets an institution
needs to provide as margin when interest rates change. For instance, suppose a pension fundholds an interest rate swap to hedge against falling rates. We measure how many liquid
assets the fund must pay to its counterparty when the value of the swap falls because rates
have risen. We also discuss how to apply our methods to measuring LASH risk for othermarkets and hedging strategies, such as foreign exchange (FX) risk and FX swaps. We apply
the measure to regulatory data from the Bank of England on the universe of sterling repo
transactions, the universe of pound sterling interest rate swap positions and the universe of
UK government bond transactions. Our measure is available at the institution level and in3

Nevertheless LASH risk can also apply to banks, when they use derivatives or other funding strategies
to hedge their solvency risk.

2

real time, starting from 2019. We find that LASH risk is large: at the peak level of risk, a
100bps rise in interest rates would have generated liquidity needs close to the cash balancesof the entire UK pension fund and insurance sector.
Our second contribution is to argue that low interest rates cause LASH risk. To start,
we find that in the aggregate time series, low interest rates associate with high LASH risk.
LASH risk increases from 2019 through 2022 as interest rates fall; and then falls as interest
rates rise. This association remains when we remove mechanical effects of interest rates on
LASH risk due to the convexity of the hedging strategy. However, other factors could havecaused these patterns. For instance, macroeconomic conditions could have affected both ratesand LASH risk. Therefore, to identify the causal effect of interest rates on LASH risk, wepursue a cross-sectional identification strategy. We identify non-banks that are particularly
exposed to a decline in interest rates, as they hold relatively short-duration assets. These
investors experience declining solvency as interest rates fall. Our framework predicts theseinvestors should hedge more against interest rate risk, in order to avoid costly insolvency,
and in doing so raise LASH risk. Consistent with our framework, the exposed institutions
raise their LASH risk as interest rates fall, relative to investors with higher-duration assets.
Our final contribution is to show that when rates rise sharply, the LASH risk causedby the previous decline in rates leads to liquidity crises. We study the liquidity crisis in
the UK pension fund sector in October 2022. That period was characterized by sharply
rising interest rates, and margin calls and gilt sales by UK pension funds. We find thatinvestors with larger LASH exposures sold substantially higher quantities of gilts during the
LDI crisis: a one standard deviation increase in pre-crisis LASH risk is associated with 15%
higher daily sell volumes during the crisis. The effect is particularly pronounced for indexlinked gilts, high-duration gilts, and gilts that are frequently used as repo collateral by these
hedging entities. Gilt sales due to LASH risk exacerbated the crisis further. High LASH
risk investors significantly contributed to the yield spike in the gilt market: a one standard
deviation increase in LASH-induced trading is associated with a 4.1bps daily increase in gilt
yields (or 66bps over the entire 16-day crisis period).
Figure 1 summarizes the main empirical results of the paper. The figure reports ourmeasure of LASH risk for non-bank sterling rates instruments, at weekly frequency, alongside
the ten-year government bond rate. There are several findings. First, LASH risk is large. A
100bps point rise in interest rates exhausts almost the entire cash holdings of the pension
fund and insurance sector at several points in our sample. Second, the figure captures anevident “inverse U” shape, meaning low rates associate with high LASH risk. As a result,
LASH risk is high on the eve of the September 2022 LDI crisis, which we have argued
3contributed to the ensuing market turmoil.
Figure 1 LASH risk: Non-Bank Financial Intermediaries

NOTE. Estimated liquidity needs after 100bps rise in interest rates relative to total cash holdings of UKA
pension funds and insurers (%). The measure corresponds to LASHi,tas defined in equation 4 in Section 3.

Our paper suggests that LASH risk is different from other forms of liquidity risk, with
implications for policy. With other forms of liquidity risk, policymakers tend to worry aboutproviding liquidity support during crises. The reason is that institutions often require liquidity support when their solvency deteriorates. Providing liquidity support ex post encourages
solvency risk and moral hazard ex ante (Farhi and Tirole, 2012). LASH risk is different.
Institutions increase LASH risk precisely when they hedge against solvency risk. Therefore
mitigating LASH risk ex post—for instance, by providing liquidity support during crises—
may reduce solvency risk by encouraging hedging ex ante. As such the policy trade-offs
from intervening against LASH risk may be quite different from other liquidity crises. A full
exploration is beyond the scope of the paper, but policymakers are actively debating thesequestions (e.g. Hauser, 2023a).
Related literature4

We contribute to several strands of the literature. First, we contribute to the literature on
liquidity risk, which has traditionally centered on banks and liquidity risk stemming frommaturity transformation or coordination failures (Diamond and Dybvig, 1983; Diamond andRajan, 2001; Rochet and Vives, 2004; Morris and Shin, 2004). In the context of reducing
banks’ interest rate risk, the literature explores the use of financial instruments (McPhail,
Schnabl and Tuckman, 2023), the role of maturity transformation as a hedge (Drechsler,
Savov and Schnabl, 2021) and the trade-off between interest risk and liquidity risk (Drechsler
et al., 2023). A related research strand focuses on the interactions between liquidity risk andclaims arising from mark-to-market valuations (Brunnermeier and Pedersen, 2009; Adrianand Shin, 2010). Our paper, focusing on how non-banks hedge solvency risks in the context
of interest rates, adds a new dimension complementing these papers.
Second, our work adds to general theories of investment incentives by examining how
non-banks respond to monetary policy in their pursuit of solvency (Campbell and Sigalov,2022).4 Bertaut, Bruno and Shin (2023) highlight the significant influence of non-banks
on global capital markets through their long term borrowing strategies. In their analysis,
duration risk interacts and is amplified by FX risk via valuation changes, affecting sovereign
bonds. Our paper focuses on the interaction of duration with solvency and liquidity risks.
In a similar vein, contemporaneous work studies the Dutch pension fund sector (Jansen,
Klingler, Ranaldo and Duijm, 2023), financial and non-financial sectors (Khetan, Li, Neamt, u
and Sen, 2023), and non-bank entities in the UK (Pinter and Walker, 2023). We contribute tothis literature by quantifying the liquidity implications associated with non-banks’ efforts tomaintain solvency by exploiting high-frequency data across various instruments and different
interest rate regimes.
Third, our paper links to the vast literature on the role of monetary policy, interest
rates, and financial stability. Stein (2012) develops a framework that explains the nexus
between financial stability, monetary policy, and the real economy. Theoretical and empiricalstudies study and document the risk-taking channel of monetary policy (Adrian and Shin,
2010; Jiménez, Ongena, Peydró and Saurina, 2014) or the importance of credit creation intimes of loose monetary policy on subsequent financial fragility (Grimm, Jordà, Schularickand Taylor, 2023). Moreover, Greenwood, Hanson, Shleifer and Sørensen (2022) show how
rapid credit and asset price growth predict financial crises.5 We expand this literature by
documenting how solvency hedging in low-interest rate environments has “sowed the seeds”
4

The relationship between interest rates and ‘reach for yield’ has been documented for insurers, pension
funds, mutual funds, and banks (Becker and Ivashina, 2015; Martinez-Miera and Repullo, 2017; Lu, Pritsker,
Zlate, Anadu and Bohn, 2023; Aramonte, Lee and Stebunovs, 2022).
5
Adrian and Liang (2018) and Boyarchenko, Favara and Schularick (2022) provide comprehensive reviewsof the research at the intersection of monetary policy and financial stability.

5

of future liquidity crises.
Fourth, we contribute to the literature on the regulation of pension funds and related
sectors, which considers various reforms to promote financial stability.6 Lucas and Zeldes(2009) and Lucas (2017) investigate how reforms to the discount rates applied to pension
funds’ liabilities affect the asset allocation of pension funds. Jansen et al. (2023) study
how regulatory constraints affect pension funds’ swap usage, and the resulting implications
for pension funds’ exposure to liquidity risks. Furthermore, Koijen and Yogo (2022) ask
how risk-based capital regulation affects the portfolio choice of life insurers. We argue thatLASH risk presents different challenges to regulators relative to other forms of liquidity risk,
because LASH risk rises when solvency improves.
Lastly, we contribute to the liquidity and financial crisis literature. Brunnermeier (2009);
Adrian, Kiff and Shin (2018); Bernanke (2018) document mechanisms, causes, and effectsof the liquidity dry-ups during the Great Financial Crisis. Furthermore, Borio, Claessens,
Schrimpf and Tarashev (2023) document the increased use of collateral to mitigate risk.
Recent studies analyze the market liquidity shocks during the onset of the Covid-19 pandemic(“Dash for Cash”) in the US (Haddad, Moreira and Muir, 2021), the role of mutual funds’
liquidity transformation (Ma, Xiao and Zeng, 2022; Huang, Jiang, Liu and Liu, 2021), andthe role of holding dollar assets for UK investors (Czech, Huang, Lou and Wang, 2023; CesaBianchi, Czech and Eguren-Martin, 2023). Pinter (2023) and Chen and Kemp (2023) dissect
the market dynamics and policy responses during the UK LDI crisis in Autumn 2022. This
paper sheds light on non-banks’ role in the run-up to and during the LDI crisis. More broadly,
our paper is connected to the literature on the role of liquidity providers (Holmström andTirole, 1998; Farhi and Tirole, 2012) with a more recent focus on monetary policy (Acharya
and Rajan, 2023).
The paper is organized as follows. Section 2 advances the framework and the definition of
LASH risk. Section 3 describes the measurement of LASH risk for sterling rate exposures ofnon-banks. Section 4 presents the institutional background of non banks’ hedging strategies
and describes our data in more detail. Section 5 shows stylized facts on LASH risk inthe context of sterling rates. Section 6 analyzes the causal effect of interest rates on our
behavioral LASH risk measure. Section 7 analyzes the consequences and the whiplash during
the recent LDI crisis episode. Section 8 concludes.

6

See Scharfstein (2018) for an overview.

6

2

LASH risk: A Framework

This section provides an overview of our conceptual framework, which introduces “LASH
risk” — the liquidity risk following hedging against solvency risk. To start, we focus onchanges in interest rates as the underlying threat to solvency but we will argue that LASH
risk can extend to other classes of risk. In Appendix A, we express the framework in a modelof the portfolio choice problem of a fund exposed to both interest rate and liquidity risk;
this model formalizes the discussion below.
Consider a financial institution with a portfolio characterized by short-duration assets
and long-duration liabilities, as illustrated in Figure 2. This could represent a pension fundor insurer with liabilities to its members that will realise after much of the existing stockof bonds matures. An asset or liability with a relatively longer duration will experience agreater decline in its value when interest rates rise and a greater increase when rates fall. Dueto the duration mismatch, a decline in interest rates increases the value of the institution’s
liabilities more than the value of its assets, as illustrated in 2.b, and its solvency worsens. In
contrast, when rates increase, the depreciation in the value of the institution’s liabilities isgreater than that of its short-duration assets, as depicted in 2.c, and its solvency improves.
Figure 2 Non-Bank Financial Intermediaries and Interest Rates

a. Fund with long-term liabilities vsassetsb. Rate fall worsens solvency

c. Rate rise improves solvency

How can the institution in Figure 2 institutions hedge its duration mismatch? The obvious approach is to lengthen the duration of its assets. However, the liabilities of a life insurer,
for example, can extend well beyond three decades, exceeding the maturity of most outstanding bonds. The funds needs a hedge. One option is to write a derivative contract—such as
an interest rate swap—where the institution pays a floating rate in exchange for a fixed rate7

(as in Figure 3). Such a contract will appreciate in value when rates fall, offsetting the loss
on the rest of the institution’s portfolio. The swap partially neutralises the sensitivity of theinstitution’s solvency to interest rate risk (Figure 3.b). However, such a strategy generates
liquidity risk, given that derivative contracts such as swaps are constantly revalued. The
contract requires the frequent transfer of liquid assets or cash between counterparties to keep
the contract net present value at zero based on prevailing market prices (a practice known
as variation margining). Hence, when interest rates increase, the institution may become
more solvent, but there is simultaneously a decline in the value of the hedge. Consequently,
the institution must make payments today to its derivatives counterparty (Figure 3.c). In
such a case, the hedging strategy generates an immediate demand for liquidity even if theunderlying improvement in the institutions’ solvency position has yet to be realized (Frootet al., 1993).
The institution faces a trade-off that we formalize in our model. Hedging transfers
resources to states of the world where the institution is facing a loss from states of theworld where it has potentially costly liquidity needs. Hence, despite having access to thenecessary instruments, the institution does not perfectly hedge the risks to its solvency. This
result relies on several ingredients. First, the institution cannot simply invest in longer term
assets to close its duration mismatch; this reflects a relative scarcity of very long duration
debt, and we take this inability to match duration precisely as a premise given the observed
hedging behaviour documented in Section 5. Second, the institution needs to be adverse
to insolvency, this generates effective risk aversion and a motive to hedge. Third, liquidity
must be costly to obtain, because: (i) holding liquid assets is expensive due to, for example,
a convenience premia on money-like assets; (ii) liquidating longer-term assets comes at a
cost or (iii) obtaining finance, even as solvency improves, is costly. The latter reflects thetransactional, arms-length nature of financial market transactions compared to relationshipbased finance where a verifiably more solvent, less liquid position could be handled with theextension of unsecured credit.
Importantly, this trade-off depends on the underlying solvency position of the financial
institution. A fund with a large net value is less concerned about insolvency and hence thetrade-off swings towards not bearing liquidity risk. In contrast, an institution with limited
net worth cannot afford further shocks to its solvency and so hedges more. However, thesolvency of a fund with the duration mismatch in Figure 2 depends intrinsically on the levelof the interest rate. Given imperfect hedging, a rise in rates raises net worth, which in turnlowers hedging demand and LASH risk. With low rates, the opposite is true and so a lowinterest rate environment leads to more LASH risk. In the Appendix, we demonstrate this8

rise in liquidity risks following a decline in the long term average rate.
Figure 3 Non-Bank Financial Intermediaries and Hedging

a. Buy a Swap

b. Pays out when rates fall + eliminates
solvency riskc. Liquidity needs when rates rise

Derivatives are not the only means to hedge. The institution could also manage interest
rate risk by shortening the duration of its liabilities by borrowing short term. Specifically,
the institution could use a repurchase agreement (repo) to borrow short and use the proceeds
to invest in longer-duration assets.7 This effectively replicates an interest rate swap as theinstitution pays a short term rate on its borrowing and receives the fixed, long term rateon the assets it purchases. However, repurchase agreements are also subject to margin
requirements. A fall in the value of the underlying collateral needed to secure the borrowing
either requires further assets (or cash) to be pledged or the borrowing to be repaid. Again,interest rate rises, and the subsequent fall in bond prices generates immediate liquidity needs.
The financial institution does not even have to engage in the borrowing itself. It could instead
take an equity stake in a fund that uses the equivalent repo contracts to leverage up and buy
longer-dated assets. The payoff from the stake in the fund replicates the hedging strategy.
Still, lower interest rates increase the solvency risk for the institution, while liquidity needs
rise with higher interest rates.
In the case of minor market fluctuations, this adjustment in liquidity needs is unlikely
to cause significant disturbances. Financial institutions maintain liquidity buffers, therefore
small shocks need not precipitate fire sales. However, significant asset price movements canpotentially disrupt financial stability. This leads to a semi-paradoxical situation when it is7

A repo is a form of short term borrowing where the borrower sells a financial security to a lender withthe contractual agreement to buy it back at a later date at a specified price. In our setting, we focus on theliquidity demands—rather than the rollover risks—connected with these contracts.

9the asset price movements that, in the absence of hedging, are associated with large gains
in solvency that generate liquidity crises.
Interest rate risk is one sizeable application of LASH risk, but the concept is generalizable to other financial instruments and hedging strategies. An institution that has an FX
mismatch on its balance sheet can make use of FX derivatives (e.g., swaps or forwards) tohedge movements in exchange rates. Again this reduces solvency risk, but at the expense ofincreasing liquidity risks as these derivatives are also margined. Large swings in exchange
rates can then lead to costly fire sales (e.g., the “Dash for Cash” in Spring 2020, see Czech
et al. 2023) which share the same features. Similarly, the Ukraine-Russia war led to large
margin calls in commodities markets, and the funding costs of commodity traders facingthese liquidity demands spiraled (Avalos and Huang, 2022).
The discussion—and the link between risk in financial institutions and crises—reveals distinct mechanisms. LASH risk differs from traditional notions of maturity transformation andrun-risk (Diamond and Dybvig, 1983). In this case, the risk of a bank run is linked to the mismatch between financial intermediaries’ engagement in illiquid, long-duration projects andthe provision for savers to withdraw funds on demand. However, illiquidity in our framework
is independent of callable claims or short term debt liabilities. Indeed, our example considers institutions with illiquid longer-duration liabilities actively trying to hedge solvency risk.
Our model stands apart from those studies that feature multiple equilibria and self-fulfilling
crises, such as Calvo (1988), where a cycle of high interest rates that increase the likelihoodof default, which then perpetuates higher interest rates, is observed. Our mechanism also
differs from scenarios where rollover risks are spawned by ‘sunspots’ that exacerbate underlying bad fundamentals (Cole and Kehoe, 2000). Furthermore, our mechanism is separate
from rollover crises stemming from creditors’ coordination failures (Morris and Shin, 2004).
In contrast to the prior literature, we highlight a mechanism where solvency and liquidity
risks are negatively correlated. Lastly, the change in asset values stems predominantly fromchanges in the value of fundamentals and external shocks, and not necessarily from trading
frictions that lead to fire sales.
Our perspective is also distinct from the framework proposed by Brunnermeier and Pedersen (2009), which stresses the feedback between funding and market liquidity. In particular,
their model delineates the interplay between an asset’s market liquidity and a trader’s funding
liquidity, with traders’ provision of market liquidity contingent on their funding conditions.
The authors elaborate on the dependency of traders’ funding requirements—such as capitaland margin calls—on the liquidity of assets in the market. In their analysis, margin requirements can, under specific circumstances, contribute to financial instability, and a symbiotic
10

reinforcement exists between market liquidity and funding liquidity that can incite liquidity
spirals. To further illustrate the difference, consider a fund that has entered a leveraged bet
on a risky asset with a margin requirement as in Figure 4. A shock leads to an initial loss,
which wipes out some of the bank assets/net worth, which leads to margin calls (Figure 4.b).
The financial institution sells assets to meet margin calls, which pushes down asset prices,
further raising margin requirements and causing further asset sales (Figure 4.c), leading to a“liquidity spiral” as explained by the authors (see Figure 2 in their paper). A fundamental
difference is that in our case, there are no losses; instead, as explained, solvency improves asliquidity risks materialize.
Figure 4 Comparison: Funding Liquidity (Brunnermeier and Pedersen, 2009)

a. Fund has leveraged bet on a risky
asset with a margin requirement.

3b. Initial loss wipes out some ofbank assets/net worth..
- Leads to margin calls...

c. Leads to margin calls...
- ... leading to asset sales...
- ... pushing down asset prices...
- ... raising margin requirements...
- ... add causing further asset sales.

Measurement: Interest rate LASH risk for Non-Banks

In its most general form, LASH risk measures the liquidity needs derived from the sensitivityof the net present value of a financial hedging contract with respect to changes in the valueof the hedged instrument—for example, FX, inflation, or interest rates. In this section, we
focus on LASH risk arising from interest rate hedging and consider the two most common
hedging strategies: the use of repo and the use of interest rate swaps.

11

3.1

Measurement: General Concept

LASH risk from interest rate risk for hedging contract i at time t can be conceptualised in
the following manner:
LASHi,t ≈ Λi ×

∂N P Vi,t
,
∂Rt

(1)

where N P Vi,t is the relevant net present value of the hedging contract (this could be either
the discounted value of a swap or repo collateral), and Rt is the underlying interest rate.
One can interpret∂N P Vi,t∂Rt

as the effect of a uniform shift in the yield curve. Λi capturesliquidity needs per unit of 
NPV change,
which may differ based on the contract type. Weassume Λi to be a constant

∂Λi
=0
∂Rt

, and hence we abstract from second-order effects fromR to liquidity needs, which may for instance arise from margin spirals or an increase in repo
haircuts.
For a given institution j that holds Qi,j,t of a given hedging contract, its aggregate LASH
risk is given by
LASHj,t =X

Qi,j,t LASHi,t .

(2)

iLetting Qi,t denote the aggregation of contracts across institutions, aggregate LASH risk isgiven by
LASHtA =X

Qi,t LASHi,t =i

XA
LASHj,t.

(3)jNote that liquidity claims, and LASH risk, are not unidirectional - firms can be either
net liquidity receivers or payers at any moment in time, depending on both the direction of
their exposure and the price moves of the underlying instrument. If the contract value Qi,tdecreases (increases) from the perspective of institution j, then the firm is obliged to post
(receive) margin. For example, pension funds are exposed to liquidity demands when yields
rise, whereas their counterparties (mainly dealer banks) have to post margin when rates fall.
Therefore, given that each contract involves two counterparties, the aggregate measureof LASHtA for all institutions in the economy is close to zero. When we document positive
LASH risk for the non-bank financial sector, it implies that another set of agents in theeconomy has negative LASH risk exposures (in the UK, for example, that would be thebanking sector—see, e.g., Khetan et al., 2023).

12

3.2

Measurement: Mechanical versus Behavioral LASH risk

The term∂N P Vi,t∂Rt

in equation (1) is not constant at the contract level, as it depends on thelevel of interest rates. For example, the value of a bond or the fixed leg of a long-dated
swap both become more sensitive to interest rate movements when rates are lower; this isreflected by the convexity of the hedging contract. Since a goal of the paper is to explore
how LASH risk varies with interest rates we need to account for this automatic link. We
introduce a simple decomposition of LASH risk into two separate parts, which we label its“mechanical” and “behavioral” components. The mechanical component captures convexity.
The behavioral factor captures how the financial institutions have shifted their allocation ofhedging, Qi,j,t , towards contracts i with ex-ante higher or lower LASH risk.
Consider the definition of aggregate LASH risk in equation (3). We can separate the behavioral and mechanical components via a standard first-order decomposition. In particular,
we can write the change in aggregate LASH risk asaggregate change

behavioral changez X }|
{ X
z
}|
{
X
∆
Qit LASHi,t =Qi,t ∆LASHi,t +LASHi,t−1 ∆Qi,t .
i

|i

(4)

i

{z

mechanical change}

As can be seen, the behavioral component measures how LASH risk changes as firms’
holdings of different hedging contracts change, holding fixed the duration and convexity of
the hedging contracts themselves. Equation (2) can be likewise decomposed the obtain ameasure of behavioral LASH risk at the institution level.
Both the mechanical and the behavioral components of LASH risk are relevant for liquidity needs. However, the behavioral component is of particular interest. The response of the
behavioral component to interest rate changes will measure “reach for illiquidity” behavior;that is, whether firms reallocate towards hedging strategies with greater LASH risk in a
low-rate environment.
We measure LASH risk arising from interest rates for repos and interest rate swaps, withthe methodology described in Appendix C.

4

Institutional Background and Data Sources

Next, before discussing our data sources, we give a birds-eye overview of the non-bank financial institutions for whom our measure of interest rate-based LASH risk will be particularly
13relevant.

4.1

Non-bank financial institutions

Among non-bank financial institutions, pension funds and insurers traditionally have thelargest duration gap between their assets and liabilities. Their liabilities consist of long term
payment promises to pensioners or contingent insurance beneficiaries. And they typicallyinvest in a mix of shorter duration assets, including stocks, government and corporate bonds,
or real estate. Insurance companies traditionally have a smaller duration gap than pension
funds and, as we will see, tend to exhibit lower interest rate hedging positions compared tothe pension fund sector.8 Other non-banks include, inter alia, asset managers, hedge funds,
and money market funds. Hedge funds and money market funds have a very small duration
gap, and are hence unlikely to build up substantial exposures to hedge solvency risks (in thecontext of interest rate risk).
By way of example, Figure 5 presents the aggregate balance sheet of UK defined benefit
private pension funds at the end of 2022.9 The balance sheet includes repo and investments infunds that engage in a liability hedging which we will elaborate on in a moment. However, theassets and liabilities exclude swap positions, which are off-balance sheet and noted separately.
We provide a longer discussion of the institutional details behind the UK pension fund sector
in Appendix B, but three points stand out from the figure. First, combining derivatives, shortterm borrowing and investments in specialised funds, the UK pension fund sector has interest
rate hedging exposures with a notional value the equivalent of 50% of the liabilities to fundmembers. This figure is also equivalent to three times the aggregate cash holdings of thefunds, which can limit the ability of the sector to meet margin calls.
Second, at the end of 2022, the net asset position of the funds was positive and notinsubstantial. The solvency of a pension fund is typically measured via its funding ratio,
which is defined as the fraction of the market value of its assets to the discounted value of
liabilities.10 However, this snapshot masks time series variation that illustrates the duration
gap that pension funds face. The aggregate funding ratio has swung from from approx. 90%
in 2020 to around than 130% at the end of 2022 as interest rates have risen (see Figure 6).
Third, around 10% of pension fund assets are invested in liability-driven investment (LDI)8

For instance, in the UK, insurers almost exclusively use interest rate swaps (and not repos) to hedge
their interest rate risk.
9
Calculations based on 2023 ONS data.
10
As we discuss in Appendix B, the yield curve from UK government bonds is typically used to discountUK pension fund liabilities.

14

Figure 5 UK Pension Funds: Aggregate Balance Sheetfunds. As we describe in Section 2, an alternative to the fund purchasing hedging contracts
itself is to invest in a separate fund whose equity generates the same payoffs. In practice, apension fund will transfer a small portion of its assets to the LDI fund in the form of an equity
stake, and the fund will then leverage those assets by engaging in repo borrowing to purchaselong duration assets. The equity stake in an LDI fund has a payoff structure that looks likean interest rate swap: the LDI fund receives a fixed rate on its long duration assets andpays a floating rate on its repo borrowing. Such LDI funds are advantageous as they allow
smaller pension funds to pool resources and outsource bargaining with repo counterparties.
The flip-side is that liquidity risks are potentially even greater when the liquidity needs areconcentrated in an arms-length fund due to the coordination problems that arise from thedispersion of fund investors. “Segregated” LDI funds are also available for larger individual
pension funds, addressing coordination challenges while inhibiting potential benefits from
economies of scale.

4.2

Data Sources and Coverage

To test our framework, we construct a database consisting of: i) the universe of UK government bond (gilts) transactions; ii) the universe of gilt repo transactions; iii) the universe ofsterling interest rate swap positions and iv) hand-collected UK pension fund balance sheet
data. The consolidated sample period across all datasets is January 2019 to March 2023.
15

Figure 6 Pension Funds’ Funding Ratios and Bond Yields

NOTE. Left Panel: Aggregate funding ratio (defined as total assets divided by total liabilities) of UK
pension funds in %. Source: Pension Protection Fund 7800 Data. Right Panel: Yields of UK government
bonds (gilts) at different maturities in %.

Bond Market

To analyze trading in the UK bond market, we use the transaction-level

MiFID II database maintained by the UK’s Financial Conduct Authority (FCA). The MiFID
II data provide detailed reports of all secondary-market trades of UK-regulated firms or
branches of UK firms regulated in the European Economic Area (EEA). Given that all bonddealers are UK-domiciled and hence FCA-regulated institutions, our data cover virtually alltransactions in the market. Each transaction report contains information on the transaction
date and time, ISIN, execution price, transaction size, and the legal identities of the buyer
and seller. We will focus on the UK government, or gilt, segment of the wider bond market
and from now on our usage of the term bond refers to those issued by the UK government(unless stated otherwise).11
Repo Market The Bank of England’s Sterling Money Market data (SMMD) is a transactionlevel dataset covering the sterling unsecured and secured (gilt repo) money markets. The
data are obtained from dealers in the respective money markets and have been collected
11

ISIN stands for International Securities Identification Number, and each bond issuance will have aunique ISIN.

16

since 2016. The data cover 95% of activity in which a bank or dealer is a counterparty, but
the data do not capture the small segment of non-bank to non-bank repo transactions. We
are again able to identify the identity of the counterparties, the collateral ISINs associatedwith each transaction, the transaction size, and the execution price.
Interest Rate Swap Market To analyse the interest rate swap positions, we use transactionlevel data from two EMIR Trade Repositories, DTCC and LSEG Regulatory Reporting
Limited (previously Unavista). We collect weekly positions on outstanding over-the-counter(OTC) GBP interest rate swap (IRS) and overnight index swap (OIS) trades where at least
one of the counterparties is a UK entity.12 The IRS dataset contains trade-level informationon the counterparties’ identities, notional, currency, floating rate, the direction of trade,maturity and execution date. The cleaning process of the database is largely based on
Khetan et al. (2023), with several additions that allow us to better exploit and understandthe outstanding positions of these entities.
In addition, to compute discount rates and construct our measure of LASH risk, we use
Bank of England data on OIS and yield curves as well as daily data on modified duration ofgilts from Bloomberg.
Pension Fund Balance Sheets

We construct, to the best of our knowledge, the largest

dataset with individual UK pension fund balance sheet details.13 We hand-collect data fromannual reports and newsletters for 100 individual pension funds from 2017 to 2022, covering
more than 40% of the UK pension sector by asset size in 2020.14 Our database includes
information on net investments, cash, bond and derivative holdings. Tables D.3 and D.4
summarise the cross-section of actuarial assets and liabilities, and the evolution of funding
ratios over time.

12
We retrieve the data via the Bank of England’s access to the mandatory reporting of the UK European
Markets Infrastructure Regulation (UK EMIR). More details on the reporting obligation can be found here.
For pre-2021 data (reported under EU EMIR), the Bank of England had access to (i) trades cleared by a
CCP supervised by the Bank, (ii) trades where one of the counterparties is a UK entity, (iii) trades where thederivative contract is referencing an entity located in the UK or derivatives on UK sovereign debt, (iv) trades
where the Prudential Regulation Authority (PRA) supervises one of the counterparties. For post-2020 data,
the Bank of England has access to all data reported to trade repositories under UK EMIR.
13
There is limited publicly available fund-level data on the composition of UK pension fund balance sheets.
Aggregate values can be found on the Office of National Statistics and The Pension Regulator websites, but
the breakdown at the pension scheme level is not publicly available. The closest exercise in collecting UK
data is done by Konradt (2023), covering 12 UK pension funds worth $300bn in asset size.
14
In 2020, we observe 65 pension funds worth £1046.9bn in actuarial assets, out of the total average of£2497bn in the UK pension fund sector that year. Our sample also includes 20 out of the largest 25 pension
funds by asset size—see the list here.

17

5

LASH risk from Interest Rates: Descriptive Facts

This section presents four descriptive stylized facts about our measure of LASH risk, fornon-bank financial institutions and sterling rates. In brief, we find that (i) LASH risk islarge, and higher when interest rates are low; (ii) movements in LASH risk are largely due
to behavioral rather than mechanical reasons; (iii) LASH risk is large for both interest rate
swaps and repo contracts; and (iv) LASH risk is concentrated in the pension fund (including
LDI funds) and insurance sector.
i. LASH risk is large, and higher when interest rates are low.
Figure 1 in the introduction demonstrates this fact, by reporting the aggregate LASH risk in
the non-bank financial sector from 2019 to 2023. To give a sense of scale, we normalize LASH
risk by the cash holdings of UK pension funds and insurers (who, as we will see, dominate
the measure). The units indicate that at the peak, a 100bps increase in interest rates would
have induced liquidity needs that would almost deplete the entire cash positions of both
sectors—in other words, LASH risk is very large. Moreover, LASH risk moves inversely withinterest rates. When long-dated government bond yields are relatively low, as in 2020, LASH
risk is relatively high. This fits the predictions of our framework.
ii. Movements in LASH risk are largely due to behavioral rather than mechanical reasons.
Recall that LASH risk can vary for two reasons: first, institutions might reallocate funds towards instruments with higher LASH risk; and second, the LASH risk of individual contracts
mechanically rises as interest rates fall due to convexity. Figure 7 demonstrates that behavioral effects dominate—the total LASH risk is shown in blue, and the behavioral component
in red. The two series co-move closely in the first three years of our sample. Therefore,
movements in LASH risk over time primarily reflect how institutions reallocate funding andhedging towards instruments with greater LASH risk. The divergence in the last two years of
the sample is due to mechanical effects—as interest rates rose over this period, the durationof hedging strategies fell.
The third and fourth descriptive facts are centered around the concentration of LASH
risk within the financial system.
iii. LASH risk is large for both interest rate swaps and repo contracts.
These are the two primary hedging strategies that we consider, both prevalent throughout
the non-bank financial system. In practice, both strategies generate significant LASH risk.
Figure 8 reports this result. In the figure, the blue line captures LASH risk for repo contracts,
whereas the red line is LASH risk for swaps. Both swap and repo exposures are large, and18

Figure 7 LASH risk: Behavioral Component

NOTE. This figure shows the evolution of the total LASH risk and the behavioral LASH risk component inP£bn for all non-banks. The Behavioral Component is defined as i LASHi,t−1 ∆Qi,t for interest rate swaps
and repos, respectively, as shown in equation 4 in Section 3.

the LASH risk from repo tends to be £20-30bn higher than the LASH risk from swaps.
However, towards the end of our sample, the LASH risk from swaps actually exceeds the one
from repo as pension funds sought to de-lever in the aftermath of the LDI crisis.
iv. LASH risk is concentrated in the pension fund sector.
Figure 9 displays this result. In the figure, we disaggregate LASH risk across five sectors,
namely regular pension funds, LDI funds, insurers, funds, and hedge funds. Broadly defined,
LDI funds belong to the pension fund sector. Considering LDI funds and regular pension
funds jointly, it is apparent that broad pension fund sector is the primary holder of LASH
risk.
Overall, these descriptive facts invite two questions. First, based on the first two findings,
what are the drivers of LASH risk—and do low interest rates induce investors to take on more
LASH risk? Second, based on the third and fourth finding, can LASH risk lead to financial
market turmoil, such as the distress in the pension fund sector after the announcement of
the UK “Mini-Budget” in autumn 2022? We will tackle both questions next.

19

Figure 8 Behavioral LASH risk: Swaps vs. Repo

NOTE. This figure shows the evolution of the behavioral LASH risk by instrument in £bn for all non-banks.
P
The Behavioral Component is defined as i LASHi,t−1 ∆Qi,t for interest rate swaps and repos, respectively,
as shown in equation 4 in Section 3.

Figure 9 Behavioral LASH risk: Sectoral Breakdown

NOTE. This figure shows the evolution of the behavioral LASH risk across different sectors in £bn. TheP
Behavioral Component is defined as i LASHi,t−1 ∆Qi,t for pension funds, insurers, LDI funds, hedge funds
and funds, respectively, as shown in equation 4 in Section 3.

20

6

Low Interest Rates and High LASH risk

Our descriptive evidence shows a striking pattern: in aggregate, LASH risk is high wheninterest rates are low. This is line with our theoretical framework which finds that a decline
in rates causes a loss of solvency for the relevant institution, which in turn raises hedging
demand and LASH risk. This section tests and confirms that low interest rates cause anincrease in LASH risk using a cross-sectional identification strategy.
To make causal claims, we exploit the cross-sectional variation from our rich regulatory
data. Our identification strategy analyzes how the assets held at the beginning of the sample
influence solvency afterwards. Specifically, investors holding relatively high duration assets
experience lower capital losses as interest rates fall, relative to investors holding low duration
assets. Therefore, as interest rates fall, solvency should deteriorate more for investors holding
low duration assets.15
Since low duration investors face greater solvency risk following a decrease in interest
rates, they require more hedging. As such, our simple framework predicts that low duration
investors should disproportionately increase LASH risk after interest rate falls. Appealingly,
the cross-sectional variation captures the same mechanism that we conjecture should operate
at the aggregate level. That is, LASH risk increases because falling interest rates reduce
solvency.
To implement our cross-sectional strategy, we assume that investors rebalance their portfolios each quarter, and hence estimate the following quarterly panel regression:
I
X

Behavioral∆LASHj,t= α+αj +αt +β1 ∆Y ield10Y+β2 (∆Y ield10Y(tt

ωj,i,t=0 ×ADi,t ))+ϵj,t , (5)iBehavioral
where ∆LASHj,tmeasures the quarterly change in the behavioral LASH risk of inPI
vestor j at the end of quarter t.
i ωj,i,t=0 × ADi,t is the weighted modified duration of

investor j’s assets, by calculating the investor-specific weights at the beginning of the sample
for each gilt (as proxied by investor j’s repo collateral portfolio) and multiplying these with
the quarterly change in a given gilt’s duration. ∆Y ield10Y
is the quarterly change in the tent
year gilt yield. To facilitate the interpretation of the coefficients, the dependent variable is15

Technically, net asset duration is what matters for solvency, rather than our measure of gross asset
duration. In Section E.1 of the Appendix, using our hand-collected balance sheet data, we explore the link
between pension funds’ gross asset duration and the sensitivity of their funding ratios to changes in interest
rates (as a measure of funds’ duration gap / net duration). The results confirm that there is a negative
correlation between investors’ gross asset duration and their net duration, i.e. the solvency of funds with alow gross asset duration is indeed more sensitive to a rate change.

21

transformed using the Inverse Hyperbolic Sine method. Therefore, the regression coefficientsmeasure the percent change in LASH risk, even if LASH risk is negative (see, e.g., Czech etal. 2023). The yields are denoted in percentage points, and the weighted duration variable
is standardized. We cluster standard errors at the quarterly level and include time fixed
effects to control for all time-varying macroeconomic trends. We also include institution,
institution-yield level (ten-year gilt yields) and institution-yield slope (ten-year minus twoyear gilt yields) fixed effects. Our set of fixed effects therefore absorbs both macroeconomic
and investor characteristics and hence most of the aggregate variation.
Our framework predicts that β1 is negative and that β2 is positive. That is, as bondprices rise and interest rates fall, investors with low duration assets suffer disproportionately.
Therefore, the LASH Risk of these investors increases more relative to investors with highduration assets.
Our identification assumption is that investors with initial short asset duration would
not have experienced capital losses relative to investors with initial long duration, for reason
other than their initial asset holdings. Though this assumption is difficult to verify, it iscertainly plausible. Investors hold long duration assets for many reasons that are orthogonal
to the other determinants of solvency such as fund manager skill.
Table 1 presents the results. We find that the effect is statistically and economicallysignificant and, as predicted, β1 is negative and β2 is positive. Column (1) shows that a
100bps quarterly decrease in the gilt yield index is associated with a 133% increase in the
behavioral LASH Risk of investor j. Importantly, the coefficient of the interaction term
reveals that this effect is reduced to a 44% increase (=-1.33+0.89) when the initial asset
duration of investor j increases by one standard deviation. Therefore, when yields decrease,
the LASH risk of low-duration investors increases more compared to the one their highduration counterparts.16
Therefore, falling interest rates lead to an economically and statistically significantly
greater LASH risk taken by low duration investors—consistent with our mechanism. Therefore our cross-sectional identification strategy suggests that low interest rates are associatedwith high LASH risk—reassuringly, using a different source of variation from the descriptive
time series patterns of the previous section.

16

In untabulated results, we find that the effects also remain robust when controlling for the share ofindex-linked gilts in investors’ portfolios. We also obtain qualitatively similar results when using the theyields of the S&P gilt index instead of the 10-year gilt yields.

22

Table 1 Rates and Investor-level LASH risk
(1)

(2)

(3)

(4)

∆LASH Behavioral∆Y ield10Y∆Y ield10Y × Duration
Observations
R squared
Time FE
Institution FE
Institution-Yield Level FE
Institution-Yield Slope FE-1.33***(0.37)
0.89**(0.37)

0.95**(0.35)

1.08***(0.35)

0.87**(0.37)

4657
0.016
no
yes
no
no

4657
0.024
yes
yes
no
no

4657
0.040
yes
yes
yes
no

4657
0.063
yes
yes
no
yes

Note. For each investor, we calculate the quarterly change in the behavioral LASH Risk. The independent variable
is the quarterly change in the 10-year gilt yield, interacted with the modified duration of investor j’s assets at the
beginning of the sample. The dependent variable is transformed using the Inverse Hyperbolic Sine method; the yieldchange is denoted in percentage points; and the modified duration is standardized. Clustered standard errors on thequarter level are reported in parentheses. We include investor, quarter, institution-yield level (ten-year gilt yields)
and institution-yield slope (ten-year minus two-year gilt yields) fixed effects. fixed effects. *** p<0.01, ** p<0.05, *p<0.1. Coefficients corresponding to the constant, control variables and fixed effects not reported.

7

Consequences: Backlash During Crises

Having established the pronounced build-up of LASH risk in recent years, we now examine
the link between non-banks’ pre-crisis liquidity risk exposures and their UK government
bond trading activity, and the subsequent impact on yields during a recent stress episode.
To do so, we examine the recent 2022 UK LDI crisis, when the yields of long-dated gilts
spiked by more than 100bps.

7.1

LASH risk and Investor Selling Pressure

On 23 September 2022, the then Chancellor, Kwasi Kwarteng, presented a “Mini-Budget”
proposal to the UK Parliament. The abrupt change in the fiscal stance initiated a sharp
downward adjustment in government bond prices, which was amplified by the vulnerabilities—
LASH risk—in the pension fund and LDI sector (Figure 9). 30-year gilt yields rose by 130bps
in a matter of days, as investors had to sell their holdings to obtain cash to meet margin
calls on their term repo and IRS positions.17 Importantly, these liquidity demands occurred
17

During the 2020 ”Dash for Cash”, in contrast to the LDI crisis, the principal shock was a rapid depreciation of pound sterling against the dollar, triggering large margin calls on investors’ FX hedging positions(Czech et al., 2023).

23

against the backdrop of pension funds’ improving funding ratios, as the present value of
their liabilities decreased due to higher discount rates (i.e. gilt yields, see Figure 6). As
the liquidity crisis intensified, the Bank of England was required to intervene to safeguard
financial stability. The Bank’s temporary and targeted backstop, announced on September
28 and scheduled to end on October 14, proved effective in ending the fire-sale dynamic
and helped pension funds to adjust their portfolios by reducing their repo leverage (Hauser,
2023b; Alexander et al., 2023). In total, pension and LDI funds sold nearly £30bn in the
period between September 23 and October 14 (see Figure 10 and Pinter 2023).
Figure 10 LDI Crisis: Non-Banks’ Bond Trading Volumes

NOTE. Total net gilt trading volumes of UK non-bank financial institutions following the Mini-Budget
announcement on September 23 up until the end of the BoE intervention on October 14.

Against this backdrop, we now analyze whether non-banks’ pre-crisis LASH exposures
can predict their gilt selling activities during the market turmoil. Our hypothesis is that
institutions with larger pre-crisis LASH risk, and hence a more pronounced risk of facing
large liquidity demands (i.e. margin calls) during the crisis, sold relatively higher quantities
of gilts than investors with low pre-crisis LASH exposures.
To analyze the link between LASH risk, the liquidity demands and bond trading during
the LDI crisis, we first divide the non-banks in our sample into four groups based on theirpre-crisis LASH exposures, calculated from both their repo and IRS positions. We measure
the investor-specific LASH exposure on August 30, hence well in advance of the onset of thecrisis and before the election of Liz Truss as Prime Minister.
24

At the peak of the crisis, as shown in Figure 11, the estimated cumulative change in thevalue of repo collateral—an upper bound for repo variation margin calls (i.e. the crystallization of LASH risk for repo)— reached almost £60bn across non-bank financial institutions.
Figure 11 also demonstrates how the group of non-banks with particularly large ex-ante
LASH risk (Quartile 4) was most severely affected by the sharp drop in the value of theposted repo collateral. This group explains almost the entirety of the £60bn aggregate dropin value. Unsurprisingly, this group mainly consists of pension and LDI funds, who had large
net exposures in term repo borrowing (see Figures D.3 & D.5). Consistent with this notion,
we observe a similar pattern when plotting the same graph for pension funds only, as shownin Figure D.12 of the Appendix. Conversely, the group with the lowest LASH risk was likely
a net receiver of repo variation margin during the crisis, with an estimated increase in thevalue of their repo collateral of around £6bn before the BoE intervention on September 28.
Figure 11 Estimated Cumulative Change in the Value of Repo Collateral by

Pre-crisis LASH Exposure

NOTE. Aggregate estimated changes in the value of repo collateral posted by UK non-bank financial institutions in £bn during the 2022 LDI Crisis, by quartile of their pre-crisis LASH risk: Quartile I captures
the non-banks with the lowest pre-crisis LASH exposures, while Quartile IV captures those with the highest
pre-crisis LASH exposures. Source: Sterling Money Market data collection.

We now turn our attention to the impact of LASH risk on non-banks’ bond trading
behavior. As shown in Figure 12, the group of non-banks’ with the highest pre-crisis LASH
exposure (Quartile IV) sold substantially higher quantities of government bonds compared25

to the other three groups. In total, this group sold more than £25bn during the crisis, while
the group with the lowest LASH risk (Quartile I) was in fact buying around £15bn worthof bonds. Before the crisis, the net volumes are very similar for all four groups. We again
observe a similar pattern when plotting the same graph for pension and LDI funds only:
as shown in Figure D.11 of the Appendix, the net sales of the pension fund sector wereconcentrated in the group of funds with the largest pre-crisis LASH exposures (Quartile IV).
Again, we do not observe any differential pre-crisis trends.
Figure 12 Cumulative Gilt Trading Volumes by Pre-crisis LASH Exposure

NOTE. Total net bond trading volumes of UK non-banks, by quartile of their pre-crisis LASH risk: Quartile
I captures the banks with the lowest pre-crisis LASH exposures, while Quartile IV captures those with thehighest pre-crisis LASH exposures.

To test the link between LASH risk and gilt selling pressures more formally, we use thefollowing regression specification :V olj,t = α + αs,t + β1 LASHj,t=0 + εj,t ,(6)where V olj,t measures the net trading volume of institution j at time t, including all nonbanks in our sample. We define the crisis period as the sixteen trading days between September 23 and October 14 (see Pinter 2023). We calculate a “combined” LASH measure, which
captures the LASH risk from both repo and IRS exposures, but we also run separate regressions for these two individual LASH risk components. The LASH variable is standardized to26

facilitate the interpretation of the coefficients. Furthermore, we also run separate regressions
for investors’ sell volumes, which capture whether investor j was a net seller on a given day.
Again, net and sell volumes are transformed using the inverse hyperbolic sine transformation to give the regression coefficient β1 an approximate percent change interpretation evenif volumes are negative. We include sector-day fixed effects and use standard errors clusteredon the day and sector level.
Table 2 LASH risk and Gilt Trading Volumes(1)(2)
Net Volume

LASH combined-0.21***(0.04)LASH Repo(4)
Sell Volume

0.15***(0.02)-0.16***(0.04)-0.13*(0.05)LASH IRS
Observations
R squared
Sector-Day FE

(3)

8875
0.035
yes

8875
0.035
yes

0.12***(0.02)
0.08***(0.02)
8875
0.046
yes

8875
0.046
yes

Note. For each investor, as defined in equation 3 in Section 3, ”LASH” is measured as thepotential liquidity needs following a 100bps shift in gilt yields, either for repo and IRS exposures
combined, or separately for both instruments. The dependent variable is the investor’s daily gilt
net trading volume on day t in Columns (1) and (2), and the investor’s sell volumes on day t
in Columns (3) and (4). The dependent variables are transformed using the Inverse Hyperbolic
Sine method. The LASH variable is standardized. Double-clustered standard errors on the day
and sector level are reported in parentheses. We include sector-day fixed effects. *** p<0.01, **p<0.05, * p<0.1. Coefficients corresponding to the constant, control variables and fixed effects
not reported.

The results are shown in Table 2. Consistent with Figure 12, we find that investors withlarger pre-crisis LASH exposures sold substantially higher quantities of gilts during the UK
LDI crisis: a one standard deviation increase in pre-crisis LASH risk is associated with 15%
higher daily sell volumes during the crisis period (Column 3). Importantly, this effect isrobust to the inclusion of sector-day fixed effects, hence not driven by time-varying sector
characteristics. Furthermore, the effect is economically and statistically more significant for
the LASH risk from repo exposures, consistent with the larger magnitude of overall LASH
risk in the repo market. As a robustness check, we also conduct our analysis exclusively forthe pension and LDI fund sector in Table E.1 of the Appendix. Consistent with our baseline
results, a one standard deviation increase in LASH risk is associated with a 10% increase inpension fund daily sell volumes.
27

An important feature of the LDI crisis was the pronounced selling by “pooled” LDI funds,
in which multiple (often smaller) pension funds invest together—in contrast to segregated arrangements, where the assets of a single pension scheme are invested in a separate account.18
The speed and scale of the moves in yields following the Mini-Budget announcement outpaced the ability of pooled funds’ smaller clients—who typically rebalance their positions
only on a weekly or monthly frequency—to provide new funds (Breeden, 2022). As a result,pooled funds became forced sellers and liquidated large quantities of gilts (see Figure D.10
in the Appendix). To test this more formally, we use the following specification:
Sell V olj,t = α + αs,t + β1 LASHj,0 + β2 (LASHj,0 × T ype F undj ) + εj,t ,(7)where T ype F undj is an indicator variable for segregated and pooled LDI funds, respectively.
The remaining variables are defined as in Equation (6). We again include sector-day fixed
effects and use standard errors clustered on the day and sector level.
Table 3 LASH risk and Pooled LDI Funds
(1)

(2)

(3)

Sell Volume
LASH
LASH × Segregated Fund

0.20***(0.05)-0.08(0.06)LASH × Pooled Fund
Observations
R squared
Sector-Day FE

8875
0.047
yes

0.14***(0.02)

0.93***(0.02)

0.17***(0.03)-0.05(0.03)
0.90***(0.01)

8875
0.050
yes

8875
0.050
yes

Note. For each investor, as defined in equation 3 in Section 3, ”LASH” is measured as the potential liquidity needs following a 100bps shift in gilt yields for repo and IRS exposures combined.
The dependent variable is the investor’s daily sell volume on day t. ”Segregated Fund” and”Pooled Fund” indicate segregated and pooled LDI funds, respectively. The dependent variable
is transformed using the Inverse Hyperbolic Sine method. The LASH variable is standardized.
Double-clustered standard errors on the day and sector level are reported in parentheses. We
include sector-day fixed effects. *** p<0.01, ** p<0.05, * p<0.1. Coefficients corresponding to
the constant, control variables and fixed effects not reported.

The results are presented in Table 3. We find that the effect is indeed substantially more
pronounced for pooled LDI funds: a one standard deviation increase in LASH risk is assoAt the end of 2021, approximately £200bn of the £1.4tn in UK LDI assets were in multi-investor pooled
funds (Breeden, 2022).
18

28

ciated with 90% higher daily sell volumes for pooled LDI funds relative to other non-banks(Column 3). Intriguingly, the coefficient for segregated LDI funds is insignificant, emphasizing that the coordination frictions in pooled LDI funds—in combination with elevated LASH
risk—was a particularly strong driver of gilt sales during the crisis.

7.2

Bond-level Liquidation Choices

An important question at this point is whether the selling pressure was concentrated inbonds with particular characteristics. As investors with pronounced LASH risk exposuresfrequently invest in high-duration assets, our hypothesis is that the selling pressure increases
with the duration of a bond. Furthermore, we hypothesize that the selling pressure is also
more pronounced for gilts that are frequently used as repo collateral as well as for inflationlinked gilts. To test these hypotheses, we exploit the granularity of our data and run thefollowing regression on the investor-bond-day level:
Sell V olj,b,t = α+αs,t +αb,t +β1 LASHj,0 +β2 (LASHj,0 × Bond Characteristicsb )+εj,b,t (8)where V olj,t measures the net trading volume of institution j in bond b at time t. Bond
Characteristics includes: i) three duration buckets (low, medium, high), ii) two groups
measuring the frequency of the gilt’s usage as repo collateral (as measured by the total precrisis repo borrowing amount for each bond across all non-banks), and iii) index-linked gilts.
LASHj,0 is defined as in equation (6). We include both sector-day and bond-day fixed effects
and use standard errors clustered on the day, sector and maturity-bucket level.
The results are presented in Table 4. Consistent with our baseline results, we find thathigher pre-crisis LASH risk predicts bond sales pressure, even when controlling for sectorday and bond-day fixed effects. Importantly, confirming our hypotheses, we find that theeffect is particularly pronounced for index-linked gilts. For example, a one standard deviation
increase in LASH is associated with 6% higher daily sell volumes in index-linked gilts (relative
to 4% higher sales in nominal bonds). Moreover, the effect is weakly statistically significant
for high-duration gilts and gilts that are frequently used as repo collateral.

7.3

Impact of Selling on Yields

The previous analyses have shown that non-banks with higher pre-crisis LASH risk indeed
sold significantly higher quantities of gilts during the LDI crisis, particularly in the case of
longer-maturity bonds and bonds frequently used as repo collateral. An important question
29

Table 4 LASH risk and Bond-level Liquidation Choices
(1)

(2)

(3)

(4)

Sell Volume
LASH

0.05***(0.00)LASH × Frequent Collateral Use

0.04***(0.00)
0.01*(0.00)LASH × Low Duration

0.04***(0.00)

0.01(0.01)
0.01*(0.00)LASH × High Duration
LASH × Inflation-linked
Observations
R squared
Bond-Day FE
Sector-Day FE

0.04***(0.00)

0.02**(0.01)
42481
0.115
yes
yes

42382
0.115
yes
yes

41667
0.114
yes
yes

42481
0.115
yes
yes

Note. For each investor, as defined in equation 3 in Section 3, ”LASH” is measured as the potential
liquidity needs following a 100bps shift in gilt yields, for repo and IRS exposures combined. The dependent
variable is the investor’s daily gilt sell volume in bond b on day t. ”Frequent Collateral Use” indicates thefrequent use of bond b as repo collateral, i.e. the top 50% of bonds based on their use as repo collateral.
”Duration” indicates the duration bucket of bond b (long, medium, short). ”Inflation-linked” indicate
index-linked gilts. The dependent variable is transformed using the Inverse Hyperbolic Sine method. The
LASH variable is standardized. Clustered standard errors on the day, sector and maturity-bucket level arereported in parentheses. We include sector-day fixed effects. *** p<0.01, ** p<0.05, * p<0.1. Coefficients
corresponding to the constant, control variables and fixed effects not reported.

at this point is whether and by how much this selling pressure contributed to the yield spikeduring the market turmoil in September and October 2022.
An obvious concern with this exercise is that non-banks’ selling of bonds may be driven
by many factors, including private information. To isolate the impact of LASH risk on
non-bank trading and, in turn, on yield movements, we follow Czech et al. (2023) andconstruct a measure of LASH-induced trading (LASH-IT). Specifically, we calculate each
investor’s LASH-induced trading in bond b assuming that each investor proportionally scales
up or down its holdings in response to liquidity demands. Due to the lack of complete
information on bond holdings of individual institutions, we approximate the weight of bondb in institution j’s portfolio, wj,b , by measuring the weight of the given bond in investor’s j
pre-crisis repo collateral portfolio. LASH-induced trading (LASH-IT) in bond b on day t is30then defined as:
LASH-ITb =Σj LASHj,t=0 × wj,b,t=0
Amount Outstandingb,t=0(9)where LASHj,t=0 is the estimated pre-crisis LASH exposure of institution j, and wj,b is theweight of bond b in investor’s j pre-crisis repo collateral portfolio, and Amount Outstanding b,t=0 is the bond’s amount outstanding before the crisis. We then employ the following
regression specification to measure the impact of LASH-induced trading on gilt yields during
the LDI crisis:∆Y ieldb,t = α + αm,t + αg,t + β1 × LASH-ITb + εb,t(10)where ∆Y ieldb,t is the daily change in yields. Again, we define the crisis period as the sixteen
trading days between September 23 to October 14. We also include maturity bucket-day
fixed effects (αm,t ) as well as type gilt-day fixed effects (αg,t ), which control for differential
effects for nominal and index-linked gilts. Standard errors are clustered on the bond level.
Table 5 presents the results. The effect is statistically and economically highly significant.
In most conservative specifications with maturity bucket-day and type gilt-day fixed effects(Column 4), a one standard deviation increase in LASH-IT is associated with a 4.1bps daily
increase in gilt yields. Over the entire 16-day crisis period, this would attribute around66bps of the yield spike to LASH-induced trading. For comparison, 30-year gilt yields spikedby 103bps over the same period—therefore, LASH-induced trading accounts for around two
thirds of the yield spike during the LDI crisis.
Table 5 Impact of LASH-IT on Gilt Yields
(1)

(2)

(3)

(4)

∆Y ieldt−1,tLASH-IT

9.29***(0.91)

9.72***(1.06)

3.21**(1.49)

4.13**(1.60)

Observations
R squared
Day FEDay × Type Gilt FE
Day × Maturity Bucket FE

1253
0.261
yes
no
no

1253
0.321
no
yes

1253
0.616
yes
no

1253
0.649
yes
yes

Note. As the dependent variable, we measure the daily change in yields for each bond. The
independent variable is the bond’s LASH-induced trading (”LASH-IT”) in bond b on day t as
defined in equation 9. The dependent variable is transformed using the Inverse Hyperbolic Sine
method. The independent variable is standardized. Standard errors clustered on the bond level
are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Coefficients corresponding to theconstant and fixed effects not reported.

31

8

Conclusion

In this paper, we introduce a framework to understand and measure the liquidity risk thatarises from financial institutions’ actions to mitigate solvency risk. Liquidity After Solvency
Hedging risk or “LASH risk”, arises when institutions use certain hedging strategies to reduce
solvency risk, which leads to higher liquidity needs when the value of the hedge falls andsolvency improves. We focus on LASH risk for non-banks such as pension funds, with long
duration liabilities and shorter duration assets. For these non-banks, LASH risk ought torise as rates fall, because solvency deteriorates which requires more solvency hedging.
We then make three empirical contributions. First, we measure LASH risk for the universeof non-banks’ sterling interest rate exposures, from interest rate swaps and repo, in the UKfrom 2019 onwards. LASH risk is large—at peak, a 100bps increase in interest rates leads toliquidity needs that would nearly deplete the entire cash holdings of the combined pension
fund and insurance sector. Second, we show that low rates increase LASH risk. In the timeseries, LASH risk is high when rates are low. We then exploit our granular data using a crosssectional identification strategy, comparing funds with different exposures to falling interest
rates. Funds who are more exposed, due to having shorter duration assets, increase LASH
risk by more. Third, we show that the LASH risk caused by low rates leads to liquidity
crises. In particular, during the September 2022 LDI crisis in the UK, fund-level LASH risk
is a strong predictor of bond sales by pension funds. As such, LASH risk contributed to the
spike in yields during the crisis.
The implications of LASH risk are different from some other forms of liquidity risk.
LASH arises from ‘responsible’ institutions trying to hedge solvency risks, and the riskmaterializes precisely when solvency improves. As such, LASH is different from other formsof liquidity risk that materialize when solvency deteriorates (Brunnermeier and Pedersen,2009). Therefore mitigating LASH risk ex post—through measures such as liquidity support
during a crisis—may not encourage solvency risk ex ante. As such, the policy tradeoffs fromintervening during a crisis may be different from conventional liquidity crises. We leave afull investigation of these ideas to future work. Likewise, we leave the analysis of LASH risk
and its implications in other market segments (e.g. foreign exchange or inflation) for future
research.

32

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37

AppendixA

A Model: Net Asset Values and Hedging DemandThis appendix presents a concise model that forms the basis of the conceptual framework
discussed in Section 2, mainly focusing on ‘LASH Risk’—the liquidity risk that arises fromhedging against solvency risk. The model considers the interest rate risk management problem of a non-bank financial institution, which we refer to as a fund and is best thought ofas a pension fund or an insurer.
This fund has an exogenously given perpetual liability that it needs to cover with aportfolio of assets. It can use interest rate derivatives, effectively a swap contract, alongside
manipulating the duration of it is portfolio to manage interest rate risk. The model has
four important ingredients that makes the analysis interesting and serve to highlight themechanisms we have in mind:
1. Asymmetric payoffs. For the fund (or more precisely its manager) reducing a deficit
by $1 is more beneficial than increasing a surplus by $1. Practically, this asymmetry
in payoffs might represent a regulatory penalty (e.g. in the UK, for example, pension
funds are explicitly taxed via a risk-based levy if they fall into deficit, see here.), but
broadly, it could encompass various reputational or behavioural explanations (see Lianet al. 2019).
2. Duration mismatch. The perpetual liability cannot be hedged by a perpetual bond,the fund only has access to financial assets of shorter duration. Swaps can be used tohedge (perfectly) but they generate the need for liquidity in the following period.
3. Liquid assets are expensive. The fund can self insure against liquidity needs byholding short duration assets but those assets require paying a convenience premium.
4. Illiquidity of the long duration asset. Holding only long term assets generates
liquidity costs in the case where the swap contract is out of the money and shortterm debt holdings are insufficient, selling the long duration asset requires paying a
proportional liquidation cost.
38

The net effect of the first ingredient is to introduce a kink in the objective of the fund. This
generate effective risk aversion and that motivates the hedging of interest rate risk. The
second ingredient guarantees that the fund will choose to the hedge interest rate risk partly
through the use of derivatives. The third and fourth ingredients insure that liquidity needs
generated by the hedge cannot be offset without a cost: either the fund must hold expensive
liquid assets or run the risk of liquidating a portion of its long duration portfolio. Hence,
there is an interior solution where the fund holds a combination of illiquid long duration
assets, expensive liquid assets and a hedging strategy that generates liquidity risk.
This liquidity-solvency trade-off means that the fund is imperfectly hedged. Therefore,
lower rates worsen the funds financial position. This pushes the fund closer to the kink in
its objective function which in turn raises effective risk aversion. Higher risk aversion raises
hedging demand and encourages the fund to take more liquidity risk.

A.1

Environment

We consider the investment problem of a non-bank financial institution (“the fund”). Timeruns from t = 0, 1, . . . , ∞. The fund has liabilities structured as a perpetuity that require
paying a fixed l in every period. The pension fund can invest in (i) a one period bond, at ,(ii) a geometrically decaying multi-period bond, bt , with decay rate δ: i.e. the bond has a
coupon bt in t + 1 with passive equation of motion bt+1 = δbt and (iii) an interest rate swap
st . The fund cannot short bonds: at ≥ 0 and bt ≥ 0, but the swap position, st , can bepositive or negative.
All assets are priced by a deep pocketed marginal investor active in the bond and swap
markets. The investor is competitive, risk neutral and discounts the future at rate Rt−1 . We
assume Rt−1 evolves according to a first order Markov process, F (R′ |R). This discount factor
is also used to value the fund’s liabilities. For certain results we will treat Rt−1 as i.i.d withmean R̄−1 . The marginal investor values the liquidity service from one period bond at rate
η. This is non-pecuniary. The fund does not share this service, instead the fund will receive
an endogenous liquidity benefit to one period debt.

39

Asset prices Let qtb denote the price of the geometric bond. The investor values the bond
hP
i

Qj
−1
j
b
−1 −1 −1
at qtb = Et
δ
R
Rt .
j=0
s=0 t+s . In the i.i.d. case the price becomes qt = 1 − δ R̄


P
Q
j
−1
Let qtl denote the price of a perpetuity paying one every period: qtl = ∞j=0
s=0 Et Rt+s .
−1 −1
Rt . Last, the liquidity service implies thatIn the i.i.d case, this price is qtl = 1 − R̄−1
the price of the short term bond is given by qta = Rt−1 (1 + η).
 −1 
−1
Interest rate swaps are priced fairly and have a fixed leg Et Rt+1
and floating leg Rt+1:
buying the swap means paying fixed and receiving floating. So the cashflows from the realised −1 
−1swap position are given by st Rt+1
− Et Rt+1.
We assume that the geometric bond is costly to sell. The fund bears a liquidation cost
qtb c per unit sold. The marginal investor does not discount the value of the bond due to theliquidation cost.

Fund value We can define the net asset value of the fund as wt = qta at + qtb bt − qtl l.
Accounting for liquidity costs, wt evolves according to
wt = at−1 + bt−1 − l + qtb δbt−1 + st−1 Rt−1 − Et−1 Rt−1 − cqtb max {0, δbt−1 − bt } −qtl l.
|{z}sales of geometric bondIn addition, the no shorting constraint implies that the fund must have sufficient cash on
hand from the payments it receives on its assets and bond liquidations to cover its swap
position. That is
at−1 + bt−1 − l + (1 − c)qtb max {0, δbt−1 − bt } ≥ st−1 Et−1 Rt−1 − Rt−1 .

Fund manager’s objective The fund manager is risk neutral, does not enjoy limited
liability and receives period compensation (that is negligible compared to the value of thefund) proportional toπt = wt + κ1 (wt < 0) wt ,where, in line with the above, κ > 0 is a penalty term that incentivises the manager to avoid
deficits. For simplicity, we assume the fund manager discounts the future at a fixed rate βrather than Rt−1 . How the manager discounts plays a limited role in the model and so the40assumption of a fixed rate is innocuous.

A.2

The fund manager’s problem

Let St = {Rt , Rt−1 } denote the state of the world at time t. The fund manager’s problem
can be expressed recursively as
max V (at−1 , bt−1 , st−1 ; St ) = (1 + κ1 [wt < 0]) wt + βE (V (at , bt , st ; St+1 ))at ,bt ,stsubject to
wt = qta at + qtb bt − qtl l,
qta at + qtb bt = at−1 + bt−1 − l + qtb δbt−1 + st−1 Rt−1 − Et−1 Rt−1 − cqtb max {0, δbt−1 − bt } .
The no shorting condition on at also implies the following cash flow constraint(1 − c)qtb max {0, δbt−1 − bt } ≥ max st−1 Et−1 Rt−1 − Rt−1 − at−1 − bt−1 + l, 0 . (A.1)
The right hand side is the loss on the swap contract net of the liquidity available to the fund.
When this value is positive, the fund needs to liquidate long term assets. The left hand sideis the proceeds from liquidations. When the left hand side of the above equation is positive,
we have the model analogue to LASH risk materialising: the fund is forced to sell assets ata cost to cover losses on its hedges. Since the fund will only ever liquidate if it is forced to,equation (A.1) holds with equality.
The flow budget constraint therefore can be expressed entirely in terms of past choicevariables and the interest rate:
qta at + qtb bt =at−1 + bt−1 − l + qtb δbt−1 + st−1 Rt−1 − Et−1 Rt−1 −




c
max st−1 Et−1 Rt−1 − Rt−1 − at−1 − bt−1 + l, 0 .
−
1−c

41

A.3

Analysis

We start by illustrating the fund’s exposure to interest rate risk, then discuss its optimal
hedging strategy, before discussing how the level of rates affects the demand for hedging.

The fund’s exposure to interest rate risk (excluding hedging). To start, imagine
that the fund never hedges (st = 0), then
dwt
dqtb
dqtl
=
b
−
l
.
t−1
dRt−1
dRt−1
dRt−1
Assuming the discount factor is i.i.d. with unconditional mean R̄−1 , then
1
dqtb
.
−1 =
1 − δ R̄−1
dRt
dqtl
1
dqtb
=
.
>
1 − R̄−1
dRt−1
dRt−1
dwt
So unless we have wt ≫ 0, we know dR−1 < 0 (i.e. a fall in interest rates hurts the fund).
t

The fund therefore should try to set st > 0.

Optimal hedging strategy. Consider the fund’s first order condition with respect to st :

βEt


d
(1 + κ1 [wt+1 < 0]) wt+1 = 0.
dst

Define the following conditional expectationsE:t [.] ≡ Et [.|wt+1 < 0] ,
 −1 

−1E⊚t [.] = Et .|st Et Rt+1 − Rt+1 − at − bt + l > 0 , −1 

−1
E⊖t .|st Et Rt+1 − Rt+1 − at − bt + l > 0, wt+1 < 0 .
These correspond to the expectations conditional on the fund having a deficit, having to⊖⊚liquidate and being exposed to both (deficit and liquidation). Define p:
t , pt and pt thecorresponding probabilities. By Leibnitz’s rule, we can ignore the effect of decisions on
42

probabilities at the margin.
Splitting along the dimension of whether the fund pays liquidity costs allows us to rewrite
the first order condition on st as −1 
 −1 
 −1 
 −1 
βcp⊚
t
:
E⊚
+ p:
+
t Rt+1 − Et Rt+1
t βκ Et Rt+1 − Et Rt+1
1−c
 −1 
 −1 
p⊖
t βκc
E⊖
= 0.
t Rt+1 − Et Rt+1
1−cNow, note that absent liquidity costs, the fund would be perfectly hedged against interest
 −1 
 −1 
:⊚rate risk and either set p:
t = 0 or Et Rt+1 = Et Rt+1 . But assuming pt > 0, this is not
optimal as insuring all interest rate risk ignores the costs of liquidity risk.
dwt
Since the fund is imperfectly hedged, we know that dR−1 < 0 and st . This means thatt

 −1 
E:− Et Rt−1 > 0,t Rt
the states of the world where the fund is in deficit are ones where the discount factor ishigher than expected (rates lower than expected). In contrast, the fund will have a liquidity
deficit if −1 
−1st Et Rt+1
− Rt+1− at − bt + l > 0.
So
 −1 
 −1 
E⊚
t Rt+1 − Et Rt+1 < 0,
the discount rate is low (interest rate high) when the fund faces a liquidity shortfall.
How about p⊖
t ? This means that the fund faces a deficit and a liquidity shortfall at thesame time. This is only possible if the fund’s initial deficit (i.e. wt ≪ 0) is so big that evena positive interest rate surprise, which causes a liquidity shortfall, still has the fund in a
deficit. So we still have −1 
 −1 
E⊖
t Rt+1 − Et Rt+1 < 0.
However, for simplicity, consider the case where p⊖
t = 0 (i.e. wt ≈ 0). Then the optimal43

hedging strategy sets −1 
 −1 
 −1 
 −1 
c:p:= p⊚
Et Rt+1− E⊚.
t κ Et Rt+1 − Et Rt+1
tt Rt+1
1−c
The fund trades off the fact that a swap transfers cashflows to states of the world where
the fund is in deficit, against the fact that the swap transfers cashflows away from states of
the world where the fund has a liquidity shortfall.

Low rates and LASH risk. The unhedged cashflows generated by the fund are given byat−1 + bt−1 − l,these are independent of Rt , where as we have
wt = qta at + qtb bt − qtl l,which are linked to current and future interest rates.
It follows that p:t , the probability of a deficit, is more sensitive to rates than current cash
flows. Holding st fixed, a fall in rates raises p:t , (via lower wt ) but it does not have much
impact on p⊚t . Hence, the left hand side of the hedging optimality condition rises more than
the right hand side in response to a fall in rates. So a fall in rates raises hedging demand.
To illustrate this, we solve the model numerically using value function iteration, assuming
an i.i.d. interest rate and parameterizing the model as described in Table A.1:
Parameter
c
δ
l
η
κ
β

Description
Value
Cost of liquidation
0.015
Decay rate of long term bond
0.91
Fund payment to its members at each period 0.04
Short term bond premium
0.014
Penalty for fund’s deficit
0.3
Discount factor
0.96
Table A.1 Summary of Parameters

We choose δ such that the duration of the long term bond is equal to 10 years. The
44

values for c and η are from Harris and Piwowar (2006) and Nagel (2016), respectively. To
show that funds are incentivized to increase their swap holdings after decreases in interest
rates, we solve the model on 12 different grids for R−1 , in which average R−1 ranges from1
0.8 to 0.95. This is equivalent to having average interest rates rt , defined as Rt =1 + rtranging from 25% to 5%.
We then simulate the response of the model to a persistent decrease in interest rates. We
start from the state a = 1, b = 1, s = 0.2 and R−1 =0.95 and then for the rest of the time,the interest rate falls so that R−1 =1.06 (this is equivalent to a fall in the interest rate from
5% to -6%). Figure A.1 displays the results.

2

1.5

1

0.5

High Average r
Moderate Average r
Low Average r

0

-0.5
0

5

10

15

20

25

Figure A.1 Swaps holding response to a fall in interest rate across different average values

for rHigh, Moderate, and Low average interest rates in the figure correspond to 14%, 10%,and 7%, respectively.19 The results are consistent with the intuition. When the interest rate
goes down, funds hedge more by increasing their swap holdings.

19

The result is qualitatively robust to the choice of higher/lower average interest rates.

45

B

Institutional background on the UK pension fundsector

The pension fund sector, and specialized funds that service it, is a major source of LASH riskin the non-bank sector. Pension funds can be categorized as defined benefit (DB) or defined
contribution (DC) funds. Defined benefit pension funds promise a guaranteed return totheir beneficiaries upon retirement, while defined contribution funds have variable returns.
By construction, defined benefit funds have higher hedging needs, as they need to meetcertain guaranteed payments in the far future. For the UK pension fund system, out of thetotal £2.2tn of assets under management in Q1 2023, £1.8tn can be attributed to public andprivate defined benefit funds.20
Hedging strategies are not always the same—even for similar balance sheet structures—and depend not only on the duration gap and the pension fund type, but also on the way
future liabilities are discounted. Differences in regulations and discounting practices acrossjurisdictions lead to diverging optimal hedging strategies. For instance, UK pension funds
predominantly use gilt yields to discount their liabilities, while Dutch pension funds include
the euro interest rate swap rate in their calculations, and US pension funds take a morebespoke approach and use a so-called asset-led discounting approach. As a consequence,
Dutch pension funds almost exclusively hedge using interest rate swaps (Jansen et al., 2023),
US pension funds have higher incentives to take on riskier assets as a hedging strategy(Andonov et al., 2017), and in our paper we find that UK pension funds more frequently use
repos than swaps as part of their hedging strategy.
Pension fund market fragmentation also impacts the hedging landscape. In countries witha concentrated market, funds have sufficiently large balance sheets and in-house expertise
to design and implement their individual hedging strategies. By contrast, in a fragmented
pension fund system, small pension schemes would not have the size or capacity to make inhouse hedging a viable solution, giving rise to alternative strategies. A solution is to delegate
a part of the portfolio to alternative investment funds, which are designed to attract funds
from one (segregated fund) or multiple pension funds (pooled fund). These funds then select20

See The Office for National Statistics (2023) dataset for details.

46

their assets, derivatives and repo leverage based on the desired duration profile of theirclients.
The UK had over 5,300 defined benefit pension schemes in 2022, making it a very fragmented market.21 It is therefore perhaps unsurprising that the UK saw a rapid rise inalternative investment funds in the recent decade, such as Liability Driven Investment funds(LDIs). In fact, we find that the LASH risk from repo exposures is mainly concentrated in
the LDI sector, emphasizing the frequent use of repo leverage in this market segment.

C

LASH risk from interest rates: Repo and interest
rate swap measurement

We apply equation (1) to repos and interest rate swaps.

Repos As explained in the previous section, repos are short-dated collateralized borrowing
arrangements that allow institutions to shorten the duration of their liabilities. The majority of repo transactions are overnight, but pension funds and other interest rate hedgers
predominantly use term repos with a maturity of one month or more. LASH risk arises via
price changes of the underlying collateral. As the collateral value decreases, ceteris paribus,
a counterparty would need to pledge more collateral (or cash) to be able to borrow the sameamount.
We approximate LASH risk for repos using the modified duration of the underlying
collateral, which measures the impact of a 100bps change in interest rates on the value ofthe bond. Therefore, in the context of repo, LASH risk resembles the conventional DV01
(or “dollar duration”). For each contract i with bond collateral b of maturity m years andcoupon payments c times a year, LASH risk for a 100bps increase in interest rates at time treads:
Qi,t
Repo
LASHi,t=×PK

k=1 (1 + rt )100

· CFb,k · kb

Pb,t
|

21

−kb

{z


−1
Y T Mb,t
× 1+
cb}

Modified duration of bond b

See Pension Regulator Annual report.

47

(C.1)

where Qi,t is the borrowing amount of a given repo contract. Pb,t is the market price of bondb, kb is the time to each cash flow CFb,k‘ of bond b from time t perspective (in years), andY T Mb,t is the bonds’ yield to maturity. We assume zero haircuts as most of the LASH risk
in our sample is due to longer-term repos, which are of course less frequently rolled overcompared to overnight contracts (where haircuts play a bigger role, e.g., during the Great
Financial Crisis). This implies a one-to-one liquidity need with respect to the cash flow
sensitivity to interest rates, hence Λi = 1.

Interest Rate Swaps An interest rate swap is a contract where two counterparties agree
to exchange a fixed interest rate with a variable one, e.g., LIBOR, SOFR, SONIA, c times a
year, for a duration of m years. The interest is calculated on a notional amount, Q, but only
the difference in interest payments is exchanged. The fixed interest rate is set so that the
NPV of the contract is zero at initiation; that is, neither side needs to pay the other to enter
the agreement. To guard against counterparty credit risk, entering a swap also requires apledge of liquid collateral in the form of initial margin.
LASH risk arises in swaps due to variation margin. The counterparties are required
to exchange variation margin on a daily basis to maintain the zero net present value ofthe contract as interest rates change. The floating rate payer will post variation margin
to the fixed rate payer when rates rise (and vice versa when rates fall). In practice, this is
implemented through daily (cash) margin calls that reflect the change in the mark-to-market
price of the contract.22
The size of the margin calls, and the demand for liquidity, depend on the sensitivityof the swap’s fixed versus floating cash flows to changes in interest rates. We extend themethodology proposed by Bardoscia et al. (2021) to calculate the liquidity needs from agiven interest rate move and hence to obtain an estimate of LASH risk. Imagine an interest
rate swap of net notional value Q. We are at time zero and the swap matures at year T ,and makes c coupon payments per year. Let k index coupon periods. There is a swap curve
which defines the time zero sequence of annualised forward floating rates given by rk,k−1 ,22

Variation margin is a regulatory requirement, and the requirements may differ between centrally-cleared
and bilateral swaps. A centrally cleared swap requires daily cash pledges for variation margin, while bilateralswaps can have more bespoke conditions if permitted by regulation, e.g., the use non-cash collateral.

48

and a fixed rate r̄ (for an at the money swap (r̄ ≡ rT,0 ) ). Cashflows are discounted at rate
rk,0
− c k
rk,0 −kdk = (1 +) ≈ec

The present value of the floating and fixed leg of the swap is given bycT

P Vf loating = Q

X

dk

k=1

rk,k−1ccT

P Vf ixed = Q

X

dk

k=1

r̄
c

Now the NPV of the contract for the floating rate payer is given by:cTQX
N P V = P Vf ixed − P Vf loating =dk (r̄ − rk,k−1 ).
c k=1
For a ex-post shift upwards of the swap curve, the sensitivity reads:




cT

∂N P VQ X=−∂rc k=1 ∂dk
dk +rk,k−1∂r|{z}change in value of floating leg

−

∂dk
r̄
|∂r
{z }


.


(C.2)

change in value of fixed leg

Solving in continuous time yields:cT∂N P VQXk=−dk + dk (r¯i − rk,k−1 ) .
∂r
c k=1
c
Hence, LASH risk from a 100bps increase in interest rates for a swap contract i withmaturity T based on notional Q and with c cash flow swaps a year reads:

IRS
LASHi,t
=

cT 

k
Qi X
dk + dk (r¯i − rk,k−1 ) .
100c k=1c(C.3)

where the discount rate for cash flow k, e−Rk,t ·(Tk −t) , is evaluated based on the daily OvernightIndex Swap (OIS) yield curve for maturity Tk − t from time t perspective. We derive the49forward rates rk,k−1 as implied by the OIS curve. We assume the fixed rate to be theprevailing OIS rate at the start of contract i corresponding to the trade maturity. Lastly,
standard contracts have bi-annual coupons, so c = 2, without loss of generality.

23

The

LASH risk for swaps via variation margin implies a one-to-one liquidity need with respect
to the cash flow sensitivity to interest rates, hence Λ = 1.

D

Data: Additional Information & Summary Statistics

This section of the Appendix provides additional information and summary statistics for thevarious data sources used in the empirical analysis.
Table D.1 Summary Statistics: Average Net Positions and LASH risk
Repo net borrowing

IRS net receive fixed

Sector

2019

’20

’21

’22

’23

2019

’20

’21

’22

’23

Pension fund
LDI
Insurer
Hedge Fund
Fund
Other financial

38
99
0
-7
9
7

64
121
0
11
7
20

74
130
0
-3
7
18

69
113
0
-34
4
10

48
73
0
-15
4
5

65
17
10
59
23
-8

96
37
23
82
21
-11

101
40
27
-14
11
-3

132
38
72
-108
18
-9

112
23
60
-81
15
-14

Repo behavioral LASH

IRS behavioral LASH

Sector

2019

’20

’21

’22

’23

2019

’20

’21

’22

’23

Pension fund
LDI
Insurer
Hedge Fund
Fund
Other financial

8
22
0
0
2
2

15
28
0
1
1
4

18
30
0
-1
1
3

16
26
0
-3
1
2

11
17
0
-1
1
1

5
2
0
1
2
-2

11
5
6
0
1
-2

12
5
6
-1
1
-1

12
5
8
-1
0
-1

10
3
7
-1
0
-1

Note. Sample: Summary statistics on repo and IRS positions from 2019 to 2023. Values reported in £bn. Repo net borrowing
captures the daily average cash borrowing per sector in a given year. The IRS net position captures the average holding of net
receive fixed positions (negative values read as net pay fixed) per sector in a given year. Behavioural LASH risk captures theaverage for each sector in a given year.

23

In ongoing work, we incorporate second order effects coming from non-linearity of the yield curve.

50

Table D.2 Summary Statistics: Cross-sectional variation of Net positionsand LASH risk
Repo net borrowing

Repo behavioral LASH

SectorN

MeanMedianStd dev

Mean

MedianStd dev

Pension fund
LDI
Insurer
Hedge Fund
Fund
Other financial

273
337
16
284
203
13

259.3
360.6
45.2
-59.7
117.6
-10.5

144.3
113.6
36.7
-0.6
3.7
0.0

388.3
1275.5
205.3
561.4
626.6
116.7

59.4
82.6
6.3
-4.0
22.9
-1.1

31.5
25.5
3.6
0.0
0.6
0.0

89.3
300.6
43.4
65.6
143.7
21.1

IRS net receive positions

IRS behavioral LASH

SectorN

MeanMedianStd dev

Mean

MedianStd dev

Pension fund
LDI
Insurer
Hedge Fund
Fund
Other financial

450
231
76
149
869
217

297.9
199.3
971.4
-231.054.2-148.8

32.0
48.2
17.0
10.0
0.8
-6.5

1372.2477.14034.6
19493.3
565.0
1266.4

29.9
24.9
139.2
-7.4
2.6
-14.1

2.6
3.0
0.2
0.0
0.0
-0.2

183.9
72.6
691.3
186.4
29.4
107.3

Note. Sample: Firm level summary statistics for repo (2017-2023) and IRS positions (2019-2023). Values are reported in £m,and N denotes the number of firms in each sector of our sample. The mean and median of repo net borrowing capture thetotal daily cash borrowing in the cross-section, and the IRS net position captures the outstanding net receive fixed positions(negative values read as net pay fixed). Behavioural LASH risk measures the outstanding LASH exposure at firm level in agiven day.

Figure D.1 LASH risk: Additional Examples

a. FX Swaps

b. Infrastructure fund with indexedlinked assets

51

c. Reduce solvency risk but
increase Liquidity Risk

Table D.3 Summary statistics: UK Pension fund balance sheets
2017

2018

2019

2020

2021

2022

2023

N
Total assets (£bn)
Total liabilities (£bn)

10
115.0
117.2

22
553.7
560.7

50
801.3
815.2

65
1046.91099.9

68
956.5
900.0

69
876.9
807.9

10
55.1
50.8

Actuarial assets
Min
MeanMedianMax
Std deviation

907
11501
3600
60000
18973

933
25170
4360
358175
75692

179
15711
3767
395867
55560

62
15863
3676
444167
55490

145
14066
3611
463022
56579

177
12709
3029
406597
49732

916
5513
2364
23500
7605

Actuarial liabilitiesMin
MeanMedianMax
Std deviation

1074
11724
3673
67500
20615

1044
25485
4501
368981
78046

193
15985
3499
404974
56894

95
16665
3642
475130
59416

125
13235
3511
418665
51396

162
11709
2960
366574
45031

835
5078
2195
20300
6659

Note. Cross-sectional dispersion and total actuarial values and liabilities for the UK pension funds in our hand-collected
sample. Values are reported in £m, unless otherwise stated, and N denotes the total number of pension funds in each year of
our sample.

Table D.4 Summary statistics: UK Pension fund funding ratios

N
Underfunded PFs

2017

2018

2019

2020

2021

2022

2023

13
0.62

23
0.52

52
0.56

70
0.60

76
0.33

74
0.27

11
0.27

0.78
1.02
1.00
1.39
0.12

0.81
1.00
0.99
1.40
0.11

0.65
0.98
0.98
1.49
0.12

0.80
1.04
1.04
1.54
0.10

0.91
1.06
1.05
1.42
0.10

0.91
1.07
1.07
1.23
0.09

Pension fund funding ratios
Min
0.81
Mean
0.98
Median
0.94
Max
1.31
Std deviation
0.13

Note. Cross-sectional dispersion of funding ratios for the UK pension funds in our hand-collected sample. N denotes thetotal number of pension funds in each year of our sample, and the underfunded PFs denotes the share of pension funds with anegative funding ratio (so assets<liabilities) in the given year. A ratio of 1 indicates that the actuarial value of assets exactly
matches the actuarial value of liabilities.

52

Figure D.2 Repo Net Borrowing Stocks Across Sectors

NOTE. Aggregate repo net borrowing across all sector types in £bn. “Others” include sovereign entities
and other financials. Source: Sterling Money Market data collection.

Figure D.3 Pension & LDI Funds’ Repo Net Borrowing Stocks

NOTE. Aggregate repo net borrowing stocks of UK pension and LDI funds in £bn. Source: Sterling Money
Market data collection.

53

Figure D.4 Pension & LDI Funds’ Repo Net Borrowing Stocks & 10Y Gilt

YieldsNOTE. Aggregate repo net borrowing stocks of UK pension and LDI funds in £bn and 10Y gilt yields in%. Source: Sterling Money Market data collection & Bank of England.

Figure D.5 Pension & LDI Funds’ Repo Net Borrowing Stocks by Maturity

NOTE. Aggregate repo net borrowing stocks of UK pension and LDI funds by the maturity bucket atinitiation in £bn. Source: Sterling Money Market data collection.

54

Figure D.6 IRS Net Notionals Across Sectors

NOTE. Aggregate IRS net notionals across all sector types in £bn. “Others” include sovereign entities andother financials. Source: EMIR Trade Repository Data.

Figure D.7 Pension & LDI Funds’ IRS Net Notionals by Sector

NOTE. Aggregate IRS net notionals of UK pension and LDI funds in £bn. Source: EMIR Trade Repository
Data.

55

Figure D.8 Pension & LDI Funds’ IRS Net Notionals & 10Y Gilt Yields

NOTE. Aggregate IRS net notionals of UK pension and LDI funds in £bn and 10Y gilt yields in %. Source:
EMIR Trade Repository Data & Bank of England.

Figure D.9 Pension & LDI Funds’ IRS Net Notionals by Maturity

NOTE. Aggregate IRS net notionals of UK pension and LDI funds by maturity bucket in £bn. Source:
EMIR Trade Repository Data.

56

Figure D.10 LDI Crisis: Pension & LDI Funds’ Gilt Trading Volumes

NOTE. Total net gilt trading volumes of UK pension & LDI funds’ (split into pension funds, segregated
LDI funds and pooled LDI funds) following the Mini-Budget announcement on September 23 up until theend of the BoE intervention on October 14.

Figure D.11 LDI Crisis: Pension & LDI Funds’ Cumulative Gilt Trading

Volumes based on pre-crisis LASH exposure

NOTE. Total net gilt trading volumes of UK pension funds and LDI funds, by quartile of their pre-crisis
LASH risk: Quartile I captures the non-banks with the lowest pre-crisis LASH exposures, while Quartile IV
captures those with the highest pre-crisis LASH exposures.

57

Figure D.12 LDI Crisis: Estimated Cumulative Changes in the Value of Repo

Collateral posted by Pension & LDI Funds

NOTE. Aggregate estimated changes in the value of repo collateral posted by UK pension and LDI funds in£bn during the 2022 LDI Crisis, by quartile of their pre-crisis LASH risk: Quartile I captures the non-bankswith the lowest pre-crisis LASH exposures, while Quartile IV captures those with the highest pre-crisis LASH
exposures. Source: Sterling Money Market data collection.

58

E

Additional Results

This section of the Appendix provides additional results for the regression analyses in ourempirical section.

E.1

Pension Funds’ Gross Asset Duration and Solvency

In Section 6, we show that falling interest rates lead to an economically and statisticallysignificantly greater LASH risk taken by investors with low asset duration. Technically,rather than gross asset duration, the duration gap between assets and liabilities (i.e. net
duration) is what matters for solvency. In the absence of granular information on the durationof investors’ liabilities, however, we use investors’ initial gross asset duration (measured via
the bonds in their repo collateral portfolio) as a proxy for their duration gap. To test thecorrelation between net and gross duration, we use our hand-collected balance sheet data for
UK pension funds.
First, we measure the sensitivity of the funding ratios of individual pension funds tochanges in the ten-year UK gilt yield using seemingly unrelated regressions:∆F undingRatioj,t = α + β1 ∆Y ieldt + +εj,t ,(E.1)

where ∆F undingRatioj,t measures the annual change in the funding ratio—which is definedas the value of the fund’s assets over liabilities—of pension fund j in year t. ∆Y ieldt is theannual change in the ten-year UK gilt yield.
Figure E.1 shows a scatter plot of these estimates in comparison to the gross asset duration of these funds. Each are in standardized units, the funding ratio sensitivities on thevertical axis, and the gross asset duration on the horizontal axis. The association is clearly
negative, even though the number of matched funds is relatively small. In other words, thefunding ratio of funds with lower asset duration is more sensitive to a change in yields—andhence the solvency of these funds will decrease more sharply in response to lower interest
rates relative to funds with higher asset duration. Therefore, the results emphasize thenegative correlation between gross and net duration, and support our choice of gross asset
59duration as a viable proxy for investors’ duration gap.
Figure E.1 Sensitivity of Pension Funds’ Funding Ratios to Yield Changes

and Gross Asset Duration

NOTE.This figure shows a scatter plot of the sensitivity of individual pension funds’ funding ratios to changes
in the yield of the ten-year UK gilt yield, and the funds’ gross asset duration. Each are in standardized
units, the funding ratio sensitivities on the vertical axis, and the gross asset duration on the horizontal axis.

60

E.2

Pension & LDI Funds’ LASH risk and Gilt Trading Volumes
Table E.1 LASH risk and Gilt Trading Volumes - Pension &LDI Funds only
(1)

(2)
Net Volume

LASH combined-0.12**(0.05)LASH Repo(4)
Sell Volume

0.10***(0.02)-0.10***(0.03)-0.04(0.07)LASH IRS
Observations
R squared
Day FE

(3)

2325
0.036
yes

2325
0.036
yes

0.08***(0.02)
0.05(0.04)
2325
0.044
yes

2325
0.044
yes

Note. For each investor, as defined in equation 3 in Section 3, ”LASH” is measured as the potential
liquidity needs following a 100bps shift in gilt yields, either for repo and IRS exposures combined, or
separately for both instruments. The dependent variable is the investor’s daily gilt net trading volume
on day t in Columns (1) and (2), and the investor’s sell volumes on day t in Columns (3) and (4). The
dependent variables are transformed using the Inverse Hyperbolic Sine method. The LASH variable
is standardized. Clustered standard errors on the day level are reported in parentheses. We include
day fixed effects. *** p<0.01, ** p<0.05, * p<0.1. Coefficients corresponding to the constant, control
variables and fixed effects not reported.

61