## wpiea2021267-print-pdf - Section 2 we give an overview of the gilt repo market and in particular the overnight segment.

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### Overview
- Paper focuses on the overnight gilt repo market and provides background on the COVID-19 stress episode (March 3rd–23rd, 2020).
- Empirical contributions:
  - Unique granular dataset covering almost the entire universe of transactions in the gilt repo market, including different segments, market participants and their repo trades volumes, rates and haircuts.
  - First to jointly analyse the bilateral and the cleared segment of the gilt repo market and to quantify empirically inter-sectoral changes in repo market activity in these segments during times of stress.
  - First to document the dynamics of the COVID-19 “dash for cash” in March 2020 in the repo market using granular transaction level data.
  - Evidence that networks change in times of stress, suggesting static networks with continuous roll-over assumptions may be ill-suited to capture contagion risk in collateralized debt markets.

### Definitions and scope (overnight gilt repo market)
- Market definition:
  - Overnight gilt repo market = secured sterling money market where the underlying security is a UK government bond denominated in British pounds (a gilt).
  - The party selling the gilt is borrowing cash (doing the repo); the party buying the gilt is lending cash (doing the reverse repo).
- Repo spread definition:
  - Repo spread = interest rate of the trade (the repo rate) minus the Bank of England’s Bank Rate at the time of the trade.
- Repo transaction mechanics (as specified):
  - Party 1 does the repo and borrows V >0 in cash from party 2 by selling a gilt with market value g >0. Typically, V≤g. V is the volume of the transaction. At maturity date T, party 1 repays V(1 + R), where R∈R and usually R∈[0,∞). R is the repo rate.
  - Overnight timeline: trade date t, settlement same day t; maturity T = t + 1, party 1 repays V(1 + R) on T.

### Data
- Sample coverage:
  - Bank of England Sterling Money Market data sample spans from 1 March 2019 until 31 October 2020.
  - Reporting requirement: institutions with significant activity (top 95% of activity at either overnight or up to one-year maturity). Some activity where neither party is a bank or major broker dealer is not captured.
- Aggregate market size and maturity distribution:
  - Total transaction volumes in the aggregate gilt repo market are around £180 trillion on average in the data sample.
  - Maturity concentration: Almost 50% at overnight maturity; 35% at maturities greater than overnight but less than two weeks.
  - Average daily transaction volumes in the overnight gilt repo market are £80 billion.
  - Average daily number of transactions in the overnight market is close to 1600.
- Settlement methods (average shares):
  - 36% of daily overnight gilt repo volumes are settled through a central counterparty (CCP).
  - 2% is settled tri-party.
  - The majority of volumes are settled bilaterally.
- Temporal patterns:
  - Wide fluctuations in volumes and repo spreads around quarter- and year-ends (window dressing).
  - Repo spreads measured as overnight volume-weighted repo rate minus the Bank Rate; spreads show large negative spikes at year-end and quarter-end aligned with volume movements.

### The COVID-19 crisis (March 2020 stress episode)
- Defined stress window: period between 3rd and 23rd of March 2020.
- Market dynamics during the episode:
  - Described as an extreme “dash for cash”.
  - Asset prices adjusted sharply; margin calls on derivative exposures rose sharply generating strong liquidity pressure.
  - Yields on advanced-economy government bonds fell between February and mid-March 2020 as investors de-risked; however, in mid-March even government bonds came under forced selling pressure and saw little demand.
  - Overnight repo rates rose sharply and repo borrowing costs increased as demand increased while dealers’ ability and willingness to intermediate was constrained.
  - Repo volumes increased sharply up to March 11, 2020 as demand for liquidity built up.
- Policy responses and effects:
  - March 11, 2020: Bank of England reduced the Bank Rate by 50 basis points to 0.25%.
  - March 19, 2020: Bank of England decided to buy gilts in large size.
  - March 24, 2020: Bank activated the Contingent Term Repo Facility (CTRF), committing to lend unlimited amounts of sterling at close to Bank Rate against a broad range of collateral.
  - These operations, together with the passing of the March quarter end, contributed to bringing repo rates back to more normal levels.

### Financial institutions trading in the repo market
- Activity at institution level (sample March 2019–October 2020):
  - Total institutions trading at least once in overnight repo market: 156.
  - Daily average number of institutions active: 58.
  - In full sample:
    - Average daily repo transaction volume by active institution: £0.6 billion.
    - Average trade size: £0.05 billion.
    - Average number of daily repo transactions by institution: 13.
- During the COVID-19 stress episode:
  - Institutions active at least once: 125.
  - Market activity increased:
    - Average daily repo transaction volume by active institution rose to £2 billion.
    - Average trade size rose to £0.06 billion.
    - Average number of daily repo transactions by institution rose to 36.

### Institutional network: formal definition and structure
- Time set:
  - T = {t0, t1, ..., tT} with t0 = 1 March 2019, tT = 31 October 2020, and T + 1 = 400.
- Institutional network of volumes (Definition 3.1):
  1. Nodes:
     - N(I) = {1,...,N(I)}, N(I) = 156, representing institutions engaging in the overnight gilt repo market.
     - For every day t∈T, V(I)ij(t), i,j∈N(I), denotes the total notional amount of cash that node i lends to node j in an overnight repo transaction at time t. If V(I)ij(t) > 0, the pair (i,j) is an edge and V(I)ij(t) is the weight (volume).
  2. Matrix representation:
     - V(I)(t) = (V(I)ij(t))i,j∈N(I) ∈ [0,∞)N(I)×N(I) is the matrix of total notional cash lent at time t in the institutional network.

### Institutional network of volumes: definitions and measurements
- Adjacency matrix at time t:
  - A(I)(t) = (A(I)ij(t))i,j∈N(I) ∈ {0,1}N(I)×N(I), where A(I)ij(t) = 1 if V(I)ij(t) > 0; 0, else.
- Aggregate average transaction-volume matrix over the whole sample:
  - V̄(I) = (V̄(I)ij)i,j∈N(I) ∈ [0,∞)N(I)×N(I), where V̄(I)ij = ∑t∈T V(I)ij(t) / (T+1).
- Aggregate empirical transaction-probability matrix:
  - Ā(I) = (Ā(I)ij)i,j∈N(I) ∈ [0,1]N(I)×N(I), where Ā(I)ij = ∑t∈T A(I)ij(t) / (T+1).
- Interpretation:
  - V̄(I)ij: average transaction volume between two institutions over the whole sample.
  - Ā(I)ij: empirical probability that institution i lends institution j cash in a repo transaction on an average day over the whole sample.

### Core–periphery structure and pairwise trading characteristics
- Core–periphery observed:
  - Core institutions borrow from, and lend to, at least one institution in the periphery and intermediate between periphery institutions.
  - Periphery institutions may only lend to, or borrow from, the core and do not lend to each other.
- Empirical observations:
  - Dense cluster in the lower left corner corresponds to the core (higher average transaction volumes).
  - Large empty grey area in the middle/top right corner indicates no trading among periphery institutions.
  - Only banks and gilt dealers are in the core; non-banks constitute the periphery. The CCP is classified as neither core nor periphery.
- Transaction-probability highlights:
  - Darkest red in Ā(I) corresponds to values ranging from 0.9 to 1 (trade between 90 and 100 percent of days).
  - Overall, empirical transaction probabilities in the core are rather low for the majority of institution pairs; only a few core pairs show almost daily roll-over.

### Degree distributions and connectivity
- Network size and bounds:
  - Institutional network has N(I) = 156 nodes; maximum possible in- or outdegree is N(I) − 1.
- Empirical survival-function facts:
  - At degree = 5, probability node has in- or outdegree larger than 5 is roughly 0.2 (around 80% of nodes have less than 5 incoming edges and less than 5 outgoing edges).
  - If degree = 50, the probability that a node has degree larger than 50 is 0.
  - The maximum number of incoming or outgoing edges is around 50.
- Summary:
  - Majority of nodes have a small number of connections; a small number of nodes are highly connected.
  - Tails of the degree distribution appear linear on a log-log plot, indicating a power law could fit the tails.

### Changes under stress: density and use of existing relationships
- Network density definition:
  - density(t) = [1 / (N(I)(N(I) − 1))] ∑i=1^N(I) ∑j=1^N(I) A(I)ij.
- Key density observations:
  - Average density for the whole sample is 0.005 (on average, 0.5% of possible edges are present).
  - Average degree is around 1 (on average, institutions trade with one other institution on any given day).
  - Clear dips at year ends and smaller dips at quarter ends (window dressing effects).
  - Two notable spikes in density:
    - Highest peak: March 2020 at the height of the COVID-19 crisis.
    - Second highest spike: September 2019 (coincides with turmoil in the US repo market).
- Formation of trading links during COVID-19:
  - 755 unique directed trade pairs from 1 March 2019 - 8 March 2020.
  - 287 unique directed trade pairs during the COVID-19 stress (3–23 March 2020).
  - Of those 287, 9 were new bilateral trading relationships during COVID-19 relative to the 755 before COVID-19.
    - Of these 9 new trading pairs, 4 transact again at least once after the crisis, whereas 5 do not transact again.
  - Interpretation:
    - Vast majority relied on existing trading relationships to secure liquidity during COVID-19.
    - Rolling over repo contracts and using established counterparties reduced searching costs; absence of daily roll-over could exacerbate liquidity stress.

### Sectoral activity in the overnight gilt repo market (overview)
- Sectors and end users:
  - 10 sectors used in analysis.
  - Providers of collateral in return for cash: funds, pension funds, hedge funds, insurance companies.
  - Lenders of cash receiving collateral: money market funds (MMFs), hedge funds, corporate treasurers.
- High-level sectoral observations:
  - Gilt dealers and banks have trade relationships with all other sectors and intermediate between all sectors.
  - Gilt dealers and banks are the only sectors with self-loops.
  - Gilt dealers and banks are the only sectors that are clearing members and hence interact with the CCP sector.
  - Non-banks only trade bilaterally with gilt dealers and banks, but not amongst each other.
- Sectoral volumes (volumes expressed in £billion; full sample vs COVID-19 crisis averages):
  - Bank:
    - Full sample: #Av. lend 263.16; Av. borrow 11.02; Av. net lend -7.87
    - COVID-19 crisis: #Av. lend 156.77; Av. borrow 9.95; Av. net lend -3.18
  - CCP:
    - Full sample: #Av. lend 634.30; Av. borrow 29.56; Av. net lend 4.74
    - COVID-19 crisis: #Av. lend 440.26; Av. borrow 32.62; Av. net lend 7.64
  - Fund:
    - Full sample: #Av. lend 182.40; Av. borrow 0.04; Av. net lend 2.36
    - COVID-19 crisis: #Av. lend 122.73; Av. borrow 0.01; Av. net lend 2.72
  - Hedge Fund:
    - Full sample: #Av. lend 281.23; Av. borrow 1.39; Av. net lend -0.15
    - COVID-19 crisis: #Av. lend 141.32; Av. borrow 2.59; Av. net lend -1.28
  - Insurer:
    - Full sample: #Av. lend 41.81; Av. borrow 0.10; Av. net lend 1.71
    - COVID-19 crisis: #Av. lend 42.33; Av. borrow 0.08; Av. net lend 2.25
  - MMF:
    - Full sample: #Av. lend 95.58; Av. borrow 0.16; Av. net lend 5.42
    - COVID-19 crisis: #Av. lend 54.39; Av. borrow 0.00; Av. net lend 4.39
  - Pension fund:
    - Full sample: #Av. lend 152.57; Av. borrow 0.58; Av. net lend 1.99
    - COVID-19 crisis: #Av. lend 83.39; Av. borrow 0.35; Av. net lend 3.04
  - UK Gilt dealer:
    - Full sample: #Av. lend 613.97; Av. borrow 15.87; Av. net lend -1.91
    - COVID-19 crisis: #Av. lend 515.94; Av. borrow 19.68; Av. net lend -3.74
  - US Gilt dealer:
    - Full sample: #Av. lend 58.67; Av. borrow 12.52; Av. net lend -3.85
    - COVID-19 crisis: #Av. lend 58.62; Av. borrow 14.85; Av. net lend -6.23
  - Other Gilt dealer:
    - Full sample: #Av. lend 77.59; Av. borrow 10.33; Av. net lend -2.74
    - COVID-19 crisis: #Av. lend 76.96; Av. borrow 12.96; Av. net lend -6.00

### Sectoral spreads (average volume weighted spreads expressed in percent)
- Full sample vs COVID-19 crisis (sector is borrower for repo spread and lender for reverse repo spread):
  - Bank: Full sample repo spread -0.04; reverse repo spread -0.01. COVID-19 crisis repo spread 0.02; reverse repo spread 0.14.
  - CCP: Full sample repo spread -0.04; reverse repo spread -0.03. COVID-19 crisis repo spread 0.08; reverse repo spread 0.08.
  - Fund: Full sample repo spread -0.02; reverse repo spread -0.03. COVID-19 crisis repo spread 0.13; reverse repo spread 0.04.
  - Hedge Fund: Full sample repo spread 0.01; reverse repo spread -0.08. COVID-19 crisis repo spread 0.13; reverse repo spread 0.03.
  - Insurer: Full sample repo spread 0.00; reverse repo spread -0.02. COVID-19 crisis repo spread 0.06; reverse repo spread 0.07.
  - MMF: Full sample repo spread -0.07; reverse repo spread -0.03. COVID-19 crisis repo spread -0.03.
  - Pension fund: Full sample repo spread 0.13; reverse repo spread -0.04. COVID-19 crisis repo spread 0.32; reverse repo spread 0.04.
  - UK Gilt dealer: Full sample repo spread -0.04; reverse repo spread -0.03. COVID-19 crisis repo spread 0.07; reverse repo spread 0.08.
  - US Gilt dealer: Full sample repo spread -0.02; reverse repo spread -0.06. COVID-19 crisis repo spread 0.07; reverse repo spread 0.08.
  - Other Gilt dealer: Full sample repo spread -0.02; reverse repo spread -0.05. COVID-19 crisis repo spread 0.11; reverse repo spread 0.06.
- Interpretation:
  - On average in the full sample, spreads for repo and reverse repo transactions faced by gilt dealers (and several other sectors) are negative; during the COVID-19 crisis spreads become positive for many sectors.

### Roles and dynamics of key sectors
- Gilt dealers:
  - Defined as banks that are Gilt-Edged Market Makers (GEMMs); split into UK, US, and other gilt dealers.
  - Repo lending to clients is a core business; a large part of repo borrowing finances matched-book lending.
  - Leverage requirements have encouraged more pro-active balance sheet management, including limiting repo activity or increasing its price.
  - All gilt dealer sectors are net borrowers on average; UK gilt dealers are closest to a matched book, US and other gilt dealers are larger net borrowers.
  - All three gilt dealer sectors increased net borrowing during the COVID-19 crisis; ranking of net borrowing size remains the same.
- Banks:
  - Banks that are not GEMMs are grouped separately.
  - Banks are the largest net borrowers on average in the overnight gilt repo market.
  - During the COVID-19 crisis, banks more than double their average lending and decrease their borrowing, resulting in a decrease in net borrowing.
  - Banks entered the COVID-19 crisis with sizeable buffers and were not at the centre of the financial turmoil.
- Central counterparties (CCPs):
  - CCPs do not actively provide liquidity; they clear trades between members and lend cash collected from margin payments as reverse repo to gilt dealers and banks.
  - CCPs invest cash margin into the overnight gilt repo market, explaining positive net lending positions.
  - CCP sector is one of the largest net lenders and their net lending increases substantially during COVID-19, reflecting increased cash margin investment.
  - Bank of England (2020) finding cited: relative to average over January and February, UK CCPs initial margin requirements had grown by around 58 billion in March — a 31% increase — with a daily peak increase of around 10 billion. Around half of the additional initial margin was provided in cash, most of which the CCPs reinvested in the repo market.
  - Repo spreads with CCPs are negative on average in the full sample but become positive during COVID-19; spreads remain among the lowest.
- Non-banks (MMFs, insurers, pension funds, funds, hedge funds):
  - MMFs, insurers, pension funds and funds are net lenders; MMFs are the largest net lenders.
  - MMFs place cash safely short-term in the overnight repo market; lending volumes are stable and increase in the second half of 2020.
  - Hedge funds are marginal net borrowers on average and use repo to increase leverage; during COVID-19 hedge fund borrowing increases significantly more than lending and faced significantly higher spreads.
  - Pension funds are net lenders in overnight repo but net borrowers in longer maturity segments (1 month to 1 year) for liability driven investment strategies (LDI).
  - Non-banks transact bilaterally with banks and gilt dealers but not with each other.

### 4.2 The sectoral repo network — definition and data structure
- Sectoral network of volumes:
  - N(S) = {1,...,N(S)}, N(S) = 10, representing the sectors.
  - For every day t ∈ T, V(S)ij(t) denotes total notional cash that sector i lends to sector j at time t. If V(S)ij(t) > 0, (i,j) is an edge and V(S)ij(t) is the weight.
  - V(S)(t) = (V(S)ij(t))i,j∈N(S) ∈ [0,∞)N(S)×N(S).
- Adjacency matrix:
  - A(S)(t) = (A(S)ij(t))i,j∈N(S) ∈ {0,1}N(S)×N(S) with A(S)ij(t) = 1 if V(S)ij(t) > 0; 0 else.

### Transaction likelihood (empirical probability matrix)
- ̄A(S) = (̄A(S)ij)i,j∈N(S) ∈ [0,1]N(S)×N(S), where ̄A(S)ij = ∑t∈T A(S)ij(t) / (T + 1).
- Interpretation:
  - ̄A(S)ij represents empirically observed probability that sector i lends sector j cash in a repo transaction on a given day.
  - Darkest red (0.9 to 1) means two sectors trade between 90 and 100 percent of days (almost continuous daily roll-over).
- Empirical patterns:
  - CCP sector active on both sides with all gilt dealers and banks essentially daily.
  - Within core, only UK gilt dealer borrows on a daily basis from US and UK gilt dealers and banks; other core sectors show no daily roll-over within core.
  - Periphery→core lending (MMF, fund, insurer, pension fund, hedge fund to core) occurs with high probabilities, almost daily.
  - Hedge funds and pension funds are the periphery sectors who borrow most often.
  - A grey square reflects CCP and non-banks/non-gilt dealers do not trade with each other or amongst each other in the dataset.

### Stress episodes and time windows
- Two stress episodes (Definition 5.1):
  - T_CS_COVID-19 ⊂ T: 03 March 2020 - 23 March 2020.
  - T_CS_US ⊂ T: 03 September 2019 - 17 September 2019.
- Empirical context:
  - In both stress periods, spikes in average daily transaction volumes in the overnight gilt repo market of a similar magnitude.
  - Spreads spiked very sharply only during the COVID-19 stress.

### Linear model for volumes and spreads (specification)
- Observations:
  - Yijt := V(S)ij(t), i,j ∈ {1,...,N(S)} and t ∈ ̃T. In the data: N(S) = 10 and ̃T = |̃T| = 381, giving 10^2 · 381 = 38100 observations.
- Linear model with categorical explanatory variables:
  - Yijt = β(Normal, Vol)ij I{i lending sector} I{j borrowing sector}
    + β(CS2, Vol)ij I{i lending sector} I{j borrowing sector} I{t ∈ T_CS_US}
    + β(CS3, Vol)ij I{i lending sector} I{j borrowing sector} I{t ∈ T_CS_COVID-19}
    + εijt.
- Parameter matrices:
  - 3(N(S))^2 = 300 model parameters as three (N(S) × N(S)) matrices:
    - β(Normal, Vol)ij: average daily volume outside stress periods.
    - β(CS3, Vol)ij: change in average daily volume during COVID-19 (3-23 March 2020); average at t ∈ T_CS_COVID-19 is β(Normal, Vol)ij + β(CS3, Vol)ij.
    - β(CS2, Vol) analogous for US stress episode.
- Spreads model:
  - Same linear model with Yijt equal to volume weighted repo spreads for non-zero V(S)ij(t).
  - Corresponding matrices: β(Normal, Spread), β(CS2, Spread), β(CS3, Spread).

### Estimation of significance: block bootstrap
- Time series and bootstrap:
  - Quarter ends removed by deleting two first and two last days in each quarter; remaining ̃T days split into blocks of length b = 10.
  - N_B = b ̃T/bc blocks of length b and one block of length ̃T − N_B b.
  - New time series sampled by drawing with replacement N_B blocks of length b and one block of length ̃T − N_B b; linear model fitted to each bootstrapped series.
  - R = 1000 repetitions yield R estimates of model parameters.
- Interpretation of heatmaps:
  - Coloured fields have numbers between 0 and 100 representing percentile of observed parameter estimate relative to bootstrap distribution.
  - Very high numbers (e.g., 99 or 100) indicate parameter estimate in right tail → highly significant.
  - Very low numbers (e.g., 0 or 1) indicate parameter estimate in left tail → highly significant.

### 5.2 Results — Normal times
- Largest volumes traded between CCP sector and gilt dealers and banks.
- UK gilt dealers borrow and lend large volumes in the centrally cleared segment.
- CCPs can do reverse repo as proprietary trading for cash margin management; supply of cash from CCPs goes to gilt dealers and banks.
- Within core:
  - Banks are net borrowers and borrow largest quantities from CCP sector, funds and MMFs.
  - Gilt dealers are net borrowers and borrow largest amounts from CCP sector.
  - UK gilt dealers additionally borrow large amounts from MMFs.
- In periphery:
  - Hedge funds are the only net borrowers (small margin); they borrow and lend similar volumes to and from gilt dealers and banks.
  - All other periphery institutions are net lenders.
- Repo spreads in normal times are small and very close to zero; little variation across sectors.
  - Spreads on reverse repos from the core to the periphery tend to be positive and higher on average.

### 5.2 Results — COVID-19 stress period: repo volumes
- Key finding: overall volumes traded with the CCP sector increase significantly compared to normal times during COVID-19.
- Drivers of increased CCP volumes:
  - Banks lend more cash through cleared markets during COVID-19 compared to normal times, while lending less bilaterally to gilt dealers and decreasing borrowing from almost all sectors.
    - Banks remain net borrowers but net borrowing positions decrease markedly; some lending positions are in highest percentiles of bootstrap distribution.
    - Increased bank repo lending into cleared markets goes to gilt dealers (gilt dealers borrow higher volumes from CCP sector).
    - Motivations: cleared segment less capital-intensive due to netting benefits; reduces balance sheet impact.
  - CCP sector increases reverse repo trades with gilt dealers.
    - CCPs reinvested most additional cash margin collected during March 2020 volatility in the repo market.
    - Average net lending by CCP sector during COVID-19 was almost double the sample average and the largest compared to other sectors.
    - Large increase in net lending by CCPs reflects sharp increase in initial margin collected.
    - Bank of England (2020) finding cited: initial margin requirements grown by around 58 billion in March — a 31% increase — daily peak ~10 billion; around half additional initial margin provided in cash, most reinvested in repo market.
  - UK gilt dealers lend higher volumes via cleared markets; US and other gilt dealers decrease their lending through cleared markets and appear to use the gilt repo market more to acquire sterling cash via cleared markets.
  - Overall, both lending and borrowing via cleared markets increase significantly during COVID-19.
- Bilateral segment changes:
  - Core→periphery lending: core lends more to hedge funds; hedge funds faced increased short-term funding needs during mid-March 2020 from forced unwinds and margin calls.
  - Periphery→core lending: selected non-banks (pension funds, hedge funds, insurers) invest more cash into overnight repo than in normal times, mainly lending more to gilt dealers.
  - MMFs:
    - MMFs are generally net-lenders; in normal times lending particularly large to UK gilt dealers and banks.
    - During mid-March 2020, MMFs experienced liquidity issues due to large outflows and had less cash available to lend.
    - MMFs remain net lenders in overnight gilt repo during COVID-19 but with slightly lower net lending position; they do not borrow at all while still lending to core sectors.
    - MMFs increase lending to UK gilt dealers, decrease lending towards other core sectors.
    - MMF lending shifted toward shorter maturities (overnight), reflecting a preference for cash availability to meet redemptions.
    - MMF lending to UK gilt dealers at maturities longer than overnight completely stopped during COVID-19.
    - For US and other gilt dealers, MMF lending at maturities of one month and more stopped.
    - For other gilt dealers, MMF lending at short maturities (2 days to less than 2 weeks) also completely stopped.
    - For US gilt dealers, MMF lending at short maturities drastically declined.

### 5.2 Results — COVID-19 stress period: repo spreads
- Overall repo spreads increase significantly during COVID-19, reflecting severe liquidity stress.
- Highest spreads occur when core sectors engage in reverse repo transactions; concentration of higher spreads in transactions between core sectors.
- UK gilt dealers’ spreads on reverse repo consistently between the 98 or 100 percentiles and between 10 and 30 basis points higher than in normal times.
- Highest average increase in spreads is when banks are lending to US gilt dealers; these transactions are associated with a decrease in volumes relative to normal times (located at the 38th percentile), signaling market strains.
- Spreads increase more when core sectors lend to non-banks compared to when they borrow from non-banks, except for hedge funds.
  - Repo spreads for lending from core to periphery are on average higher also in normal times; during stress core sectors lend at higher rates than borrowing rates when trading with non-banks in the periphery.
  - Consistent with theory that dealers price in the shadow cost of intermediation on their balance sheet due to regulatory constraints (in particular the leverage ratio) when lending to leveraged investors and borrowing from cash-rich investors.
  - Aggregate evidence supports that channel at transaction level across sectors.

### 5.3 Comparison to the stress in the US repo market in 2019
- Context and trigger (September 2019):
  - Event date: 17th September 2019.
  - Metric: secured overnight funding rate (SOFR).
  - On 17th September 2019, SOFR "more than doubled", reaching "3.15% above the interest paid on reserves (IOR)".
  - Short-term drivers: temporary liquidity demand to satisfy a due date for US corporate taxes and a large settlement of US Treasury securities.
  - Observed intraday volatility: typical intra-day range 10 basis points (at most 20); on 17th September SOFR intra-day range jumped to about "700 basis points".
  - Structural factors compounding strains: Fed reducing balance sheet → reduction of cash reserves; increased demand from leveraged institutions; liquidity and leverage regulations constraining banks’ ability to lend.
- Spillovers to gilt repo market and policy response:
  - Aggregate gilt repo volumes spiked on 17th September 2019, indicating a large temporary increase in borrowing volumes.
  - US gilt dealers more than doubled their borrowing in the gilt repo market during that time compared to normal times.
  - Federal Reserve launched operations to return market to target policy range; these measures stabilised the market and helped limit spillovers.
- Empirical comparison (US repo stress vs COVID-19 stress):
  - Common pattern: both stress episodes show significant increase in volumes traded in cleared segment (preference for cleared markets due to netting benefits).
  - US repo stress volume changes:
    - US gilt dealers significantly increased borrowing and decreased lending, more than doubling net borrowing.
    - Significant increase in liquidity to US gilt dealers came via CCP sector.
    - In core, UK gilt dealers and banks significantly increased lending through cleared markets, enabling passthrough to US gilt dealers via CCP.
    - Periphery→core lending: US gilt dealers’ additional liquidity needs met by increased lending from insurers and hedge funds.
  - Differences in spreads:
    - Both episodes experienced spread increases, but increase during COVID-19 was significantly higher.
    - COVID-19: most percentiles at 100; repo spreads reached elevated levels up to "60 basis points".
    - US repo: rates increased with high percentiles (between "90 and 99") but did not exceed "more than 20 basis points".
  - Sector-specific during US repo stress:
    - When US gilt dealers increased borrowing from non-banks and CCP, repo spreads increased up to "0.1 percentage points" more than normal.
    - When US gilt dealers borrowed more from other gilt dealers, spreads increased between "0.1 and 0.2 percentage points".
    - When US gilt dealers lent to banks, they did so at a substantially lower spread than in normal times; reduction significant at the "5 percentile".
- Interpretation and conclusion:
  - Spillover magnitude: September 2019 US repo crisis spillovers to gilt repo market were visible but limited.
  - Relative severity: COVID-19 crisis exposed substantially larger strains on liquidity in the repo market, evidenced by significantly higher increases in spreads.
  - Implication: gilt dealers were probably less constrained during the US repo stress in 2019 than during the COVID-19 stress episode.

*Source: wpiea2021267-print-pdf - Section 2 we give an overview of the gilt repo market and in particular the overnight segment.*

### Section 2 we give an overview of the gilt repo market and in particular the overnight segment.

### wpiea2021267-print-pdf - Section 2 we give an overview of the gilt repo market and in particular the overnight segment.

### Overview
- Paper focuses on the overnight gilt repo market and provides background on the COVID-19 stress episode (March 3rd–23rd, 2020).  
- Empirical contributions:
  - Unique granular dataset covering almost the entire universe of transactions in the gilt repo market, including different segments, market participants and their repo trades volumes, rates and haircuts.
  - First to jointly analyse the bilateral and the cleared segment of the gilt repo market and to quantify empirically inter-sectoral changes in repo market activity in these segments during times of stress.
  - First to document the dynamics of the COVID-19 “dash for cash” in March 2020 in the repo market using granular transaction level data.
  - Evidence that networks change in times of stress, suggesting static networks with continuous roll-over assumptions may be ill-suited to capture contagion risk in collateralized debt markets.

### Definitions and scope (overnight gilt repo market)
- Market definition:
  - Overnight gilt repo market = secured sterling money market where the underlying security is a UK government bond denominated in British pounds (a gilt).
  - The party selling the gilt is borrowing cash (doing the repo); the party buying the gilt is lending cash (doing the reverse repo).
- Repo spread definition:
  - The repo spread refers to the difference between the interest rate of the trade (the repo rate) and the Bank of England’s Bank Rate at the time of the trade.
- Repo transaction mechanics (as specified):
  - Party 1 does the repo and borrows V >0 in cash from party 2 by selling a gilt with market value g >0. Typically, V≤g. V is the volume of the transaction. At maturity date T, party 1 repays V(1 + R), where R∈R and usually R∈[0,∞). R is the repo rate.
  - Overnight timeline: trade date t, settlement same day t; maturity T = t + 1, party 1 repays V(1 + R) on T.

### Data
- Sample coverage:
  - Bank of England Sterling Money Market data sample spans from 1 March 2019 until 31 October 2020.
  - The Bank requires reporting by institutions with significant activity (top 95% of activity at either overnight or up to one-year maturity). Some activity where neither party is a bank or major broker dealer is not captured.
- Aggregate market size and maturity distribution:
  - Total transaction volumes in the aggregate gilt repo market are around £180 trillion on average in the data sample.
  - Maturity concentration: Almost 50% at overnight maturity; 35% at maturities greater than overnight but less than two weeks.
  - Average daily transaction volumes in the overnight gilt repo market are £80 billion.
  - Average daily number of transactions in the overnight market is close to 1600.
- Settlement methods (average shares):
  - 36% of daily overnight gilt repo volumes are settled through a central counterparty (CCP).
  - 2% is settled tri-party.
  - The majority of volumes are settled bilaterally.
- Temporal patterns:
  - Wide fluctuations in volumes and repo spreads around quarter- and year-ends (window dressing).
  - Repo spreads are measured as overnight volume-weighted repo rate minus the Bank Rate; spreads show large negative spikes at year-end and quarter-end aligned with volume movements.

### The COVID-19 crisis (March 2020 stress episode)
- Defined stress window: period between 3rd and 23rd of March 2020.
- Market dynamics during the episode:
  - Described as an extreme “dash for cash”.
  - Asset prices adjusted sharply; margin calls on derivative exposures rose sharply generating strong liquidity pressure.
  - Yields on advanced-economy government bonds fell between February and mid-March 2020 as investors de-risked; however, in mid-March even government bonds came under forced selling pressure and saw little demand.
  - Overnight repo rates rose sharply and repo borrowing costs increased as demand increased while dealers’ ability and willingness to intermediate was constrained.
  - Repo volumes increased sharply up to March 11, 2020 as demand for liquidity built up.
- Policy responses and effects:
  - March 11, 2020: Bank of England reduced the Bank Rate by 50 basis points to 0.25%.
  - March 19, 2020: Bank of England decided to buy gilts in large size.
  - March 24, 2020: Bank activated the Contingent Term Repo Facility (CTRF), committing to lend unlimited amounts of sterling at close to Bank Rate against a broad range of collateral.
  - These operations, together with the passing of the March quarter end, contributed to bringing repo rates back to more normal levels.

### Financial institutions trading in the repo market
- Activity at institution level (sample March 2019–October 2020):
  - Total institutions trading at least once in overnight repo market: 156.
  - Daily average number of institutions active: 58.
  - In full sample:
    - Average daily repo transaction volume by active institution: £0.6 billion.
    - Average trade size: £0.05 billion.
    - Average number of daily repo transactions by institution: 13.
- During the COVID-19 stress episode:
  - Institutions active at least once: 125.
  - Market activity increased:
    - Average daily repo transaction volume by active institution rose to £2 billion.
    - Average trade size rose to £0.06 billion.
    - Average number of daily repo transactions by institution rose to 36.

### Institutional network (formal definition and structure)
- Time set:
  - T = {t0, t1, ..., tT} with t0 = 1 March 2019, tT = 31 October 2020, and T + 1 = 400.
- Institutional network of volumes (Definition 3.1):
  1. Nodes:
     - N(I) = {1,...,N(I)}, N(I) = 156, representing institutions engaging in the overnight gilt repo market.
     - For every day t∈T, V(I)ij(t), i,j∈N(I), denotes the total notional amount of cash that node i lends to node j in an overnight repo transaction at time t. If V(I)ij(t) > 0, the pair (i,j) is an edge and V(I)ij(t) is the weight (volume).
  2. Matrix representation:
     - V(I)(t) = (V(I)ij(t))i,j∈N(I) ∈ [0,∞)N(I)×N(I) is the matrix of total notional cash lent at time t in the institutional network.

*Source: wpiea2021267-print-pdf - Section 2 we give an overview of the gilt repo market and in particular the overnight segment.*

### 3.  We denote byA

### 3.  We denote byA

### Institutional network of volumes: definitions and measurements
- Adjacency matrix at time t: A(I)(t) = (A(I)ij(t))i,j∈N(I) ∈ {0,1}N(I)×N(I), where
  - A(I)ij(t) = 1, if V(I)ij(t) > 0; 0, else. (1)
- Aggregate average transaction-volume matrix over the whole sample:
  - V̄(I) = (V̄(I)ij)i,j∈N(I) ∈ [0,∞)N(I)×N(I), where V̄(I)ij = ∑t∈T V(I)ij(t) / (T+1). (2)
- Aggregate empirical transaction-probability matrix:
  - Ā(I) = (Ā(I)ij)i,j∈N(I) ∈ [0,1]N(I)×N(I), where Ā(I)ij = ∑t∈T A(I)ij(t) / (T+1). (3)
- Interpretation:
  - V̄(I)ij: average transaction volume between two institutions in the overnight gilt repo market over the whole sample.
  - Ā(I)ij: empirical probability that institution i lends institution j cash in a repo transaction on an average day over the whole sample.

### Core–periphery structure and pairwise trading characteristics
- The overnight gilt repo market exhibits a core-periphery structure as defined by Craig & Von Peter (2014):
  - Core institutions borrow from, and lend to, at least one institution in the periphery and intermediate between periphery institutions.
  - Periphery institutions may only lend to, or borrow from, the core and do not lend to each other.
- Empirical observations from heatmaps:
  - A dense, darker cluster in the lower left corner corresponds to the core (higher average transaction volumes).
  - A large empty grey area in the middle/top right corner indicates no trading among periphery institutions.
  - Only banks and gilt dealers are in the core; non-banks constitute the periphery. The central counterparty (CCP) is classified as neither core nor periphery.
- Transaction-probability highlights:
  - The darkest red in Ā(I) corresponds to values ranging from 0.9 to 1, i.e., two institutions trade between 90 and 100 percent of days in the sample (almost continuous daily roll-over).
  - Overall, empirical transaction probabilities in the core are rather low for the majority of institution pairs, implying no daily roll-over for most core pairs.
  - A few select pairs in the core show almost daily roll-over for the whole period; there are no such high-probability pairs in the periphery.

### Degree distributions and connectivity
- Network size and bounds:
  - Institutional network has N(I) = 156 nodes; maximum possible in- or outdegree is N(I) − 1.
- Empirical survival-function facts (Figure 3):
  - The empirical survival function 1 − F(d) is used for average in- and outdegrees d ∈ {1,...,N(I) − 1}.
  - Example: at degree = 5 on the x-axis, the probability that a node has in- or outdegree larger than 5 is roughly 0.2, i.e., around 80% of nodes have less than 5 incoming edges and less than 5 outgoing edges.
  - If degree = 50 on the x-axis, the probability that a node has degree larger than 50 is 0.
  - The maximum number of incoming or outgoing edges is around 50.
- Summary:
  - The majority of nodes have a small number of connections; a small number of nodes are highly connected.
  - The tails of the degree distribution appear linear on a log-log plot, indicating that a power law distribution could fit the tails.

### Changes under stress: density and use of existing relationships
- Network density definition (time-t):
  - density(t) = [1 / (N(I)(N(I) − 1))] ∑i=1^N(I) ∑j=1^N(I) A(I)ij.
- Key density observations (Figure 4 and text):
  - Average density for the whole sample is 0.005.
    - Interpretation: on average, 0.5% of possible edges are present in the network.
  - Average degree is around 1 (on average, institutions trade with one other institution on any given day).
  - Clear dips at year ends and smaller dips at quarter ends (window dressing effects).
  - Two notable spikes in density:
    - Highest peak: March 2020 at the height of the COVID-19 crisis.
    - Second highest spike: September 2019 (coincides with turmoil in the US repo market).
- Formation of trading links during the COVID-19 stress:
  - Unique directed trade pairs:
    - 755 unique directed trade pairs from beginning of sample up to beginning of COVID-19 crisis (March 1 2019 - March 8 2020).
    - 287 unique directed trade pairs during the COVID-19 stress.
    - Of those 287, 9 were new bilateral trading relationships during the COVID-19 crisis relative to the 755 trading relationships before COVID-19.
      - Of these 9 new trading pairs, 4 transact again at least once after the crisis, whereas 5 do not transact again.
  - Interpretation:
    - The vast majority of market participants relied on existing trading relationships to secure liquidity during the COVID-19 stress.
    - While few pairs are active almost exclusively during the stress episode, many pairs that traded during COVID-19 also traded before and/or after the crisis.
  - Related empirical insight:
    - Rolling over repo contracts and keeping trading with the same counterparty can be beneficial in times of stress by suggesting stable funding sources; however, the absence of daily roll-over could exacerbate liquidity stress. The finding that institutions used previously established relationships during stress reduces searching costs.

### Sectoral activity in the overnight gilt repo market (overview)
- Repo market participants classified into sectors (10 sectors used in the analysis).
- Two types of end users:
  - Providers of collateral in return for cash: funds, pension funds, hedge funds, insurance companies.
  - Lenders of cash receiving collateral: money market funds (MMFs), hedge funds, corporate treasurers.
- High-level sectoral observations (Figure 5 and Table 1):
  - Gilt dealers and banks are the only sectors that have trade relationships with all other sectors; they intermediate between all sectors.
  - Gilt dealers and banks are the only sectors with self-loops (repo/reverse repo agreements among same-sector members).
  - Gilt dealers and banks are the only sectors that are clearing members and hence interact with the CCP sector.
  - Non-banks only trade bilaterally with gilt dealers and banks, but not amongst each other.
- Sectoral volumes (Table 1, volumes expressed in £billion; full sample vs COVID-19 crisis averages):
  - Bank:
    - Full sample: #Av. lend 263.16; Av. borrow 11.02; Av. net lend -7.87
    - COVID-19 crisis: #Av. lend 156.77; Av. borrow 9.95; Av. net lend -3.18
  - CCP:
    - Full sample: #Av. lend 634.30; Av. borrow 29.56; Av. net lend 4.74
    - COVID-19 crisis: #Av. lend 440.26; Av. borrow 32.62; Av. net lend 7.64
  - Fund:
    - Full sample: #Av. lend 182.40; Av. borrow 0.04; Av. net lend 2.36
    - COVID-19 crisis: #Av. lend 122.73; Av. borrow 0.01; Av. net lend 2.72
  - Hedge Fund:
    - Full sample: #Av. lend 281.23; Av. borrow 1.39; Av. net lend -0.15
    - COVID-19 crisis: #Av. lend 141.32; Av. borrow 2.59; Av. net lend -1.28
  - Insurer:
    - Full sample: #Av. lend 41.81; Av. borrow 0.10; Av. net lend 1.71
    - COVID-19 crisis: #Av. lend 42.33; Av. borrow 0.08; Av. net lend 2.25
  - MMF:
    - Full sample: #Av. lend 95.58; Av. borrow 0.16; Av. net lend 5.42
    - COVID-19 crisis: #Av. lend 54.39; Av. borrow 0.00; Av. net lend 4.39
  - Pension fund:
    - Full sample: #Av. lend 152.57; Av. borrow 0.58; Av. net lend 1.99
    - COVID-19 crisis: #Av. lend 83.39; Av. borrow 0.35; Av. net lend 3.04
  - UK Gilt dealer:
    - Full sample: #Av. lend 613.97; Av. borrow 15.87; Av. net lend -1.91
    - COVID-19 crisis: #Av. lend 515.94; Av. borrow 19.68; Av. net lend -3.74
  - US Gilt dealer:
    - Full sample: #Av. lend 58.67; Av. borrow 12.52; Av. net lend -3.85
    - COVID-19 crisis: #Av. lend 58.62; Av. borrow 14.85; Av. net lend -6.23
  - Other Gilt dealer:
    - Full sample: #Av. lend 77.59; Av. borrow 10.33; Av. net lend -2.74
    - COVID-19 crisis: #Av. lend 76.96; Av. borrow 12.96; Av. net lend -6.00

### Sectoral spreads (Table 2)
- Overview of average volume weighted spreads by sector (expressed in percent). The sector is a borrower for the repo spread and a lender for the reverse repo spread.
- Full sample vs COVID-19 crisis:
  - Bank: Full sample repo spread -0.04; reverse repo spread -0.01. COVID-19 crisis repo spread 0.02; reverse repo spread 0.14.
  - CCP: Full sample repo spread -0.04; reverse repo spread -0.03. COVID-19 crisis repo spread 0.08; reverse repo spread 0.08.
  - Fund: Full sample repo spread -0.02; reverse repo spread -0.03. COVID-19 crisis repo spread 0.13; reverse repo spread 0.04.
  - Hedge Fund: Full sample repo spread 0.01; reverse repo spread -0.08. COVID-19 crisis repo spread 0.13; reverse repo spread 0.03.
  - Insurer: Full sample repo spread 0.00; reverse repo spread -0.02. COVID-19 crisis repo spread 0.06; reverse repo spread 0.07.
  - MMF: Full sample repo spread -0.07; reverse repo spread -0.03. COVID-19 crisis repo spread -0.03.
  - Pension fund: Full sample repo spread 0.13; reverse repo spread -0.04. COVID-19 crisis repo spread 0.32; reverse repo spread 0.04.
  - UK Gilt dealer: Full sample repo spread -0.04; reverse repo spread -0.03. COVID-19 crisis repo spread 0.07; reverse repo spread 0.08.
  - US Gilt dealer: Full sample repo spread -0.02; reverse repo spread -0.06. COVID-19 crisis repo spread 0.07; reverse repo spread 0.08.
  - Other Gilt dealer: Full sample repo spread -0.02; reverse repo spread -0.05. COVID-19 crisis repo spread 0.11; reverse repo spread 0.06.
- Interpretation:
  - On average in the full sample, spreads for repo and reverse repo transactions faced by gilt dealers (and several other sectors) are negative; during the COVID-19 crisis spreads become positive for many sectors.

### Roles and dynamics of key sectors
- Gilt dealers:
  - Defined as banks that are Gilt-Edged Market Makers (GEMMs).
  - Divided by headquarters into UK gilt dealers, US gilt dealers, and other gilt dealers.
  - Repo lending to clients is a core business; a large part of repo borrowing finances matched-book lending.
  - Leverage requirements have encouraged more pro-active management of balance sheets, including limiting repo activity or increasing its price.
  - All gilt dealer sectors are net borrowers on average; UK gilt dealers are closest to a matched book, US and other gilt dealers are larger net borrowers.
  - All three gilt dealer sectors increased net borrowing during the COVID-19 crisis; ranking of net borrowing size remains the same.
- Banks:
  - Grouped as banks that are not GEMMs.
  - Overall, banks are the largest net borrowers on average in the overnight gilt repo market.
  - During the COVID-19 crisis, banks more than double their average lending and decrease their borrowing, resulting in a decrease in net borrowing.
  - Banks entered the COVID-19 crisis with sizeable buffers and were not at the centre of the financial turmoil (Giese & Haldane (2020)).
- Central counterparties (CCPs):
  - CCPs do not actively provide liquidity; they:
    - Clear trades between their members (gilt dealers and banks).
    - Lend cash collected from margin payments as reverse repo to gilt dealers and banks.
  - CCPs are the only sectors interacting with gilt dealers and banks in the dataset; their investments of cash margin into the overnight gilt repo market likely explain positive net lending positions.
  - CCP sector is one of the largest net lenders and their net lending increases substantially during the COVID-19 crisis, partially reflecting increased cash margin investment.
  - Repo spreads with CCPs are negative on average in the full sample but become positive during COVID-19; spreads remain among the lowest.
- Non-banks (MMFs, insurers, pension funds, funds, hedge funds):
  - MMFs, insurers, pension funds and funds are net lenders in the overnight gilt repo market; MMFs are the largest net lenders.
  - MMFs use the overnight repo market to place cash safely short-term; their lending volumes are stable through the sample, increasing in the second half of 2020.
  - Hedge funds are marginal net borrowers on average; they are active on both sides of the market and can use repo to increase leverage.
    - During COVID-19, hedge fund borrowing increases significantly more than lending, and the repo spreads they face increase significantly during the stress episode.
  - Pension funds are net lenders in overnight repo but are net borrowers in longer maturity segments (1 month to 1 year) for liability driven investment strategies (LDI).
  - Funds (residual category) and other non-banks have sector-specific patterns; non-banks transact bilaterally with banks and gilt dealers but not with each other.

*Source: IMF Working Paper content unit "3.  We denote byA" (wpiea2021267-print-pdf).*

### 4.2    The sectoral repo network

### 4.2    The sectoral repo network

### Definition and data structure
- The sectoral network of volumes consists of a set of nodes denoted by N(S) = {1,...,N(S)}, N(S) = 10, representing the sectors engaging in the overnight gilt repo market.
- For every day t ∈ T, V(S)ij(t), i,j ∈ N(S), denotes the total notional amount of cash that node i lends to node j in an overnight repo transaction at time t. If V(S)ij(t) > 0, the pair (i,j) is an edge and V(S)ij(t) is the weight.
- V(S)(t) = (V(S)ij(t))i,j∈N(S) ∈ [0,∞)N(S)×N(S) is the matrix of total notional cash lent at time t in the sectoral network.
- The adjacency matrix A(S)(t) = (A(S)ij(t))i,j∈N(S) ∈ {0,1}N(S)×N(S) corresponds to the sectoral network of cash lent, with
  - A(S)ij(t) = { 1, if V(S)ij(t) > 0; 0, else. }

### Transaction likelihood (empirical probability matrix)
- Define ̄A(S) = (̄A(S)ij)i,j∈N(S) ∈ [0,1]N(S)×N(S), where
  - ̄A(S)ij = ∑t∈T A(S)ij(t) / (T + 1).
- ̄A(S)ij represents the empirically observed probability that sector i lends sector j cash in a repo transaction on a given day.
- Interpretation of heatmap (Figure 7, sector-level version of Figure 2(b)):
  - Each cell is the probability that two sectors trade with each other on any given day in the whole sample.
  - The darkest red ranges from 0.9 to 1 and means the two sectors trade between 90 and 100 percent of days in the sample (almost continuous daily roll-over of trades).
- Empirical patterns reported:
  - The CCP sector is active on both sides (repo and reverse repo) with all possible trading partners (all types of gilt dealers and banks) essentially daily.
  - Within the core, only UK gilt dealer borrows on a daily basis from US and UK gilt dealers and banks. All other core sectors display no daily roll over of transactions within the core.
  - Lending from periphery sectors (MMF, fund, insurer, pension fund and hedge fund) to core sectors (UK and US gilt dealers and banks) occurs with high probabilities, almost daily.
  - Periphery sectors lend slightly less frequently to other gilt dealers.
  - Hedge funds and pension funds are the periphery sectors who borrow most often.
  - In terms of periphery sectors borrowing from the core:
    - Hedge funds borrow (almost) daily from all types of gilt dealers and slightly less frequently from banks.
    - Pension funds mainly borrow daily from UK gilt dealers and banks.
    - The other periphery sectors (insurer, fund and MMF) borrow much less frequently.
  - A grey square in the top right (as observed in Figure 5) reflects that the CCP sector and the non-banks and non-gilt dealers do not trade with each other or amongst each other in the data set.

### Stress episodes and time windows
- Two stress episodes are defined (Definition 5.1):
  - T_CS_COVID-19 ⊂ T: dates associated with the COVID-19 “dash-for-cash”, i.e., 03 March 2020 - 23 March 2020.
  - T_CS_US ⊂ T: dates associated with the US repo market turmoil, i.e., 03 September 2019 - 17 September 2019.
- Empirical context:
  - In both stress periods, there were spikes in the average daily transactions volumes in the overnight gilt repo market of a similar magnitude.
  - Spreads spiked very sharply only during the COVID-19 stress.

### Linear model for volumes and spreads (specification)
- Daily observations for volumes: Yijt := V(S)ij(t), where i,j ∈ {1,...,N(S)} and t ∈ ̃T. ̃T denotes the set of time points T in which quarter ends were removed.
- In the data: N(S) = 10 and ̃T = |̃T| = 381. Hence, there are 10^2 · 381 = 38100 observations to fit the model.
- The linear model with only categorical explanatory variables:
  - Yijt = β(Normal, Vol)ij I{i lending sector} I{j borrowing sector}
    + β(CS2, Vol)ij I{ i lending sector } I{ j borrowing sector } I{ t ∈ T_CS_US }
    + β(CS3, Vol)ij I{ i lending sector } I{ j borrowing sector } I{ t ∈ T_CS_COVID-19 }
    + εijt,
  - I{·} denotes the indicator (1 if condition satisfied, 0 otherwise); εijt are error terms.
- Parameter matrices:
  - The model consists of 3(N(S))^2 = 300 model parameters, represented as three (N(S) × N(S)) matrices:
    - β(Normal, Vol) = (β(Normal, Vol)ij) represents the average daily volume traded between sector pairs outside the two stress periods. β(Normal, Vol)ij is the average daily volume lent from sector i to sector j for t ∈ ̃T \ (T_CS_US ∪ T_CS_COVID-19).
    - β(CS3, Vol) = (β(CS3, Vol)ij) represents the change in average daily volume between sector pairs during the COVID-19 stress (3-23 March 2020). The average daily volume lent from sector i to sector j at t ∈ T_CS_COVID-19 is β(Normal, Vol)ij + β(CS3, Vol)ij.
    - β(CS2, Vol) is defined analogously for the US stress episode.
- Model for spreads:
  - Same linear model (6) with observations Yijt equal to the volume weighted repo spreads associated with repo transactions with non-zero volume V(S)ij(t).
  - Corresponding parameter matrices estimated: β(Normal, Spread), β(CS2, Spread), β(CS3, Spread).

### Estimation of significance: block bootstrap
- Time series length and bootstrap setup:
  - The time series has ̃T data points (days). The quarter ends were removed by removing the two first days and the two last days in each quarter.
  - A simple block bootstrap for time series is used: split the ̃T days into blocks of length b = 10. Hence, there are N_B = b ̃T/bc blocks of length b and one block of length ̃T − N_B b.
  - A new time series is sampled by drawing with replacement N_B blocks of length b and one block of length ̃T − N_B b and piecing those blocks together as a new time series.
  - The linear model (6) is fitted to each bootstrapped series. The process is repeated R = 1000 times, yielding R estimates of the model parameters.
- Interpretation of heatmaps (Figures 8 and 9):
  - Coloured fields have numbers between 0 and 100 representing the percentile of the parameter estimate from the observed time series relative to the empirical cumulative distribution generated by the bootstrap.
  - Very high numbers (e.g., 99 or 100) indicate the parameter estimate is in the right tail of the bootstrap distribution and therefore highly significant.
  - Very low numbers (e.g., 0 or 1) indicate the parameter estimate is in the left tail of the bootstrap distribution and therefore highly significant.

*Source: 4.2 The sectoral repo network (wpiea2021267-print-pdf)*

### 5.2    Results

### 5.2    Results

### 5.2.1    Normal times
- Largest volumes are traded between the CCP sector and gilt dealers and banks.
- UK gilt dealers are borrowing and lending large volumes in the centrally cleared segment of the market.
- CCPs can also do reverse repo as proprietary trading for cash margin management; this supply of cash from CCPs can go to gilt dealers and banks.
- Within the core:
  - Banks are net borrowers (see Table 1) and borrow the largest quantities from the CCP sector, funds and MMFs.
  - Gilt dealers are net borrowers and borrow the largest amounts from the CCP sector.
  - UK gilt dealers additionally borrow large amounts from MMFs.
- In the periphery:
  - Hedge funds are the only net borrowers, albeit only by a small margin; they borrow and lend very similar volumes to and from all gilt dealers and banks.
  - All other institutions in the periphery are net lenders.
- Repo spreads in normal times are small and very close to zero (see times series in Figure 1(b)).
  - Very little variation in normal times across sectors.
  - Spreads on reverse repos from the core to the periphery sectors tend to be positive and higher on average, relative to the rest.

### 5.2.2    COVID-19 stress period - repo volumes
- Key finding: overall volumes traded with the CCP sector increase significantly compared to normal times during the COVID-19 stress episode (see Figure 8(b)).
- Drivers of increased CCP volumes:
  - Banks lend more cash through cleared markets during the COVID-19 episode compared to normal times, while lending less bilaterally to gilt dealers and decreasing borrowing from almost all sectors.
    - Banks remain net borrowers (see Table 1) but their net borrowing positions decrease markedly relative to normal times; some lending positions are in the highest percentiles of the bootstrap distribution in Figure 8(b).
    - Increased repo lending of banks into cleared markets goes to gilt dealers (gilt dealers borrow higher volumes from the CCP sector, whereas banks do not).
    - Possible motive: cleared segment is less capital-intensive due to netting benefits, increasing the proportion of trades on which banks face a single counterparty and reducing balance sheet impact for regulatory purposes.
  - CCP sector increases reverse repo trades with gilt dealers.
    - CCPs invested additional cash margin collected during the period of increased volatility; most additional cash margin collected during the March 2020 volatility was reinvested in the repo market (Bank of England, 2020).
    - Average net lending by the CCP sector during COVID-19 was almost double the sample average and the largest compared to the other sectors during that stress (see Table 1).
    - Large increase in net lending by CCPs reflects a very sharp increase in initial margin collected.
    - Bank of England (2020) finds that relative to the average level over January and February, UK CCPs initial margin requirements had grown by around 58 billion in March   a 31% increase   with a daily peak increase of around 10 billion. Around half of the additional initial margin was provided in cash, most of which the CCPs reinvested in the repo market.
  - UK gilt dealers also lend higher volumes via cleared markets; US and other gilt dealers decrease their lending through cleared markets and appear to use the gilt repo market more to acquire sterling cash via cleared markets.
  - Overall, both lending and borrowing via cleared markets increase significantly during the COVID-19 stress period.
- Bilateral segment changes:
  - Core to periphery lending: core lends more to hedge funds; hedge funds increased reliance on short-term funding via repo since 2018 and faced increased short-term funding needs during COVID-19 (mid-March 2020), driven by forced unwinds and margin calls.
  - Periphery to core lending: selected non-banks (pension funds, hedge funds, insurers) invest more cash into the overnight repo market than in normal times, mainly lending more to gilt dealers.
  - MMFs:
    - MMFs are generally net-lenders in the repo market; in normal times their lending is particularly large to UK gilt dealers and banks.
    - During mid-March 2020, MMFs experienced liquidity issues due to large outflows and had less cash available to lend (Hauser, 2020).
    - MMFs remain net lenders in the overnight gilt repo market during the COVID-19 stress episode but with a slightly lower net lending position.
      - They do not borrow at all while still lending to sectors in the core.
      - They increase lending to UK gilt dealers, while decreasing lending towards the other sectors in the core.
    - MMF lending behavior shifted toward shorter maturities:
      - Lending in the overnight segment reflects a shortening of maturities during the “dash for cash.”
      - MMFs show a preference for the overnight segment so cash remains available to meet redemption requests the next day.
      - MMF lending to UK gilt dealers at maturities longer than overnight completely stopped during the COVID-19 episode.
      - For US and other gilt dealers, MMF lending at maturities of one month and more stopped.
      - For other gilt dealers, MMF lending at short maturities (2 days to less than 2 weeks) also completely stopped.
      - For US gilt dealers, MMF lending at short maturities drastically declined.

### 5.2.3    COVID-19 stress period - repo spreads
- Overall, repo spreads increase significantly during the COVID-19 stress period, reflecting the severity of the liquidity stress (see Figure 1(b) and Table 2 for sectoral averages).
- Highest spreads occur when core sectors engage in reverse repo transactions, with concentration of higher spreads in transactions between core sectors.
- UK gilt dealers’ spreads on reverse repo are consistently between the 98 or 100 percentiles and between 10 and 30 basis points higher than in normal times.
- The highest average increase in spreads is when banks are lending to US gilt dealers; these transactions are associated with a decrease in volumes relative to normal times (located at the 38th percentile of the distribution in Figure 8(b)), which can be taken as a sign of strains in the market.
- Spreads increase more when sectors in the core lend to non-banks compared to when they borrow from non-banks, with the exception of hedge funds.
  - Repo spreads for lending from the core to the periphery are on average higher also in normal times; during stress core sectors lend at higher rates than borrowing rates when trading with non-banks in the periphery.
  - This is consistent with the theory that dealers priced in the shadow cost of intermediation on their balance sheet due to regulatory constraints (in particular the leverage ratio) when lending to leveraged investors (e.g., hedge funds) and borrowing from cash-rich investors (e.g., MMFs).
  - The channel supported by aggregate evidence is shown to hold at the transaction level across sectors in the gilt repo market.

*Source: 5.2 Results (wpiea2021267-print-pdf).*

### 5.3    Comparison to the stress in the US repo market in 2019

### 5.3    Comparison to the stress in the US repo market in 2019

### Context and trigger of the US repo stress (September 2019)
- Event date: 17th September 2019.
- Metric highlighted: the secured overnight funding rate (SOFR).
- On 17th September 2019, SOFR "more than doubled", reaching "3.15% above the interest paid on reserves (IOR)".
- Short-term drivers attributed: very high temporary liquidity demand to satisfy a due date for US corporate taxes and a large settlement of US Treasury securities.
- Observed intraday volatility: repo rates typically fluctuate in an intra-day range of 10 basis points, or at most 20 basis points; on 17th September SOFR intra-day range jumped to about "700 basis points".
- Structural factors potentially compounding strains:
  - Fed reducing the size of its balance sheet → reduction of cash reserves at the Fed.
  - Increased demand for funding from leveraged financial institutions such as hedge funds via Treasury repos.
  - Liquidity and leverage regulations constraining banks’ ability to lend large amounts of cash (evidence of dealers subject to more binding leverage ratio reducing liquidity supply after January 2017).

### Spillovers to the gilt repo market and policy response
- Although the stress did not originate in the UK, aggregate gilt repo volumes in the overnight market spiked on 17th September 2019, indicating a large temporary increase in borrowing volumes.
- US gilt dealers more than doubled their borrowing in the gilt repo market during that time compared to normal times.
- The Federal Reserve launched a number of operations aimed at returning the market to conditions consistent with its target monetary policy range; these policy measures “stabilised the market [...] and helped to limit spillovers to broader market conditions”.

### Empirical comparison of market structure and activity (US repo stress vs COVID-19 stress)
- Methodology referenced: parameter estimates β(CS2, Vol) for change in average volume and β(CS2, Spread) for change in average spread (Figures 9(a) and 9(b) for US repo stress; Figures 8(b) and 8(d) for COVID-19 stress).
- Common patterns in volumes:
  - Both stress episodes show a significant increase in volumes traded in the cleared segment of the market.
  - Interpretation: preference for dealers and banks to transact in the cleared rather than the bilateral segment because of netting benefits.
- Detailed volume changes during US repo stress (Figure 9(a) summary):
  - US gilt dealers significantly increased borrowing and decreased lending, more than doubling their net borrowing position compared to normal times.
  - Significant increase in liquidity to US gilt dealers came via the CCP sector.
  - In the market core, UK gilt dealers and banks significantly increased their lending through cleared markets, enabling passthrough to US gilt dealers via the CCP.
  - Periphery-to-core lending: US gilt dealers’ additional liquidity needs were met by increased lending from insurers and hedge funds.
- Differences in spread behavior:
  - Both episodes experienced spread increases, but the increase during the COVID-19 stress was significantly higher.
  - COVID-19 episode: highest increase in the level of spreads relative to other case studies; most percentiles at 100; repo spreads reached elevated levels up to "60 basis points".
  - US repo episode: rates increased with high percentiles (most are between "90 and 99") but did not exceed "more than 20 basis points".
- Sector-specific spread dynamics during US repo stress:
  - When US gilt dealers increased borrowing from non-banks and the CCP, repo spreads increased but only up to "0.1 percentage points" more than in normal times.
  - When US gilt dealers borrowed more from other gilt dealers, they faced a significant increase in spreads between "0.1 and 0.2 percentage points".
  - When US gilt dealers lent to banks, they did so at a substantially lower spread than in normal times; this reduction is significant at the "5 percentile".

### Interpretation and conclusion about relative severity and spillovers
- Spillover magnitude: During the US repo crisis in September 2019 spillover effects to the gilt repo market were visible but limited.
- Relative severity: The COVID-19 crisis exposed substantially larger strains on liquidity in the repo market, evidenced by the significantly higher increase in spreads during that time.
- Implication: gilt dealers were probably less constrained during the US repo stress in 2019 than during the COVID-19 stress episode.

*Source: 5.3 Comparison to the stress in the US repo market in 2019 (wpiea2021267-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021267-print-pdf.pdf_