Collateral rehypothecation, safe asset scarcity, and unconventional monetary policy

Journal Pre-proof Collateral rehypothecation, safe asset scarcity, and unconventional monetary policy Ruggero Grilli, Federico Giri, Mauro Gallegati PII:

S0264-9993(19)30547-4

DOI:

https://doi.org/10.1016/j.econmod.2019.12.004

Reference:

ECMODE 5097

To appear in:

Economic Modelling

Received Date: 12 April 2019 Revised Date:

4 December 2019

Accepted Date: 7 December 2019

Please cite this article as: Grilli, R., Giri, F., Gallegati, M., Collateral rehypothecation, safe asset scarcity, and unconventional monetary policy, Economic Modelling (2020), doi: https://doi.org/10.1016/ j.econmod.2019.12.004. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Collateral rehypothecation, safe asset scarcity, and unconventional monetary policy ∗

December 10, 2019

Abstract We build a mark-to-market model where commercial banks can enlarge their balance sheets, repledging the available collateral several times to exchange liquidity through the interbank market. In bad times, the fall of risky asset price disrupts the length of the repledging chain due to the increase of the haircut and the decrease of external assets’ value. In such a scenario, the central bank can intervene implementing unconventional monetary policies by purchasing a fraction of the banking system’s external assets, both safe treasury bonds, and risky asset-backed securities, to inject liquidity. Our results show that a quantitative easing policy that purchases only safe assets is highly ineffective in restoring the intermediation activity to the pre-crisis level due to its inability to sustain the risky asset price and the repledging chain of collateral. Instead, focusing on risky assets only, the monetary authority can sustain risky asset prices, avoiding the freezing of the money market.

Keywords: Quantitative Easing, Rehypothecation chain of collateral, Interbank Network, Safe assets scarcity. JEL classification codes: E44, E47, E51, E52, E58.

∗ This paper previously circulated under the name of ”The dark side of quantitative easing”. The authors would like to thanks all the participants to the conference Finance and Economic Growth in the Aftermath of the Crisis - Milan, 11-13 September 2017. Moreover, we would like to thank I˜ naki Aldasoro, Michele Fratianni, two anonymous referees and the editor for their useful comments and suggestions. All errors remain ours.

1

1

Introduction

The aim of this paper is to investigate the interrelation between unconventional monetary policy measures and the rehypothecation of collateral. In order to do that, we build an accounting model of the interbank market similar in spirit to Adrian and Shin (2009); Shin (2009); Singh (2012) including risky assets into the banks’ balance sheet and a monetary authority that can purchase a fraction of banks’ assets. We use this model in order to answer the following questions: a) Is the repledging of collateral an important component of the money market? b) Is an unconventional monetary policy based on the purchase of only risky assets more effective than the one based on the exchange of safe assets for liquidity? The last two decades were characterized by a growing degree in the complexity of financial products available to investors. In this context, the money market is not an exception. According to Gorton and Metrick (2012b), the so-called repurchase agreement (henceforth repo) became the most used instrument in the money market.1 What is a repo? Following Antinolfi et al. (2015), a repo is a contract where a collateral lender and a cash lender decide to exchange collateral for liquidity establishing that, at a certain date in the future, the collateral lender will reacquire the underlying asset. If the collateral lender will not be able to reimburse, the cash provider will definitely take possess of the collateral. In general, the cash lender gives liquidity for a lesser amount with respect to the fair value of the asset. In this case, the lender applies a haircut to the value of the collateral. Usually, several assets are eligible as collateral in a repo contract with a special preference for the so-called safe assets (Gorton, 2017). Such assets include government bonds (eg, Tbills, and Bunds), AAA corporate bonds or assets back securities. Given, among others, the rising importance attributed to the repo market, it becomes clear how in modern money market collateral plays a crucial role in the intermediation of funds. Understanding its proper functioning can, therefore, help support monetary policy interventions. In this sense, the traditional narrative attributes the main cause of the 2007/2008 financial crisis to a negative house price shock that propagated across financial markets through the shrinkage of banks’ balance sheet due to the fire sales of assets and mortgages backed securities previously assumed to be safe (Shleifer and Vishny, 2011). The contraction of banks’ asset side reduces the amount of assets that can be pledged as collateral, ultimately causing a reduction in the supply of credit. However, the deleveraging generated by declining asset prices is only part of the story. According to Singh (2012), we should also take into account ”The 1 Gorton and Metrick (2012a, p. 132) quantified the share of the repo market about 20-30 % of US GDP.

2

other deleveraging ”: the contraction of available liquidity due to the shortening of the chain of collateral rehypothecation. In a highly interconnected financial system, collateral can be re-pledged several times before reaching their final destination. Empirically, Fuhrer et al. (2016) highlights the importance of the rehypothecation channel, finding that about 10 % of interbank transactions are made against re-use collateral. In this context, Singh (2012); Singh and Stella (2012) find evidence that a contraction of the re-pledging mechanism due to the lack of ”good collateral ” accounts for a significant portion of money market freezing in the post-Lehman era. How does monetary policy interact with the repledging chain of collateral by private intermediaries? Monetary policy, especially in the form of Quantitative Easing (henceforth QE) with operations such as the large-scale-asset-purchase (LSAP), can have a huge impact on the availability of safe asset. 2 The purchase of safe assets by the monetary authority can withdraw collateral from the private interbank market. Even if the subsequent liquidity injection can partially compensate for the reduction of collateral, ultimately, the length of the re-pledging chain can be squeezed causing a contraction of interbank market transactions (Singh, 2012). Caballero et al. (2017, p. 42) highlights how ”...if a shortage of safe assets is the main reason behind the economic downturn, and the constraints on those that demand these assets to shift their portfolios into riskier assets are severe, reducing the available supply of safe assets via central bank purchases may aggravate the problem”. In this context, our contribution attempts to feed the literature on the role of safe assets in the modern economy and its relation to monetary policy, especially with unconventional measures. In order to quantify the effect of unconventional monetary policy on the repledging chain of collateral, we propose an accounting model, in the spirit of Adrian and Shin (2009), in which all the variables are taken to their mark-to-market values. In our model, the core of the intermediation system is the interbank market, where banks can mutually exchange liquidity according to their needs, in order to re-invest it in profitable assets. However, due to the circularity of this process, even the lubrication of the money market is affected by the performance of banks’ external assets investments. In general, successful (unsuccessful) investments enlarge (shrink) banks’ balance sheet and, as a consequence, the amount of repledgeable assets in the money market raises (decreases), stretching (shrink2 In normal times, the central bank can inject liquidity into the financial system through open market operations swapping a variety of safe collaterals in exchange for cash (Nyborg, 2017). After 2007, central banks launched several unconventional purchase programs, enlarging significantly the size of their balance sheet, willing to accept lower-quality collateral. Cecioni et al. (2011) provides a detailed description of the unconventional operations put in place by the Fed and the ECB. Fawley and Neely (2013) extends the analysis to the operations of the Bank of England and Bank of Japan.

3

ing) the intermediation chain length. According to Singh (2012) this deleveraging process is the sum of two combined effects: a balance sheet shrinkage, due to haircuts and declining assets’ price - that we call price effect - and a reduction in financial system interconnectedness, due to a shorter collateral chain - hereafter chain effect. While the fall of asset prices has been widely investigated as a source of financial distress, in the literature on financial contagion (Fecht, 2004; Cifuentes et al., 2005; Fry-McKibbin et al., 2014), much less attention has been paid to the role of a shortening of the intermediation chain. In his contribution, Singh (2012) argues that this chain component is sizable - especially after the Lehman bust. In our contribution we try to go one step forward by measuring both the price and the chain components, and how both can explain (and affect) the overall variations of money market liquidity. By taking into account not only the market value but also the network implications of deleveraging, we aim to provide insights on the role of unconventional monetary policy - such as QE - can play in sustaining or harming the collateral chain, and thus the whole intermediation’s system.

2

The Model

In the following section, we will describe the main component of the intermediation model.

2.1

Banks

The accounting framework approach allows us to derive the main banks’ variables simply from their balance sheet identity. We define the latter in a very standard and general way: the market value of bank’s i total assets ai is the sum of the market value of i’s total liabilities xi and its equity ei . a i = xi + ei .

(2.1)

On the assets side of their balance sheet, banks own different kinds of assets: r a risky asset yit , whose value is linked to the dynamic of its price prt , a safe s asset yit - similar to a treasury bond - whose price pst is fixed by the monetary authority and an interbank asset, in case a bank lends funds in the money market3 . For the purpose of our analysis, it is convenient to define as external assets yit the sum of risky and safe assets 4 . 3 The fourth type of asset - namely a reserve account at Central Bank - will be introduced when the Central Bank starts a Quantitative Easing program. 4 The adjective ’external’ mirrors the lack of an explicit market mechanism for risky as well as safe assets. Conversely, the only market structure fully implemented is the interbank one.

4

Due to their nature, risky assets can be subject to a haircut h, which is given by

ht =

     0,

if Rt = log

  1    φki

if Rt = log

prt prt−1 prt prt−1

! !

≥0

(2.2)

< 0.

The idea behind Eq.(2.2) is very simple. In periods where the risky asset price is rising - that we might refer to as ’good times’ - the haircut is equal to zero. Conversely, whenever risky asset price moves downward, ht > 0 mirrors the market riskiness increase. The definition of a non-zero value of haircut considers the negative part of the support of the risky assets returns time series (Rt < 0). The observations of this subset, with negative returns, have been ranked in ascending order - ki - then passed to the second branch of equation (2.2). In this way we ensure that the lowest value of returns will have rank equal to 1 and will be associated with the highest haircut according to equation (2.2). In other words, in a (negative) returns-haircut plane, Eq.(2.2) draws approximatively a hyperbola: when the returns approach zero, also the haircut vanishes. This assumption about the functional form of the haircut allow us to mimic its increase when the underlying asset became riskier (see Gottardi et al. 2019 and Baklanova et al. 2019). Finally, we define φ ∈ R>0 as a smoothing parameter. The assets side of Eq.(2.1) can be rewritten as follow ai = (1 − h)yir + yis +

X

xj πji ,

(2.3)

j

where the last item represents bank i’s interbank claims. More precisely, xj is the market value of bank j liabilities5 , of which bank i holds a share equal to πji . As a proxy of how leveraged a bank’s balance sheet is, we use the debt to assets ratio di di = 1 −

ei ai

=1− 

,

(2.4) ei

(1 − ht )yir + yis +

P

j xj πji

.

(2.5)

Finally, solving Eq.(2.1) for liabilities and making use of Eq.(2.5) we can express 5 Since

banks can only borrow in the money market, the only type of liabilities allowed are the interbank ones. Hereafter, we will refer to ’interbank liabilities’ simply as ’liabilities’.

5

banks’ liabilities in terms of their assets and leverage: xi = a i − ei ,

(2.6)

a i − ei

(2.7)

xi ai xi ai

=

ai

,

= di ,

(2.8)

xi = di ai ,   X xi = di (1 − h)yir + yis + xj πji .

(2.9) (2.10)

j

Until now we have essentially rearranged the balance sheet identity in different ways, but to solve the model and to avoid recursiveness issues, we need to clarify the order of the events. Since two out of three assets markets do not provide an explicit bargaining mechanism (as for the liabilities side), we assume that - initially - banks decide how much to lend or borrow in the money market according to their assets dynamic. As time goes by, the upward or downward trends of external assets will be amplified by banks’ leverage. Through this channel - clearly expressed by Eq.(2.10) - the liability side (i.e. interbank borrowing) enlarges and shrinks accordingly. Another interesting interpretation of Eq.(2.10) is that banks’ total assets are constantly being pledged as collateral to borrow in the money market and, this way, they determine the amount of liquidity exchanged by intermediaries. This is in line with the definition of Adrian and Shin (2010), where they state that ”the funding liquidity can be understood as the rate of growth of aggregate balance sheets”. In this way, two main factors affect the lubrication of the money market: a) the price dynamics of external assets, b) the kind of assets pledged as collateral, due to their different degrees of riskiness (good vs. bad collateral).

2.2

Money market and collateral chain

˜ whose The Money market can be described by means of a square matrix X, dimension is given by the number of banks, with each entry ˜xij representing the market value of a transaction between two intermediaries i and j.6 Figure 1 provides an example. We assume that rows represent interbank liabilities and columns are interbank assets. Therefore, x ˜ ij denotes bank i’s obligation towards 6 Few words to clarify the matrix notation we use. Bold lower case letters denote vectors, while bold upper case stands for matrices. A generic vector x is always a row vector and its transpose x0 is a column vector. We use a slightly different notation when we describe the rows and columns of a matrix. xi∙ represents the i-th row of matrix X and we treat it as a row vector. Similarly, the i-th column of X - x∙i - is always a column vector. ι is a row vector of 1s, whose length is always conformable to the element it pre(post)multiplies.

6

j, as well as bank j’s claim on i. The i-th row vector, x ˜i∙ is the amount of bank 0 i’s debt held by the other banks, and its sum - x ˜i∙ ι - corresponds to bank i’s total liabilities. Conversely, the i-th column vector, x ˜∙i , captures how much i holds of other banks’ liabilities. Total interbank assets are the sum of i’s claims on all counterparties.

bank 1 bank 2

˜ = X

∙∙∙ bank n interbank assets external assets



bank 1

bank 2

∙∙∙

x ˜12 0 .. .

∙∙∙ ∙∙∙ .. .

x ˜n1

x ˜n2

x ˜ ∙1

x ˜∙2

∙∙∙

0 x ˜  21  ..  . y1

y2

bank n

∙∙∙ ∙∙∙

x ˜1n x ˜2n .. . 0 x ˜∙n

   

liabilities

equity

x ˜1∙

e1

x ˜2∙

e2

.. .

.. .

x ˜n∙

en

yn

Figure 1: The interlocking claims and obligations of the money market matrix. In principle, claims and obligations are mutually independent - if i owes to ˜ is not necessarily symmetric. j not necessarily j owes to i - thus the matrix X Furthermore, the empirical literature on interbank markets (in ’t Veld and van Lelyveld, 2014; Craig and von Peter, 2014; Fricke and Lux, 2015; Langfield ˜ is characterized by a low density, i.e. the number et al., 2014) suggests that X of connections roughly ranges between the 5 − 15% of all the possible linkages among money market participants. The interlocking structure of money market claims and debts can be easily appreciated by rewriting Eq.(2.10) in matrix form 7 of the variables introduced in section 2.1. We aggregate external assets in vector y y = (1 − h)yr + ys ,

(2.11)

which is simply the sum of risky assets (discounted by the haircut) and safe assets. Let Δ be a diagonal matrix whose typical non-zero entry, di is the debt ratio of the i -th bank, and Π a square matrix whose generic entry πij expresses the share of i ’s liabilities held by j. Now Eq.(2.10) can be rewritten as x = yΔ + xΠΔ,

(2.12)

from which it is easy to observe the recursive nature of debt in the money market (Shin, 2009). The matrix ΠΔ is a very interesting object, which captures the circular flow of money market positions. Indeed - with a little bit of matrix algebra - it is easy to show that, for a given vector x of liabilities, xΠΔ returns 7 To

make the notation less demanding, we remove the time subscript for all the variables.

7

the vector of interbank assets. The i -th element of this vector represents the bank’s i interbank assets as a function of the share held by i of all the other banks’ liabilities. In other words, the matrix ΠΔ converts banks liabilities into assets, taking into account the nested structure of bilateral exposures, under the assumption that all claims/obligations are contained within the money market. 

0   d1 π21 ΠΔ =   ..  . d1 πn1

d2 π1,2 0 .. . d2 πn2

 dn π1n  dn π2n  ..   . 

∙∙∙ ∙∙∙ .. . ∙∙∙

(2.13)

0

In order to solve Eq.(2.12) for x, we need that the sum of any row of ΠΔ is strictly smaller than 1. Under the assumption that interbank debts are fully owned by market participants, it is equivalent to saying that all the rows of Π sum up to 1. From Eq.(2.5) it is easy to verify that di always lies in the range P P (0, 1), which ensures that j dj πij < j πij . This condition guarantees that P∞ −1 the infinite Neumann series n=0 (ΠΔ)n converges to (I − ΠΔ) enabling us to write

−1

x = yΔ (I − ΠΔ)   2 3 = yΔ I + ΠΔ + (ΠΔ) + (ΠΔ) + ∙ ∙ ∙ .

(2.14) (2.15)

Eqs.(2.14,2.15) are very close to a Leontief inverse, whose mathematical properties are largely known as well as its applications in the economic literature (Aldasoro and Alves, 2018; Miller and Blair, 2009, for an extensive treatise). At the same time, Eqs.(2.14,2.15) offer a very interesting interpretation in our framework. By defining the matrix M as M = Δ (I − ΠΔ)

−1

,

(2.16)

we can interpret it as a linear operator, which converts external assets into liabilities, by means of the connections established in the money market. More precisely, the amount of interbank funds banks can raise, x, depends on the amount of assets they can collateralize, y, and on the way in which such guarantees flow within the interbank network. Eq.(2.15) is particularly suitable to capture this salient point. For a given structure of network linkages among banks - ΠΔ -, collateralized assets are pledged in successive rounds of rehypothecation by the intermediaries who receive such guarantees. This feature is mathematically expressed by the powers of the matrix ΠΔ. To better grasp this point, let us recast the problem in terms of graph theory. The matrix ΠΔ can

8

be interpreted as the weighted adjacency matrix of the money market directed network (or digraph). We assume the direction of connection always goes from the collateral dealer to the cash provider. From the properties of random walks on graphs, the n-th power of ΠΔ returns the relative8 value of collateral after n rounds of repledging. In this fashion, the recursive chain of intermediation allows cash providers to repledge the assets received by collateral dealers, as long as the marginal contribution of the n-th (and higher) round converges to zero. As a consequence, the highest non-zero power of ΠΔ defines the length of the private intermediation chain, which will be a key variable which we are going to use to measure the effectiveness of different kinds of Quantitative Easing. The (inverse) leverage matrix Δ is the real driving force of the rehypothecation mechanism, and its role is twofold. On one side, it is a collateral multiplier which governs the speed at which external assets are converted into liabilities. On the other, it spreads the leveraging/deleveraging decisions of banks throughout the money market network. When external asset prices are falling (rising) banks’ balance sheets shrink (enlarge) accordingly. This is a standard price effect which directly affects the intermediaries’ balance sheets. However, a second-round effect acts at the network level, i.e. the reduced (increased) amount of assets to collateralized - due to the price drop (rise) - will force banks to reduce (increase) their connections because there are less (more) guarantees to pledge in transactions with cash providers. This is what Singh (2012) refers to as ’’The (Other) Deleveraging‘‘. The idea is that deleveraging is the sum of two components: a shrinking balance sheet as a consequence of price decline and/or haircut increase (price effect ) and shrinking of linkages due to a shortening of the repledging chain (chain effect ). Algebraically, the balance sheets variation Δxt breaks down into

x(h) − x(h0 ) = y(h)M(h) − y(h0 )M(h0 )

= y(h)M(h) − y(h0 )M(h) + y(h0 )M(h) − y(h0 )M(h0 )

(2.17)

= (y(h) − y(h0 )) M(h) + y(h0 ) (M(h) − M(h0 )), | {z } | {z } Price effect

Chain effect

where both price and chain effects can be further disaggregated according to assets types: (y(h) − y(h0 )) M(h) = M(h) (yr (h) − yr (h0 )) + M(h) (ys (h) − ys (h0 )) .

(2.18)

8 The

absolute value of collateral after n steps of repledging is given by y(ΠΔ)n

9

Rearranging terms in Equation (2.18), we obtain y(h0 ) (M(h) − M(h0 )) = (M(h0 ) − M(h)) yr (h) + (M(h0 ) − M(h)) ys (h).

(2.19)

Equations (2.17) accounts for banks’ balance sheet growth as a function of price and chain effects, given a certain price and haircut dynamics. In the following sections, we extend this intuition in three ways. Firstly, we show that not only price but also the chain effect can be measured. Secondly, by differentiating between safe and risky assets, we study the impact of collateral’s quality on the private intermediation chain. Lastly, we can use this conceptual framework to assess the effectiveness and the ability of a QE program to lengthen and sustain the private intermediation chain, depending on the different purchasing strategies the central bank wants to undertake.

3

The baseline scenario

Instead of using simulated data as exogenous driver of the dynamics, we feed our model with three real observable variables: we use the Standard & Poors index as a proxy for the risky assets (SP500), the effective federal funds rate (FEDFUNDS) for the short-term interest rate and the inverse of 10 years interest rate on US Treasury bond (GS10) to describe the safe asset price dynamics (see Figure 3).9 This approach has at least two advantages. First, the model dynamics are driven deterministically by real-time series rather than simulated ones, avoiding time-consuming Monte Carlo simulations. Second, it allows to fully capture the model responses to the true QE implemented by the Fed. Across different scenarios, just a few parameters need to be fixed before running the model. Empirical evidence suggests a scale-free and sparse topology for the money market network (see Bech and Atalay, 2010; Boss et al., 2004). 10 We initialize our network structure accordingly, setting graph density to 0.1. The initial configuration of banks’ external assets is assumed to follow a Zipf law, as empirically found by Janicki and Prescott (2006). We set the initial endowment of banks’ safe assets equals to 30% of total external assets according to Gorton et al. (2012). Moreover, we assume that the maximum size of CB assets purchasing, during a QE program, is about 30% of targeted assets. 11 9 All

data are taken from Fred database. a robustness check, we have run experiments also with Erdos Renyi random graphs. The main results of the model are confirmed (see the Appendix, Figure 9 and 10). 11 This value is in line with the maximum share of an asset purchased by the Fed (% 26) with respect to the total amount of assets holds by private depository institutions obtained dividing Table L.109 (FL714090005) and L.110 (FL704090005) of the flow of funds of the Fed. 10 As

10

3.1

Impulse response functions to QE shocks

Before simulating our model, we focus our attention on properly evaluating the effects on asset prices of different QE programs. 12 We build a small-scale SVAR model using the following variables at monthly frequency: industrial production as a proxy for the GDP, data on the Federal Reserve’s balance sheet as a measure of unconventional monetary policy and asset price indexes for both risky and safe assets. Differently from previous contributions, we disentangle the effect of mortgages and asset back securities purchase, a proxy of risky QE, from the effect of long term treasury purchase, a proxy of safe QE. 13 Accordingly to the previous section, we use the Standard & Poors index as a proxy for risky assets price and the inverse of 10 years interest rate on US treasury bond for the safe one. Following Weale and Wieladek (2016) and Balatti et al. (2016), we use a recursive Cholesky identification scheme with the following order: industrial production, unconventional monetary policy, and asset prices as the fastest adjusting variable. We estimate this model twice for both the risky and the safe QE. Information criteria suggest an SVAR lags specification of order two. Figure 2 reports the impulse response functions of both risky and safe asset prices to a QE shock. While a QE shock has a significant impact on the risky asset prices, it has a negligible impact on the dynamic of the safe asset prices. In what follows, we use this empirical evidence to properly calibrate the response of risky asset price to an increase in the purchase of mortgage and asset-backed securities in the simulation of our model.

3.2

Simulation results

We start by investigating the behavior of our model assuming that no unconventional monetary policy intervention takes place. We refer to this experiment as our baseline scenario (see Figures 3 and 4 ). We report in Table 1 the parameters setup which is common to each simulation experiment. 14 Our model suggests that, after the 2007/2008 Great Recession, risky asset prices collapsed, forcing the monetary authority to cut drastically the policy rate, thereby triggering ”flight-to-quality”. In this context, financial interme12 Many recent contributions investigate the effects of QE on financial markets, such as Bjørnland and Leitemo (2009), Joyce et al. (2011), Bridges and Thomas (2012), Fratzscher et al. (2018), Hesse et al. (2018), and Mallick et al. (2017) among the others. 13 The full dataset of FED’s balance sheet can be found at https://www.clevelandfed.org/our-research/indicators-and-data/credit-easing.aspx 14 In the Appendix, we provide additional robustness exercise with respect to the haircut’s smoothing parameter (φ), graph density (dG ). See Figure 9 and 10.

11

Figure 2: Impulse response functions to a QE shock: risky (l) and safe(r) QE risky shock− > Standard & Poor index

QE safty shock− > 10Y Tresury bond price

Note: the solid line is the impulse response function calculated at the mean, the dashed line the impulse response function calculated at the median, the grey shadow area the 90 % confidence interval.

Simulation B σ φ dG

parameters 100 0.07 10 0.1

Table 1: Set of simulation parameters: number of banks (B), GBM spread (σ), haircut’s smoothing parameter (φ), graph density (dG ). diaries reduce the total amount of risky assets in their balance sheet while enhancing the exposition towards safe assets. As a consequence, safe asset prices increased. The contraction of risky asset price has a direct impact on the size of the banks’ external assets and hence on available collateral. Figure 4 shows that the value of collateral shrinks by about 50 %, slowly returning to the pre-crisis level only after 2011. Although the increase in safe asset prices partially offsets the contraction in banks’ balance sheet size, such an increase is not enough to fully dampen the contraction of risky asset values and the overall size of external assets. Moreover, in line with Equation 2.2, negative risky asset returns generate a spike of haircuts further reducing collateralizable assets. Lastly, the repledging chain of collateral rehypothecation dramatically shortens in the time span 2007-2012 confirming the crucial role played by the ”other deleveraging”.

12

1.0 0.6

Price P(t)

1.4

Figure 3: Baseline scenario: S&P index, policy rate and safe asset price

2005

2007

2010

2012

2015

2002

2005

2007

2010

2012

2015

2002

2005

2007

2010

2012

2015

rt Psafe t

0.985

1.000

1.015

0.00

0.02

0.04

2002

Note: The Figure shows the three real data time series used to simulate the model. The upper panel is the S&P index normalized for the value of July 2002. Furthermore the sample mean is substracted in order to obtain the series in the simulation. The same methodology is also applied for safe asset price. The middle panel reports the Fed policy rate, the lower panel shows the behavior of safe asset price obtained using the inverse of 10 years interest rate on US Treasury bond.

13

Figure 4: Simulation results: baseline scenario Collateral value, Δ%

-0.5

0.0

ΔtCollateral value

0.06 0.04 0.02 0.00 2002

2005

2007

2010

2012

2015

2002

2005

2005

2010

2010

2012

2015

15 14 13 12

Repledging chain length

10

11

Safe Assets

39000 39200 39400 39600 39800 40000 40200

6e+05 5e+05

Risky Assets

4e+05 3e+05 risky

2007

Repledging chain

7e+05

External Assets

2e+05

Haircut

0.08

0.5

0.10

Haircut, %

2002

2015

2005

2007

2010

2012

2015

safe

Note: The Figure shows the behavior of haircut in percentage (upper left panel), the percentage change of the value of the whole collateral (upper right panel), the absolute value of risky external assets (black line) and the absolute value of safe external assets (red line, lower left panel), and the length of the repledging chain of collateral (lower right panel).

14

Figure 5: Baseline scenario: price and repledging chain effect on the banking system aggregate liabilities 1.00

Δt Aggregate liabilities

0.75

Δt chain

0.50

Δt price

0.25

0.00 2003-01-01

2005-01-01

2007-01-01

2009-01-01 time

2011-01-01

2013-01-01

2015-01-01

Note: The Figure reports the contribution of the price (blue bars) and of the length of the repledging chain variation (red bars) on the dynamics of aggregate liabilities.

Figure 5 decomposes aggregate liabilities into the contribution of price and repledging chain length variations according to the dynamic describes by eq 2.17-2.19. In line with Singh (2012), the role of the repledging chain predominates before the great recession, accounting on average for 75% of aggregate banks’ balance sheet variation. During the 2007/2008 financial crisis, the interconnection among banks drastically reduced due to the increase of counterparty risk.15 At this point, the Fed’s supplementary monetary stimulus, taking on part of the market riskiness, offsets the shrinkage of the rehypothecation chain, sustaining the balance sheet variation by means of the asset price effect. In the post-Lehman world, these two effects appear to be more balanced, with a predominance of the chain effect. 15 The importance of financial system interconnections is investigated by Kapadia et al. (2012) and Schwaab et al. (2011) whereas Dungey et al. (2018) extends the analysis to the role of connections among financial intermediaries and nonfinancial firms.

15

4

Policy experiment

We modify the original set-up to perform two unconventional monetary policy experiments. QE is implemented by the monetary authority by buying external assets from banks in exchange for reserves. Banks then decide how to re-invest these additional funds looking at money market riskiness: if the haircut on collateral is different from zero, banks hoard liquidity in the form of excess of reserves at the CB. Otherwise, they allocate the excess of reserves in the interbank market. In the first scenario, the monetary authority only purchases risky assets in order to expand the liquidity available in the interbank market. We compare the outcome with a second scenario in which the central bank targets only safe assets. Technically, such analysis presents a difficulty, as, the real-time series used to characterize the dynamics of the model are affected by several different QE programs implemented by the Fed. Under these circumstances is impossible to perform a ceteris paribus experiment. In order to overcome such problem, we implement the following strategy for the risky and safe QE, respectively: once the risky QE has started, we simulate the risky asset price dynamic using a a geometric Brownian motion with a starting value equal to the last observable data before QE implementation; whereas under safe QE we approximate the safe asset price dynamic using the inverse of the interest rate implied by a Taylor rule without Zero Lower Bound policy. Moreover, we also assume, based on the insights from our previous impulse response function analysis, that the central bank can only affect the deterministic component of the risky asset price whereas QE has no effect on the deterministic component of the price of safe assets (see left panel of Figure 2). The risky asset price dynamic is described by the following Geometric Brownian motion:    2 μt − σ2 t+σWt r pt = p0 e , (4.1) where p0 is the last observable risky asset price before QE implementation, σ is the standard deviation of the series of returns and Wt is a stochastic Wiener process with zero mean and σ 2 standard deviation. In our exercise, μt evolves according to the estimated impulse response function with respect to risky QE found in Section 3.1.

4.1

Policy experiment results: Risky vs. Safe QE

In this section, we compare the outcome of the two different QE scenarios. As described in details in section 2.2, Equation 2.17 is the key element that linked together with the dynamic of external assets, both safe and risky (y and y r ,

16

respectively), the haircut (h) and the repledging matrix (M ). Figure 6 shows the effect of unconventional monetary policy on risky asset prices (left column) and the behavior of haircut (right column) under risky (upper panels of Figure 6) and safe QE (lower panels of Figure 6), respectively. Our starting point is the assumption that a fall in asset prices causes a drop in external asset value and, as a consequence, an increase in the haircut, as described by Equation 2.2, due to the increased perception of default by the counterpart (Baklanova et al., 2019). Dashed blue lines represent the time interval in which, in our simulation, the QE policy is active. The main policy implications of the paper are drawn taken into consideration what happens in the time interval in which the QE is actives. In our simulation exercise, the risky QE is much more effective than the safe version in dampening the negative effects of a collapse of asset prices stabilizing it at an higher level (a value close to 0.75 under risky QE, on the contrary, 0.6 under safe QE, see the left column of Figure 6). Moreover, under the risky QE, the haircut is stabilized close to zero (see right column of Figure 6) whereas, in the safe QE scenario, it jumps on impact to a level close to 10 % and it remains higher in the subsequent period of active safe QE. In this context, haircut stabilization can be interpreted as a signal that counterparty risk is kept under control fostering the exchange of liquidity through the interbank market network.

17

Figure 6: Risky asset price and haircut dynamics Haircut

0.06

Haircut

0.00

0.6

0.02

0.04

0.9 0.8 0.7

Price P(t)

1.0

0.08

1.1

0.10

Risky asset price

2002

2005

2007

2010

2012

2015

2002

2005

2007

2010

2012

2015

2005

2007

2010

2012

2015

0.06

Haircut

0.04

0.9

0.02

0.8

0.00

0.7

Price P(t)

1.0

0.08

1.1

0.10

Safe QE

2002

2005

2007

2010

2012

2015

2002

Risky QE Note: The Figure shows the dynamic of risky asset price (left column) and haircut (right column) under safe (upper panel) and risky QE (lower panel). Blue dashed bars indicate the time span in which the QE is active in the simulation.

18

Figure 7: External assets and repledging chain dynamics

2010

13 12

Repledging chain length

11 10

Safe Assets

7e+05 6e+05 5e+05

Risky Assets

4e+05 3e+05 2e+05

2005 risky

14

Repledging chain 26000 28000 30000 32000 34000 36000 38000 40000

External assets

2002

2015

2005

2007

2010

2012

2015

2005

2007

2010

2012

2015

safe

2010

14 13 12

Repledging chain length

10

11

38500 37500 37000 2005

risky

Safe Assets

38000

5e+05 4e+05 3e+05

Risky Assets

6e+05

39000

7e+05

39500

Safe QE

2002

2015

safe

Risky QE Note: The Figure shows the dynamic of the value of external asset (left column), both safe (red line) and risky asset (black line), and the repledging chain of collateral (right column) under safe (upper panel) and risky QE (lower panel). Blue dashed bars indicate the time span in which the QE is active in the simulation.

19

5000 4000 3000 2000 0

50000

1000

CB Reserves

200000 100000

Collateral Value

300000

Figure 8: Aggregate Central Bank reserves and Collateral value in case of Safe (a) and Risky (b) QE.

2005 Collateral value

2010

2015

CB reserves

40000 20000 10000

CB Reserves

30000

100000 150000 200000 250000 300000

0

50000

Collateral Value

(a) Safe QE

2005 Collateral value

2010

2015

CB reserves

(b) Risky QE Note: The Figure shows the dynamic of the value of central bank reserves and collateral value under safe (upper panel) and risky QE (lower panel). Blue dashed bars indicate the time span in which the QE is active in the simulation.

The risky QE plays a crucial role in the haircut stabilization through two channels: it dampens the fall of risky assets market value (see Figure 7, left column, black line) and it does not withdraw ”good” safe collateral from the money market (see Figure 7, left column, red line). For the sake of clarity, it

20

is useful to refer to Equation 2.5 to clarify the mechanism of transmission of unconventional monetary policy. The risky QE sustains the value of y r and kept unchanged the value of y s . Moreover, since the risky asset price is stabilized by the effect of the QE, haircut, that depends, negatively, by returns (see Equation (2.2), is maintained close to zero as well. The final combined effect stabilizes the value of banks’ leverage (di ). Since higher leverage allow banks to do more repledging, according to Equation (2.16) where Δ is the matrix notation of di , rehypothecation under risky QE (see Figure 7, right bottom panel) is stabilized in a period of distress. On the contrary, safe QE, withdrawing good collateral during the drop of the bad one, exacerbates the severity of the situation (Caballero et al., 2017). On the other hand, the reaction of the banking system is to hoard reserves at the CB (see Figure 8a, red line). Differently, the risky QE is able to substantially counteract this mechanism while the QE is ongoing (see Figure 8b, red line).

5

Conclusion

The contribution explores the impact of several unconventional monetary policy scenarios on the length of the repledging chain of collateral. Our model suggests that the impact of the ”other deleveraging” is sizable and it is an important factor driving the money market dynamics. Our results suggest that, during a large downturn, a monetary authority that purchases highly risky assets produced the best possible outcome in terms of asset price and repledging chain stabilization. Moreover, such a policy allows the ”good” collateral to remain in the banking system stabilizing the private intermediation chain and the lubrication of the interbank market. All in all, our proposal suggests that, during a large crisis, central banks should move from a ”lender of last resort” to a ”buyer of last resort” claiming risks that no other players on the market are willing to take on. In this sense, our contribution supports programs such as the purchases of agency debt and agency MBS implemented by the Fed in the aftermath of the great financial crisis. In fact, potentially, great conflicts might arise between boosting the economy through monetary injection and avoiding at the same time an increase of financial fragility. Secondly, another open issue can be related to exit strategy implementation. Our model suggests that a slow unwind from the QE may be preferable. However, further investigations in the field are needed.

21

References Adrian, T., Shin, H.S., 2009. Collateral shortage and debt capacity. Princeton University (unpublished note) . Adrian, T., Shin, H.S., 2010. Liquidity and leverage. Journal of financial intermediation 19, 418–437. Aldasoro, I., Alves, I., 2018. Multiplex interbank networks and systemic importance: An application to European data. Journal of Financial Stability 35, 17–37. Antinolfi, G., Carapella, F., Kahn, C., Martin, A., Mills, D., Nosal, E., 2015. Repos, Fire Sales, and Bankruptcy Policy. Review of Economic Dynamics 18, 21–31. Baklanova, V., Caglio, C., Cipriani, M., Copeland, A., 2019. The use of collateral in bilateral repurchase and securities lending agreements. Review of Economic Dynamics 33, 228 – 249. Balatti, M., Brooks, C., Clements, M.P., Kappou, K., 2016. Did Quantitative Easing Only Inflate Stock Prices? Macroeconomic Evidence from the US and UK. SSRN Working Papers. Bech, M., Atalay, E., 2010. The topology of the federal funds market. Physica A: Statistical Mechanics and its Applications 389, 5223–5246. Bjørnland, H.C., Leitemo, K., 2009. Identifying the interdependence between US monetary policy and the stock market. Journal of Monetary Economics 56, 275–282. Boss, M., Elsinger, H., Summer, M., 4, S.T., 2004. Network topology of the interbank market. Quantitative Finance 4, 677–684. Bridges, J., Thomas, R., 2012. The impact of QE on the UK economy – some supportive monetarist arithmetic. Bank of England working papers 442. Bank of England. Caballero, R.J., Farhi, E., Gourinchas, P.O., 2017. The safe assets shortage conundrum. Journal of Economic Perspectives 31, 29–46. Cecioni, M., Ferrero, G., Secchi, A., 2011. Unconventional Monetary Policy in Theory and in Practice. Questioni di Economia e Finanza (Occasional Papers) 102. Bank of Italy, Economic Research and International Relations Area.

22

Cifuentes, R., Ferrucci, G., Shin, H.S., 2005. Liquidity risk and contagion. Journal of the European Economic Association 3, 556–566. Craig, B., von Peter, G., 2014. Interbank tiering and money center banks. Journal of Financial Intermediation 23, 322 – 347. Dungey, M., Luciani, M., Veredas, D., 2018. Systemic risk in the us: Interconnectedness as a circuit breaker. Economic Modelling 71, 305 – 315. Fawley, B.W., Neely, C.J., 2013. Four stories of quantitative easing. Review , 51–88. Fecht, F., 2004. On the stability of different financial systems. Journal of the European Economic Association 2, 969–1014. Fratzscher, M., Duca, M.L., Straub, R., 2018. On the international spillovers of us quantitative easing. The Economic Journal 128, 330–377. Fricke, D., Lux, T., 2015. Core–periphery structure in the overnight money market: Evidence from the e-mid trading platform. Computational Economics 45, 359–395. Fry-McKibbin, R., Martin, V.L., Tang, C., 2014. Financial contagion and asset pricing. Journal of Banking & Finance 47, 296–308. Fuhrer, L.M., Guggenheim, B., Schumacher, S., 2016. Re-Use of Collateral in the Repo Market. Journal of Money, Credit and Banking 48, 1169–1193. Gorton, G., 2017. The history and economics of safe assets. Annual Review of Economics 9, 547–586. Gorton, G., Lewellen, S., Metrick, A., 2012. The Safe-Asset Share. American Economic Review 102, 101–106. Gorton, G., Metrick, A., 2012a. Getting Up to Speed on the Financial Crisis: A One-Weekend-Reader’s Guide. Journal of Economic Literature 50, 128–150. Gorton, G., Metrick, A., 2012b. Securitized banking and the run on repo. Journal of Financial Economics 104, 425–451. Gottardi, P., Maurin, V., Monnet, C., 2019. A theory of repurchase agreements, collateral re-use, and repo intermediation. Review of Economic Dynamics 33, 30 – 56. Hesse, H., Hofmann, B., Weber, J.M., 2018. The macroeconomic effects of asset purchases revisited. Journal of Macroeconomics 58, 115–138.

23

Janicki, H., Prescott, E., 2006. Changes in the size distribution of u.s. banks: 1960-2005. Economic Quarterly , 291–316. Joyce, M.A.S., Lasaosa, A., Stevens, I., Tong, M., 2011. The Financial Market Impact of Quantitative Easing in the United Kingdom. International Journal of Central Banking 7, 113–161. Kapadia, S., Drehmann, M., Elliott, J., Sterne, G., 2012. Liquidity Risk, Cash Flow Constraints, and Systemic Feedbacks, in: Quantifying Systemic Risk. National Bureau of Economic Research, Inc. NBER Chapters, pp. 29–61. Langfield, S., Liu, Z., Ota, T., 2014. Mapping the uk interbank system. Journal of Banking & Finance 45, 288 – 303. Mallick, S.K., Mohanty, M., Zampolli, F., 2017. Market volatility, monetary policy and the term premium. BIS Working Papers 606. Bank for International Settlements. Miller, R.E., Blair, P.D., 2009. Input-output analysis: foundations and extensions. Cambridge University Press. Nyborg, K.G., 2017. Central bank collateral frameworks. Journal of Banking & Finance 76, 198–214. Schwaab, B., Koopman, S.J., Lucas, A., 2011. Systemic risk diagnostics: coincident indicators and early warning signals. Working Paper Series 1327. European Central Bank. Shin, H.S., 2009. Securitisation and financial stability. The Economic Journal 119, 309–332. Shleifer, A., Vishny, R., 2011. Fire Sales in Finance and Macroeconomics. Journal of Economic Perspectives 25, 29–48. Singh, M., 2012. The (Other) Deleveraging. IMF Working Papers 12/179. International Monetary Fund. Singh, M., Stella, P., 2012. Money and Collateral. IMF Working Papers 12/95. International Monetary Fund. in ’t Veld, D., van Lelyveld, I., 2014. Finding the core: Network structure in interbank markets. Journal of Banking & Finance 49, 27 – 40. Weale, M., Wieladek, T., 2016. What are the macroeconomic effects of asset purchases? Journal of Monetary Economics 79, 81 – 93.

24

Appendix: sensitivity analysis Figure 9: Sensitivity analysis: repledging chain and haircut

2002

2005

2007

2010

2012

12 8

10

Repldeging chain

12 10

dG0.2 dG0.3 dG0.4 dG0.5 dG0.9

8

Repledging chain

14

Repledging chain, network topology

14

Repledging chain, graph density

Scale-free Erdos

2015

2002

2012

2015

0.10 0.06

0.08

Scale-free Erdos

0.00

0.02

0.05

0.10

Haircut

0.15

2010

Haircut, network topology

φ5 φ7.5 φ10 φ12.5 φ15

0.00

Haircut

2007

0.04

0.20

Haircut, haircut’s smoothing parameter

2005

2002

2005

2007

2010

2012

2015

2002

2005

2007

2010

2012

Note: The Figure shows the dynamic of the value of the repledging chain (upper panles) and haircut (bottom panels). The repledging chain dynamic is tested under different graph density (left upper panel) and different initial network topology (right upper panel). The behavior of haircut is tested under different combination of the smoothing parameter (φ in Equation 2.2, bottom left panel) and different network topology (bottom right panle).

25

2015

Figure 10: Sensitivity analysis: risky and safe asset dynamics Network topology

5e+05

Risky Assets 2002

3e+05

4e+05

4e+05

φ5 φ7.5 φ10 φ12.5 φ15

Scale-free Erdos

2e+05

2e+05

Risky Assets

6e+05

6e+05

7e+05

8e+05

Graph density

2005

2007

2010

2012

2015

2002

2005

2007

2010

2012

2015

40200 2002

2005

2007

2010

2012

39800 39400

Safe Assets

39800 39400

Scale-free Erdos

39000

φ5 φ7.5 φ10 φ12.5 φ15

39000

Safe Assets

40200

Risky assets

2015

2002

2005

2007

2010

2012

Safe assets Note: The Figure shows the dynamic of the value of the risky (upper panles) and safe assets (bottom panels). The left column shows the evolution of asset value under different graph density while the right columnunder different initial network topology.

26

2015

Highlights • We build a mark-to-market interbank model with collateral rehypothecation. • Sizable effects of deleveraging due to the collapse of collateral rehypothecation. • Unconventional monetary policy can purchase both risky and safe assets. • Purchasing only safe assets is highly ineffective in restoring rehypothecation. • Differently, risky asset purchase sustained the interbank market rehypothecation.

1