An Agent-based Model for Financial Vulnerability

An Agent-based Model for Financial Vulnerability∗

Richard Bookstaber†

Mark Paddrik‡

Brian Tivnan§

This version: March 10, 2017

Accepted for publication atJournal of Economic Interaction and Coordination

Abstract

This study addresses a critical regulatory shortfall by developing a platform to extend stresstesting from a microprudential approach to a dynamic, macroprudential approach. This paperdescribes the ensuing agent-based model for analyzing the vulnerability of the financial systemto asset- and funding-based fire sales. The model captures the dynamic interactions of agentsin the financial system extending from the suppliers of funding through the intermediation andtransformation functions of the bank/dealers to the financial institutions that use the funds totrade in the asset markets. The model replicates the key finding that it is the reaction to initiallosses, rather than the losses themselves, that determine the extent of a crisis. By building on adetailed mapping of the transformations and dynamics of the financial system, the agent-basedmodel provides an avenue toward risk management that can illuminate the pathways for thepropagation of key crisis dynamics such as fire sales and funding runs.

Keywords: Agent-based models, financial intermediation, financial networks, contagion, macro-prudential, stress testing.

JEL Classification Numbers: G01, G14

∗We wish to thank additional members of the MITRE team: Zoe Henscheid, David Slater, Matt Koehler, TonyBigbee, Matt McMahon and Christine Harvey. We also would like to thank Nathan Palmer for his work on theconceptual model. Finally we would like to thank Charlie Brummitt, Jill Cetina, Gregory Feldberg, Paul Glasserman,Benjamin Kay, Blake LeBaron, Eric Schaanning, Julie Vorman, Larry Wall, and participants of MIT’s Consortiumfor Systemic Risk Analysis 2013, the INET Conference Toronto 2014, and Atlanta Federal Reserve’s Conference onNonbank Financial Firms and Financial Stability for their valuable comments.†Head of Risk Management and Managing Director, Office of the Chief Investment Officer, Regents of the Univer-

sity of California, email: [email protected]. This paper was produced while Richard Bookstaber was employedby the Office of Financial Research.‡Office of Financial Research, U.S. Department of the Treasury, email: [email protected].§MITRE Corporation, email: [email protected].

1 Introduction

Stress testing gained momentum among financial regulators after the 2007-09 financial crisis

because risk measures based on historical relationships failed to provide adequate insight. Although

stress testing provides a better picture of a firm’s exposure in the face of proposed scenarios, the tests

remain microprudential exercises that do not examine the impact of firms on one another beyond

the initial stress event. Without incorporating the dynamics, feedback, and related complexities of

financial intermediations, it is difficult to understand the impact that stress scenarios will have on

lending, borrowing, and asset markets, and impossible to assess the stability risk to the aggregate

financial system.

Agent-based models (ABMs) are well suited for incorporating these transformations to explore

crisis dynamics. ABMs follow the agents period by period, assessing their reaction to events and

updating the macro system variables compiled from micro-level agent decisions. This paper develops

an ABM to provide a macroprudential view of the transformations and dynamic interactions of

agents in the financial system. The model extends from the suppliers of funding, such as money

market funds, through the channels of bank/dealers to the financial institutions that use the funds,

and the collateral that moves in the opposite direction. The ABM integrates various channels for

crisis dynamics from specific failures in the transformations provided by the intermediaries.

This paper builds on the literature about financial shocks and their impact on collateralization.

We examine the impact of bank/dealers in financing and collateralizing, as done by Cifuentes et al.

(2005), and additionally consider the bank/dealers’ multi-faceted roles as prime brokers in trading

and market making, in capital-raising, and as a counterparty. We integrate the funding side of

the market by incorporating money market funds and pension funds (Copeland et al. (2010)) and

hedge funds, which are major borrowers of cash and sources of leverage (Thurner et al. (2012)).

Our contribution integrates these related literatures into a multi-agent framework of the major

participants typically seen in U.S. funding markets.

Our model captures several interconnected, network-like relationships that can cause reverbera-

tions across a stressed financial system. The integration of market asset-price correlations through

overlapping portfolios with funding networks provides the mechanisms for feedback cycles to occur.

This is integral to explaining how the credit crises in 2008 unfolded for several financial institutions

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(Brunnermeier and Pedersen (2009); Tasca and Battiston (2016)). The model’s more detailed and

integrated representation of the financial system depicts the various paths of fire sale cascades and

contagion, including those that occur from leverage and funding-based fire sales, and from credit

and redemption stress.

Through the integration and use of ABMs, this paper moves various facets of the analysis

of cascades and contagion closer to implementation. An ABM can provide the macroprudential

community, regulators, and financial institution risk managers, with a flexible tool for enhanced

stress and scenario analysis to discover vulnerabilities and forecast the potential implications of

financial tail events. To demonstrate the value of the model, we test the effectiveness of critical

regulatory risk measures during periods of market dislocation and crisis. We examine the ability of

these risk measures to capture the propagation of asset and funding risks during systemic shocks

such as sudden price declines, funding restrictions, erosions of credit, or investor redemptions.

The remainder of the paper is organized as follows: Section 2 reviews the role of market par-

ticipants in the dynamics of fire sales, and the function of the asset, funding, and credit channels.

Section 3 presents an ABM to address these dynamics. Section 4 demonstrates the model’s re-

sponse to market shocks, and includes tests of model validation and robustness. Section 5 provides

additional details of the impact that leverage, liquidity and crowding play in market dynamics.

Section 6 presents the performance of regulatory risk measures within the ABM during periods of

shocks and their subsequent dynamics. The paper concludes with a summary in Section 7.

2 Literature Review

A summary of the prevailing literature relevant to our study begins with an overview of current

approaches to stress testing and their limitations. We follow with a review of the literature of the

funding and asset markets, highlighting the dearth of literature that focuses on the interdependency

of these two markets. We conclude with an overview of agent-based modeling and its potential to

represent the dynamic stressors of actual markets.

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2.1 Stress Testing

Prior to the 2007-09 crisis, financial regulators placed a lower priority on assessing systemwide

characteristics of the financial system (Haldane and May (2011)). Since the crisis, bank supervisors

have honed their financial stability monitoring tools and significantly expanded the use of stress

testing with the largest financial institutions.

Though useful, stress testing such as the Federal Reserve’s Comprehensive Capital Analysis

and Review (CCAR) remains essentially a microprudential exercise. It focuses on the resilience of

individual banks to specific shocks, rather than the broader and more complex macroprudential

question of how stress might be transmitted across firms, financial markets, and into the real

economy. Addressing that macroprudential question requires a broad representation of the network

of relationships among financial market participants so transmissions of risk can be observed.

As shown in Figure 1a, a run often begins with concerns about counterparty creditworthiness

and liquidity drying up, which boost funding costs and place strains on vulnerable firms. The rise in

funding costs promotes further concerns about counterparty risk and ever-wider funding spreads.

In contrast, a fire sale often begins with a news development that prompts repricing of assets,

combined with a concentration of leveraged funds that are forced to sell assets to meet margin

requirements. The forced sales push prices lower and margin calls act as feedback to magnify the

effects, triggering more selling.

As identified by the Office of Financial Research (OFR Annual Reports 2012, 2013, 2014),

an important challenge is to increase the macroprudential value of supervisory stress testing by

incorporating feedback and enhancing the models to allow for runs and fire sales. Figure 1a depicts

an illustrative trajectory for a run, which often begins with a funding shock. Figure 1b depicts

an illustrative trajectory of a fire sale, which often begins with a pricing shock. Ultimately, a

macroprudential stress test should ask whether the financial system as a whole has the capital and

liquidity to support lending and to be resilient to shocks.

2.2 Modeling Direct and Indirect Stress: Funding Markets and Asset Markets

Many of the linkages needed to represent macroprudential risks in a model must consider both

funding markets and asset markets. Their relationship is important in the U.S. financial system

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Figure 1: Funding Cycle and Fire Sale

(a) Funding Cycle

(b) Fire Sale

Note:A run often begins with concerns about counterparty creditworthiness and a drying up of liquidity, whichboost funding costs, placing strains on vulnerable firms. The rise in funding costs promotes further concerns aboutcounterparty risk and ever-wider funding spreads. In contrast a fire sale often begins with news that prompts arepricing of assets, combined with a concentration of leveraged funds that are forced to sell to meet marginrequirements. As the forced selling sustains downward pressure on prices, margin calls feed back to magnify theeffects, forcing additional rounds of selling.Source: Office of Financial Research Annual Report (2012), pp.56-7

through interactions with leverage, pricing, and price discovery of assets (Copeland et al. (2010)).

Understanding the dynamics requires looking at the funding and asset markets in tandem. Yet

their interdependence is not fully specified in the extant literature.

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Traditional modeling discussions have focused on two main channels of risk contagion in the

financial system: (1) direct inter-counterparty linkages between financial institutions, such as in-

terbank lending networks, and (2) contagion due to changes in securities values. The former, which

has been given extensive empirical and theoretical study (Wells (2002); Furfine (2003); Upper and

Worms (2004)) focuses on the dynamics of loss propagation via the direct counterparty exposures

following an initial default. More directly to funding markets, Gorton and Metrick (2012) study an

interdealer, bilateral repo market and show that haircuts increased dramatically during periods of

stress, similar to haircut spirals previously modeled (See Brunnermeier and Pedersen (2009) and

Adrian and Shin (2010)).

The linkage of assets to financial institutions through portfolios can impose further downward

pressure on asset values in the market. Damage can spread to institutional investors, and the result

in risk propagation cascading throughout the system (Cifuentes et al. (2005); Tsatskis (2012)).

These, as well as the models such as those in Caccioli et al. (2012) and Chen et al. (2014), show the

importance of diversification and bank leverage on the sensitivity of the system to shocks. Tasca

et al (2014) identify a critical level of diversification, mapping to regimes where diversification can

and cannot dampen higher systemic risks from leverage.

Though many models exist in these distinct research programs, few studies link the two channels

in a single model that allows the dynamics to be transmitted across the financial system. This is

important to understand because during a financial crisis these flows and agent objectives can be

strained from the interaction of declines in prices and funding, and forced liquidations. These events

lead to the dynamics associated with cascade and contagion among financial entities. The paths for

these dynamics are variously characterized as fire sales (Shleifer and Vishny (2011)), balance sheet

constrictions (Danielsson et al. (2012)), liquidity or margin spirals (Brunnermeier and Pedersen

(2009)), leverage cycles (Adrian and Shin (2013); Fostel and Geanakoplos (2008); Sato and Tasca

(2015)), and panics (Gorton (2010)).

2.3 Modeling Dynamic Stress: Agent-based Models

Evaluating the implications to systemic risk within institutions and markets broadly requires

modeling the individual participants as they make decisions and react to the decisions of other

participants, both individually and in aggregate. ABMs are well suited for incorporating these

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transformations to explore crisis dynamics (OFR (2013); OFR (2014)). ABMs follow the agents

period by period, assessing their reactions to events and updating the system variables accordingly.

ABMs that seek to explain how the behavior of individual firms or agents can affect outcomes

in complex systems offer the opportunity to understand potential vulnerabilities and paths through

which risks can propagate across the financial system. Additionally, such models offer the ability

to depict the heterogeneity of agents, as well as idiosyncratic rules for how financial institutions

operate, which are important to replicate real market conditions.

This paper develops a systemwide view of the transformations and dynamic interactions of

agents in the financial system. This integration captures the individual differences of agents from

the perspective of a network of relationships and from the perspective of behavior decisions. An

ABM can depict the interdependent relationship between the funding and asset markets. It can

also incorporate dynamic, stress testing by transmitting agent-level decisions through these inter-

connections.

2.4 Key Regulatory Constraints in Stress Testing

Key elements of the current international regulatory agenda established higher requirements for

bank capital and liquidity ratios (Haldane and May (2011)). The traditional rationale for micro-

prudential requirements is that they reduce idiosyncratic risks to the balance sheets of individual

institutions. A macroprudential interpretation is that such requirements strengthen the financial

system as a whole by limiting the potential for network spillovers.

Acknowledging that the implementation of these new regulations is complex, this paper focuses

on three principal regulatory constraints on capital in our model: leverage, liquidity, and a Value-

at-Risk (VaR) measure (Jorion (1997)). Specifically focusing on the impacts wholesale funding and

trading book portions of financial institutions.1 An immediate application of this method is to

use the ABM framework to produce a VaR-like view of the risk of the financial entities when the

dynamics of the system are considered.

Typically, liquidity requirements are specified as a minimum ratio of a bank’s unencumbered

liquid assets to its net expected stressed outflows over 30 days. This liquidity ratio can be seen

1We will not include the traditional bank balance sheet parts of bank holding companies, as Section 23a of theFederal Reserve Act limits the amount of balance sheet deposit that can be used to fund the prime brokerage andproprietary trading subsidiaries.

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as a means of short-circuiting the potential for systemic liquidity spillovers arising from fire sales

on the asset side of the balance sheet (liquidity shocks) or liquidity hoarding on the liabilities

side (liquidity-hoarding shocks). The primary risk measure for this is the liquidity coverage ratio

(LCR) described in Basel Committee (2013). We can evaluate the dynamic implications of shocks

to short-term funding liquidity using the methods discussed above for stress testing in two ways:

First, a given shock will propagate through funding and credit channels to affect the funding

liquidity and the LCR, and this will be seen in the simulation. Second, we can impose a shock

to the funding liquidity, and see how that initial shock creates a cascade affecting further funding

liquidity, markets, and agents.

When either of these issues occurs, a combined asset-based and funding-based fire sale can occur

due to degrading credit quality (Drehmann and Nikolaou (2013)). As credit quality of an agent

drops, funding is reduced, leading to further credit degradation and feeding the asset-based and

funding-based aspects of the fire sale (Diamond and Rajan (2001); Acharya et al. (2012); Bluhm

et al. (2014)). The decline in credit quality comes from a market perception that the agent will

be unable to pay its liabilities. Because the first liabilities to fail tend to be those that are shorter

term, a measure of credit degradation is a drop in the ratio of short-term assets to short-term

liabilities. A drop in one agent’s credit quality can also affect its counterparties, such as in the

interbank market (see Georg (2013), Ladley (2013)).

3 Model Formulation

The objective of our ABM is to integrate the network of relationships and functions of partici-

pants in lending and borrowing transformations to learn more about risk in financial intermediation

transformations. The model also helps explore how the asset portfolio creates a second level of link-

ages between agents.

The model includes the three classes of agents described above: cash providers, bank/dealers,

and hedge funds (collateral providers). The C cash providers, lend cash for collateral to K

bank/dealers. The K bank/dealers can then intermediate that lending to N hedge funds. In

addition, the K bank/dealers and N hedge funds can invest in M assets, which they will buy (or

sell) as their capital grows (or decreases) (see Figure 2 for relationships). The following comprise

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Figure 2: Diagram of Model Formulation

Source: Authors’ analysis

the key variables of the model, which will later be referenced further into the model.

The set of K bank/dealers and N hedge funds hold a quantity of each of the M assets:

Qk,m(t), Qn,m(t) where k = 1, .. .,K;n = 1, .. ., N ;m = 1, .. .,M

To buy assets the K bank/dealers and N hedge funds will use their capital, Cap:

Capk(t), Capn(t) where k = 1, .. .,K;n = 1, .. ., N

The M assets have a price:

Pm(t) where m = 1, .. .,M

On a day-to-day bases, as asset values change and the K bank/dealers and N hedge funds

capital, Capk(t),Capn(t), changes their demand for the M assets:

QDn,m(t), QDk,m(t) where k = 1, .. .,K;n = 1, .. ., N ;m = 1, .. .,M

The funding of the set of K bank/dealers and N hedge funds will need to make leveraged

purchases will be:

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F k(t), Fn(t) =∑M

i=1 (Pi(t)Qk,n,i(t)− Capk,n(t)

where k = 1, .. .,K;n = 1, .. ., N

The C cash providers governs the funding using haircuts for each of K bank/dealers and N hedge

funds:

HCk,m(t) where k = 1, .. .,K;m = 1, .. .,M

The haircut implicitly determine the amount of collateral of asset m that can be purchased and

rehypothecated as collateral, CA:

CAk(t), CAn(t) =∑K,N

i=1 (Ai(t)− Capi(t))/(1−HCc,k(t))

Each of the k bank/dealers and n hedge funds govern how much funding, Fk, Fn, they use with a

leverage target, LevTarget:

LevTargetk , LevTarget

n where k = 1, .. .,K;n = 1, .. ., N

Additionally, the K bank/dealers, to maintain good standing with their lenders, the C cash

providers, they govern the amount of liquid capital on their balance sheet using a liquidity ratio

target:

LiqRatek where k = 1, .. .,K

This provides the bank/dealers with an accounting buffer, similar to capital requirements that they

can draw on in cases of liquidation constraints.

With the preceding set of variables that will govern agent behaviors in place, we will now discuss

how each of the variables interact within the model market and, the dynamics created by them.

3.1 Asset Market

Asset markets in this model represent any number of different markets: equities, futures, com-

modities, mortgage-backed securities, etc. There is extensive literature applying ABMs to market

microstructure, beginning with Maslov (2000). The price impact literature of Stoll (1978) and Kyle

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(1985) demonstrates a price impact to be linear. We employ a model along the lines of Greenwood

et al. (2015) for linear price impact with Bm determining the market impact, and PRRm is N(0, Bm).

PRm(t) = Bm

∑QDpi

n (t) + PRRm(t) (1)

Pm(t+ 1) = max (0, Pm(t)(1 + PRm(t))) (2)

To keep the model tractable, we assume the error terms for the prices are independent, so that

any correlation structure occurs through the interaction of the agents, in particular due to contagion

during the fire sales. The implication of this model is that the agents are atomistic with respect

to the market except during times of forced liquidation. Absent such forced sales, the day-to-day

movement in prices takes on a simple random process. That is, the firms are assumed to execute

their buying and selling by placing orders, QDpin (t) which typically do not affect the price of assets.

This is what would be expected during normal times, because agents have the option of spacing

out their trades to minimize the market impact. What does matter and is the focus of the model

are the occasions when a shock forces a bank/dealer or hedge fund to liquidate without regard to

the market implications of its actions. In those cases, we assume that the executed orders can have

a price impact denoted by QDpin (t).

Note that using the product of m and the quantity of forced sales will lead to a larger impact

as prices drop, because lower prices mean a higher quantity must be sold to generate the same

dollar amount. This means that we are assuming liquidity drops proportionately with price; that

is, liquidity is based on the total market value or float available to sell. An alternative is to base

forced selling on a dollar amount rather than a quantity. This, of course, will change the units and

size of Bm, or we can add a further term to the determination of Bm to allow it to increase as the

fire sale evolves. For example, the Bm can increase as a function of the forced selling that enters

the market.

3.2 Cash Provider

The cash provider, c, lends to a bank/dealer’s finance desk based on the dollar value of the

collateral received and haircut set for bank/dealer k, HCc,k. The haircut is based on the perceived

creditworthiness of a borrower and reduces the value of the asset used as collateral, CAk(t), by a

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percent of its current market value. The target amount that will be loaned based on the haircut,

which can be modeled to vary based on the cash provider’s decision rule, is:

LTargetc,k (t) = CAk(t)(1−HCc,k(t)) (3)

The loan, L, is checked to ensure it does not go over a maximum dollar amount the cash provider

is willing to lend independent of any collateral or haircut, LMaxc,k :

Lc,k(t) = min (LMaxc,k (t), LTarget

c,k (t)) (4)

This last aspect of the firm’s decision rule reflects the fact that many cash providers are ex-

tremely risk averse and set limits on their collateral holdings. The cash providers will not lend

more than a given amount, no matter the size and nature of the collateral. If LMaxc,k (t) is hit the

CAk(t) is revised to reflect the amount of collateral it will submit.

3.3 Bank/Dealer

The bank/dealer acts as an intermediary between buyers and sellers of securities and between

lenders and borrowers of funding. It employs a number of subagents to do various tasks. Just as

a hedge fund can be modeled to represent a wider set of institutions, so the bank/dealer can be

modeled to represent agents that have only a subset of these functions. For example, there might

be an intermediary that provides only the market-making function of the trading desk, or that does

not have a derivatives function. Thus, the bank/dealer category encompasses more than the major

bank/dealers that provide all these functions.

3.3.1 Prime Broker

The prime broker is the agent that interacts with all hedge funds that bank/dealer k does

business with (a subset Nk of all n hedge funds). The prime broker’s job is to gather the collateral

of the hedge funds, CAPBk , so that it can then look for funding, FPB

k , from the cash providers for

any loans that hedge funds need to cover their leveraged positions. As stated earlier, we make the

simplifying assumption that the prime broker passes through the funding from the finance desk

with no further haircuts, so the collateral of the prime broker is equal to that of the sum of the

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hedge funds it services.

3.3.2 Finance Desk

The finance desk is responsible for financing a bank/dealer’s activities, which include its trading

desk and prime broker’s funding needs. As the prime broker does for hedge funds, the finance desk

also gathers collateral, CATD(t), from the bank/dealer’s trading desk so that it can obtain funding,

F TDk (t), for the assets the trading desk holds above the value of its capital. The finance desk takes

securities posted by the prime broker and by the trading desk, CAFDk (t), and these form the basis

for the collateral it gives the cash provider. The finance desk receives FFDk (t) and distributes this

back to the prime broker and the trading desk.

3.3.3 Trading Desk

Following the adjustment mechanism of Adrian and Shin (2013) and Greenwood et al. (2015),

the trading desk uses three leverage constraints: Leverage Maximum, LevMaxn (t) set by the prime

broker of the bank/dealer, k, which the trading desk is using for financing, and is the inverse of the

haircut it receives. The trading desk governs its leverage using LevMaxn (t) to set a Leverage Buffer,

LevBuffern (t), which it rebalances in the event that it exceeds LevMax

n (t) and a Leverage Target,

LevTargetn (t), which it rebalances when the changes are small, normal fluctuations.

LevMaxn (t) ≥ LevBuffer

n (t) ≥ LevTargetn (t) (5)

The trading desk has two other parameters. The first is an initial capital, Capn(0), to fund

all initial activities. The other is an asset allocation vector, AAllocationn , that determines how to

allocate the trading desk’s capital among the set of M assets. Using these parameters as the initial

conditions, the trading desk follows a sequential updating function that to manage its asset portfolio

and governing leverage constraints for every period t in the future. The trading desk determines

current capital, Capn(t), based on its evaluation of all its assets, An(t), and subtracting any slippage

in trading, Sn, after estimating what it expects to purchase or sell assets at and funding FHFn (t−1).

An(t) =

m∑i=1

Pi(t− 1)Qn,i(t− 1) (6)

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Sn(t) =M∑i=1

(QDn,i(t))(Pi(t− 1)− Pi(t− 2)) (7)

Given its new capital level, the hedge fund computes its target asset level, the dollar assets that

the trading desk would own at its target leverage.

ATargetn (t) = Capn(t)LevTarget

n (t) (8)

The hedge fund can determine how well it to meets the constraint and target leverage by

calculating the current leverage it has after the previous price movements. This allows the hedge

fund to determine how it should change its portfolio.

LevCurrentn (t) = An(t)/Capn(t) (9)

If LevCurrentn (t) ≤ LevMn ax(t), the hedge fund receives a margin call, forcing it to reduce

assets by QDinp(t) liquidating enough shares to get back to the LevBuffer

n (t). If LevCurrentn (t) <

LevMaxn (t). The hedge fund then must buy or sell QDpi

n (t) to move its portfolio to AnTarget

dictated by LevTargetn (t). This updates the quantity of shares held by the hedge fund to Qn(t)

based on trading decisions made as a result of QDn(t). This allows the hedge fund to determine

how much funding, Fn(t), it will need achieve Qn,m(t) based on its current capital.

Qn,m(t) = Qn,m(t− 1) +QDn,m(t) (10)

This completes the sequential process each trading desk uses to manage its portfolio. If at

the end of any daily sequence, a hedge fund’s Capk is less than zero, it hedge fund will default.

Additionally, the hedge fund will sell all its assets during the next period, t + 1, and no longer

participate throughout the rest of the model’s run. The trading desk also acts as a market maker

for customers looking for liquidity in markets. The trading desk can suffer from limited liquidity

because it sources this transformation process as part of its business. We introduce the maximum

liquidation threshold, QMaxk , which is the maximum dollar value of assets that can be sold in

any period. It reflects limits on liquidity, or more generally, on a bank/dealer’s ability to remove

obligations from its portfolio.

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QMaxk ≥

M∑i=1

QDk,i(t) + Pi(t) (11)

The bank/dealer uses its liquidity reserve when the trading desk faces a drop in funding greater

than the amount of inventory it can immediately liquidate. This is discussed in the next section.

3.3.4 Derivatives Desk

Derivatives desk activities are represented by the counterparty credit exposure each bank/dealer

i has to other bank/dealers j. The total credit exposures, CETotalk , is calculated as a dollar quantity

of exposure to all other counterparties, CEk, and individual creditworthiness, CWk:

CETotalk (t) =

K∑i=1,i 6=j

CEi(t)(100− CWi(t)) (12)

Each bank/dealer has a percent of its initial capital exposed to other agents (similar to writing

a credit default swap on another agent). At the close of the day, the credit rating of each agent is

calculated based on its liquidity ratio. If an agent to whom the bank/dealer is exposed drops in its

creditworthiness, CWk, there is a mark-to-market effect represented by a drop in the value of the

exposed capital, Capk. The creditworthiness of an agent is detailed in the next section. The sum

of mark-to-market is the total credit exposure, CETotalk .

Capk(t) = Ak(t)− Fk(t− 1)− Sk(t)− CETotalk (t) (13)

3.3.5 Treasury

The bank/dealer’s treasury department acts as a maintenance agent to ensure subagents’ financ-

ing and credit risks do not hurt the bank/dealer as a whole. The treasury department manages the

bank/dealer’s liquidity reserve and creditworthiness.

Liquidity Reserve

Because of banking regulations and risks that leveraged institutions face, bank/dealers typically

are required to hold a liquidity reserve in case of transaction stresses. The liquidity reserve, LiqRek ,

is a proportion of a bank/dealer’s capital not used to buy assets. The liquidity reserve is a buffer

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if the bank/dealer’s funding drops and it cannot reduce assets by an equal amount due to market

illiquidity. The reserve amount is based on the liquidity reserve rate, LiqRatek , a parameter solved

for as a result of the liquidity ratio target, LiqRatioTargetk , which is discussed in the following section.

LiqReservek (t) = LiqRate

k × Capk(t) (14)

If a bank/dealer tries to sell more shares than allowed by its liquidation threshold QMaxk , the

shares it must continue to hold will be funded with the liquidity reserve by debiting LiqDebitk up to

the limit of LiqRk . The treasury department tries to keep the LiqDebitk at zero due to its impact on

the creditworthiness of the firm (see next section of detail). The result is the treasury department

will try to sell the shares in the next period, assuming the following conditions are met:

QMaxk ≥

M∑i=1

QDk,i(t) + Pi(t) + LiqDebitk (t) (15)

The liquidity reserve variables are also part of the difference in the capital calculation of the

bank/dealer.

Capk(t) = Ak(t)− Fk(t− 1)− Sk(t)− CETotalk (t) + LiqRk (t− 1)− LiqDebit

k (t− 1) (16)

If the bank/dealer has LiqDebitk (t) ≥ LiqReserve

k (t), it will have a liquidity default. This differs

from a default due to the bank/dealer’s equity dropping to zero. In liquidity default, the bank/dealer

may have Capk(t) ≥ 0, but it can no longer meet its short-term obligations because of liquidity

constraints. In this case, a bank/dealer’s assets go into receivership and no longer enter the market

as forced sales.

Creditworthiness

Cash providers and bank/dealers with exposures to other banks assess their counterparties with

a creditworthiness rating, CWk. For cash providers, the rating determines the haircut and how

much funding is provided to a bank/dealers. For bank/dealers, the rating determines the value

of capital exposure one bank has to another through mark-to-market based on the CWk. Both

leverage and the liquidity ratio can be used to describe creditworthiness. To reflect the functions

of the funding map, the treasury department determines the leverage measures and the liquidity

15

reserve. The key measure for creditworthiness is the liquidity ratio, LiqRatio, determined by:

LiqRatiok (t) = ((LiqRk (t)− LiqDebit

k (t)))/(F Tk D(t)) (17)

The LiqRatiok is significant in representing the bank/dealer’s ability to meet obligations (as seen

in equation 3.3.5). The bank/dealer works to target a liquidity ratio, LiqRatioTargetk , so it can

continue to have a good credit rating in the future.

LiqRatioTargetk (t) = (LiqRk (t))/(F TD

k (t))(18)

If the liquidity ratio falls below a minimum liquidity ratio, LiqRatioMink , the bank/dealer’s cred-

itworthiness begins to declines, and haircuts set by the cash provider will increase. This will cause

forced sales by the bank/dealer and potentially cause forced sales by counterparties exposed to

the bank/dealer. The adjustment rule is similar to that used for the adjustment of leverage, as

described in Greenwood et al. (2015):

CWk(t) = 100− φCW (LiqRatioMink (t)− LiqRatio

k (t)) (19)

HCc,k(t+ 1) = HCc,k(t) + φHC(LiqRatioMink (t)− LiqRatio

k (t)) (20)

Where φCW and φHC are two global parameters set at the beginning of the simulation to govern

the functions of CWk(t+ 1) and HCc,k(t+ 1) for all K bank/dealers.

3.4 Hedge Fund

The model includes hedge funds because leverage is a critical feature creating asset-based, fire

sales. A hedge fund uses its capital and borrowed cash from the prime broker of a bank/dealer to

buy assets.2 The broader universe of asset managers can be considered unleveraged hedge funds in

this model. It is important to consider these firms because they face redemption risks, that make

them susceptible to forced sale dynamics similar to leverage risks and hedge funds.

2A hedge fund agent may represent other types of institutional financial firms that have varying degrees of leveragein their portfolio.

16

Hedge funds behave like a bank/dealer’s trading desk. Most of the time, a hedge fund has the

same constraints and objectives as discussed in the trading desk section. The only difference is that

we do not bind the hedge fund by the quantity of assets it can sell into the market.

3.5 Delimitations of the Model

We identify two delimitations of our current model: absence of a central banker and absence of

new entrants during a financial crisis. Our ABM, does not include a central bank as an autonomous

agent. Adding a central bank would enhance the model from the perspective of policy analysis.

However, we can impose the policy levers of a central bank into the model exogenously. For example,

a central bank’s injection of liquidity into the asset market can be represented by an exogenous

drop in the price elasticity of demand for asset m, Bm. An injection of funding liquidity can be

represented by an exogenous increase in funding lines for a hedge fund and bank/dealer. Support

for a bank/dealer, either overall or in the specific, can be represented by increasing the value of

the bonds that reflect counterparty exposure. Insofar as a central bank has discernible rules, these

exogenous policy effects can be replaced by including the central bank explicitly.

We do not currently allow for the entry of new market participants. As described in greater

detail in the OFR’s 2012 Annual Report to Congress (p. 56), fire sales can be sweeping, cascading

events lasting for only a short duration (e.g., a month). For context, no new market participants

arose during the peak of the financial crisis in the fall of 2008, mergers notwithstanding.

4 Model Dynamics Validation

This section, presents the results from several sets of experiments testing model validity and

robustness. Table 1 provides an overview of our experimental design and the set of independent

replications. The first two experiments serve as validation testing of our baseline model and the

interaction effects of variables when under stress. This allows us to verify that the model’s dynamics

adhere to those depicted in Figure 2. Finally, we perform an extensive set of experiments as a

robustness test and validate the statistical significance of various model parameters.

17

Table 1: Design of Experiments

Experiment Independent Variables Values Replicates

Baseline - - 1,000

Benchmark Tests Price Shock {0%, 10%, 15%, 20%} 4 x 1000 = 4,000

Robustness Tests Price Shock {10%, 13%, 15%} 3Bm {0.5, 1.0. 2.0} x 3HCc,k {0.1, 0.13, 0.16, 0.19} x 4φCW {100, 200, 300, 400} x 4φHC {0.1, 0.2, 0.3, 0.4} x 4Ak(0) {10%, 20%, 40%, 80%} x 4QMax

k (t) {$500 M, $1 B, $2 B} x 3{ (0.2, 0.25, 0.15, 0.25),

(LiqRatioMin1 , LiqRatioMin

2 , (0.25, 0.3, 0.2, 0.3), x 3 x 500

LiqRatioTarget1 , LiqRatioTarget

2 ) (0.3, 0.35, 0.25, 0.35) }= 1,036,800

Source: Authors’ analysis.

4.1 The Baseline Model

To illustrate the model’s dynamics, we explore the influence of asset, funding, and credit shocks

through the system in a tractable network of three assets, two hedge funds, two bank/dealers, and

a single cash provider that treats each bank/dealer separately. Consistent with Battiston et al.

(2012), we depict the couplings between financial institutions as a network and extend the network

depiction to reflect endogenous dynamics. At initialization, all hedge funds and bank/dealers have

equal capital, and all assets have equal values of price and liquidity (A detailed description of model

parameters is in Table 7 of the Appendix).

Figure 3 depicts the relationship of agents we use in the scenario. Bank/Dealer 1 (BD1) and

Hedge Fund 1 (HF1) hold equal weights in Asset 1 (A1) and Asset 2 (A2). Bank/Dealer 2 (BD2)

and Hedge Fund 2 (HF2) hold equal weights in Asset 2 (A2) and Asset 3 (A3). Finally, the Cash

Provider (CP1) supplies funding to the bank/dealers, which in turn supply funding to the hedge

funds. All hedge funds use assets they own as collateral.

We ran 1,000 replicates of the baseline model without observing a single margin call for the

hedge funds and therefore no hedge fund defaulted. Without any margin calls, we verify that the

price returns of each asset fit the normal distribution as expected. Hence, we confirm that the

baseline model serves as a valid benchmark for stress testing. We then proceed to validate the

stress testing of our model.

18

Figure 3: Schematic of the Relationship between the Agents and Markets.

Note: This figure has two bank/dealers (BD), two hedge funds (HF); one cash provider (CP), and three assetmarkets (A). The directed edges show the flow of assets, funding, and collateral.Source: Bigbee et al. (2015)

4.2 Shocking the Baseline Model

We present results from three experiments with the baseline model, each a dynamic stress test

with increasing levels of an exogenous shock to one asset. Together, the three sets of experiments

with the baseline model represent a comprehensive set of validation testing.

Our initial experiment entails the exogenous introduction of a 10 percent price shock to Asset

1 at Time 20. We chose Time 20 to allow for the dampening of any transient dynamics from

initialization, ensuring all observed events of interest resulted from the experimental treatment

(i.e., exogenous shock). We ran the same 1,000 replicates of the baseline model as above (i.e.,

controlling for randomness at initialization) and observed a total of 13 possible events of interest,

as listed in Table 2. These events of interest include the initial price shock, margin calls (or

“qDemand Event”) for an institution with a specific asset, and defaults.

Table 2: Model Events

1. Price Shock 8. qDemand Event for Trading Unit 1 Asset 12. qDemand Event for Hedge Fund 1 Asset 1 9. qDemand Event for Trading Unit 1 Asset 23. qDemand Event for Hedge Fund 1 Asset 2 10. qDemand Event for Trading Unit 2 Asset 24. qDemand Event for Hedge Fund 2 Asset 2 11. qDemand Event for Trading Unit 2 Asset 35. qDemand Event for Hedge Fund 2 Asset 3 12. Default of Trading Unit 16. Default of Hedge Fund 1 13. Default of Trading Unit 27. Default of Hedge Fund 2

19

Figure 4: Event Sequence Diagram for the Events of Interest from 10% Price Shock of the BaselineModel.

Source: Authors’ model, Bigbee et al. (2015)

We also confirmed the validity of their sequence of these events of interest. Figure 4 depicts

the sequence of events for all 1,000 replicates from this experiment. Note that in 742 of the 1,000

instances of this experiment, the 10 percent price shock to Asset 1 did not produce any additional

events of interest. Stated another way, in 74.2 percent of the model realizations, the financial system

was robust to the 10 percent shock that was dampened throughout the system without significance.

20

We saw a few rare, but interesting events in this dynamic stress testing. In two instances, the price

shock produced contagion between the two hedge funds. Also, there were several unique instances

of extensive fire sales that cascaded throughout the financial system.

Figure 4 reflects many aspects of dynamic and macroprudential stress testing. For example,

there were two instances where the price shock generated margin calls for Hedge Fund 1. This

subsequently produced contagion between the two hedge funds and resulted in margin calls for

Hedge Fund 2, which did not hold the shocked asset. This sequence of events directly reflects the

fire sale dynamics depicted in Figure 1b. Figure 4 also shows several unique instances of extensive

fire sales that cascade throughout the entire financial system. All sequences of interest begin with

a margin call for Hedge Fund 1 in the shocked asset, then propagated across the financial system

to varying degrees.

For comparison and completeness of the discussion, we present the Event Sequence diagrams

for the 15 percent and 20 percent shock to Asset 1 in Figure 5 and Figure 6, respectively. These

figures confirm there is no Hedge Fund default without a qDemand event preceding it. As depicted

in Figure 6, the 20 percent price shock to Asset 1 generates a contagion of fire sales that sweeps

across the system to entities that do not hold the shocked asset Hedge Fund 2 and the Bank/Dealer

2.

While Figures 5 and 6 depict only event sequences that resulted in a count of six replicates or

more, for completeness, we analyzed all the event sequences for both the 15 percent and the 20

percent shock experiments to identify the following:

For the 15 Percent Price Shock:

- In 4 realizations out of 1,000, the price shock had no effect.

- In 250 realizations where Hedge Fund 1 experienced qDemand events that default, neither

Hedge Fund 2 nor the bank/dealers had any qDemand events.

- In 60 realizations, all four entities defaulted.

For the 20 Percent Price Shock:

- In 4 realizations out of 1,000, the price shock had no effect.

21





- In 250 realizations where Hedge Fund 1 experienced qDemand events that default, neither

Hedge Fund 2 nor the bank/dealers had any qDemand events.

22

- In 60 realizations, all four entities defaulted.

Taken together, these three sets of experiments with the baseline model represent a compre-

hensive set of validation tests, which clearly demonstrates our novel approach to dynamic, stress

testing.

4.3 Robustness of Validation Testing

While the validation tests of our dynamic stress testing approach varied only the size of the

exogenous shock (i.e., 0, 10 percent, 15 percent, and 20 percent), we demonstrate the robustness of

these results using a full-factorial design of experiments (Kleijnen et al. (2005)). We identified 20,736

different parametric combinations and generated 50 realizations of the model for each combination

(i.e., 20,736 combinations x 50 replicates per combination = 1,036,800 realizations of the model).

See Section 5 of the Supplementary Information for complete details of these experiments.

Figure 7 shows approximately 90 percent of the event sequences from this comprehensive set

of experiments (i.e., 935,104 of the 1,036,800 realizations). Note that approximately 26 percent of

the time, the price shock did not trigger any events of interest.

We developed a filtering capability to allow for the presentation of our event sequence diagrams

at finer resolutions. While Figure 7 provides an overview of the event sequences for this comprehen-

sive set of experiments, Figure 8 demonstrates our ability to filter those results by specific parameter

values. For example, in Figure 8, we filter by level of exogenous shock for the full factorial sweep

of the remaining parameters. The results are robust and consistent across the sets of experiments.

The size of the shock and the dampening of its effects are strongly anti-correlated The 10 percent

shock was fully dampened in two or fewer margin calls for 83 percent of the realizations. The 13

percent shock was fully dampened in two or fewer margin calls for 24 percent of the realizations

and the 15 percent shock was fully dampened in only 15 percent of the realizations.3

4.4 Significance Testing

The model contains numerous parameters, so it is important to perform significance tests to

verify the results remain valid as we explore the model’s parameter space. We examined the

3See the Supplementary Information for additional results from our robustness testing.

23

Figure 7: Event Sequence Diagram for Comprehensive

Note: Note that the figure is not exhaustive, with the first decile of event sequences excluded for spaceconsiderations.Source: Authors’ analysis, Bigbee et al. (2015)

parameter space by measuring the contribution of each parameter to the results for a specified

shock. The majority of the variables are statistically significant as shown in Table 3, . The

direction of the coefficients for Leverage Target and Max-liquidation are negative – meaning the

larger the value, the larger the size of asset sales would have to be, causing larger decreases in

price returns and capital. For the Liquidity Ratio, the direction of coefficient is positive and the

higher the value, the fewer assets would have to be sold. These results confirm that the expected

24

Figure 8: Event Sequence Diagrams filtered by Level of Exogenous Shock, for Shocks of 10 Percent,13 Percent, and 15 Percent

Note: The figure is truncated to depict only those Event Sequences that represent at least 1 percent of the modelrealizations for those parametric combinations.Source: Authors’ analysis, Bigbee et al. (2015)

interdependencies are robust to variations in shock and risk associated tolerance.

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Table 3: Significance of Model Parameters in Contributing to Behavior Dynamics when Strainedwith a 15 Percent Price Shock to Asset 1.

Leverage Target Liquidity Rate Max-Liquidation Allocation of Firms Adj. R2 F-Stat

Estimate Pr(>| t |) Estimate Pr(>| t |) Estimate Pr(>| t |) Pr(>| t |)Price ChangeAsset 1 0.0336 0.0012 -0.0868 *** *** 0.0106 34.4

-0.0189 -0.0019 -0.0088Asset 2 -0.1433 *** 0.0161 *** -0.2676 *** *** 0.1593 178.93

-0.0258 -0.0024 -0.012Asset 3 -0.1601 *** 0.0356 *** -0.3177 *** *** 0.2888 240.77

-0.0263 -0.0027 -0.0122

Capital ChangeHF 1 / BD 1 -0.092 * 0.0001 -0.0076 *** *** 0.0008 11.89

-0.0311 -0.0037 0.0015HF 2 / BD 2 0.102 * 0.0024 -0.0007 *** 0.0189 0.2

-0.0404 -0.0031 -0.0001

# of Forced SalesHF 1 / BD 1 0.1845 ** -0.0108 ** 0.4832 *** *** 0.044 36.63

-0.0212 -0.0039 -0.0124HF 2 / BD 2 0.1975 ** -0.0108 ** 0.5162 *** 0.014 3.2

-0.0211 -0.0039 -0.0125

* = 90%, ** = 95%, *** = 99% Significance

Source: Authors’ analysis.

5 Model Dynamics and Critical Constraints

This section addresses the influence of critical variables in stress dynamics, leverage, liquidity,

and crowding. We do this by running an experimental panel that, varies each of these parameters

and examines how they cause interactions among market participant portfolios and asset values.

5.1 Leverage

Studies of the role of leverage in fire sale dynamics have generally focused on asset leverage and

the influence it exerts through forced liquidation. To illustrate the effect of leverage in our model,

we apply a price shock of 10 percent to Asset 1 to the base model and measure asset prices and the

capital of the hedge funds as the permissible maximum leverage is varied. Figure 9a and Figure 9b

show the effect that varying leverage has on the capital of the agents and on prices.

The first-order effect of leverage to Asset 1, the asset that is being shocked, and to Hedge Fund

1, which holds the asset, are generally well understood and predicable. However, there is a second-

order effect because Hedge Fund 2 shares asset exposure with Hedge Fund 1: Both Hedge Fund

1 and Hedge Fund 2 have exposure to Asset 2. Leverage combined with overlapping portfolios is

a source of contagion, as one agent that is under pressure in one asset starts to liquidate other

holdings (Caccioli et al. (2012)). Figure 9 shows the expected effect of contagion with a shock

26

Figure 9: The Impact of Leverage on Hedge Fund Portfolio Values and Asset Prices

Source: Authors’ model.

having a great impact on the agents as leverage is increased. Of note, though, is that Figure 8

shows that the effect on contagion occurs at a threshold level, with the threshold lower for the asset

that is held in common across the agents, and a higher threshold for Asset 3, which is not held by

the agent that is initially under pressure.

As would be expected, an increase of leverage reduces the capital of both hedge funds and

does so at an increasing rate. The effect is more rapid and severe for Hedge Fund 1 because it

has exposure to the shocked asset, Asset 1. Contagion from Hedge Fund 1 and Hedge Fund 2

is immediately evident, because the two share Asset 2. The drop in capital accelerates once the

leverage increases toward 10; on occasion there will be forced selling with lower leverage, but for

the baseline parameters, it is at this point where forced selling starts to occur with higher frequency

and severity.

Of course, if there is contagion between the two hedge funds, there will also be contagion

between the assets. Asset 1 drops immediately based on the shock, but it is only when the leverage

approaches 10 and there is an increasing frequency of forced selling that the other two assets are

affected by the price shock. The contagion first affects Asset 2, because it is shared between the

two hedge funds, and then as leverage increases even further, the contagion moves to Asset 3. This

is a case of “collateral damage”, because Asset 3 is not even in Hedge Fund 1’s portfolio. For

very high leverage, it is Asset 2, not Asset 1, where we find the greatest price drop. Even though

Asset 1 started the process off with a 10 percent price shock, Asset 2 is more widely held and

27

becomes more embroiled in the forced selling. If a third hedge fund were exclusively in Asset 2, it

ultimately could face a greater impact on its capital than Hedge Fund 1. This resembles the path of

contagion during the near-failure of Long-Term Capital Management L.P., when the company had

little exposure to the source of the initial shock, Russian debt, but was highly leveraged to other

assets held by those who did.4 These results align with previous studies that identified a positive

feedback loop between institutional levels of leverage and asset prices that can amplify the effects

of exogenous shocks (e.g., OFR Annual Report (2012), Tasca and Battiston (2016) and Sato and

Tasca (2015)).

5.2 Liquidity

Liquidity concerns come in two forms, asset and funding. During periods of stress, the cost of

accessing markets without incurring steep price reductions or funding haircut increases becomes

difficult. Asset liquidity is critical to fire sale behavior because of the price impact caused by sizable

selling during the event. We model asset liquidity through Bm which measures the market impact

of forced sale events.

Figure 10: The Cross-Market Impact of Asset Liquidity on Hedge Fund Portfolio Values and AssetPrice


In Figure 10, we show the effect of variations in asset liquidity on capital and prices in the face

of a 10 percent shock to Asset 1. Lower liquidity has the same effect as higher leverage. The shock

4See President’s Working Group on Financial Markets (1999) and Bookstaber (2007) for a first-hand account ofone path of the contagion from of the Russian default.

28

has a larger impact on the capital of both hedge funds, as well as on the average decline of prices,

even showing that the impact of Asset 2 is the greatest when there is large erosion in liquidity.

Funding liquidity is the ability of a bank/dealer’s finance desk or prime broker to replace external

funding with cash equivalents in the event of a drop in funding. We model the funding liquidity by

the liquidity ratio, which is the ratio of liquid (cash-equivalent) assets to short-term, nondurable

funding. The liquidity ratio has a role similar to the leverage ratio, in the sense that there is a

threshold for the liquidity ratio, where a bank/dealer is forced to liquidate its inventory so as to

address the firm’s creditworthiness. Note that this is consistent with the stylized dynamics of cycles

depicted in Figure 1aa.

Figure 11: The Impact of Market Liquidity Constraints and Liquidity Ratios on Prices andBank/Dealer Portfolios


As a bank/dealer’s liquidity ratio drops below a targeted value, it must use part of its liquidity

reserves to finance assets that it cannot liquidate as a result of the max-liquidation constraint. A

bank/dealer can then attempt to liquidate the rest of its assets in the following periods. Figure

11 presents a simple case of the effect of variations in the liquidity ratio, where the bank/dealers

have the same liquidity ratio for illustrative purposes. The plot to the left shows the capital of

Bank/Dealer 1 and the plot to the right shows the price of Asset 1 for various values of its liquidity

ratio and its max-liquidation constraint.

29

5.3 Crowding

Crowding is a loose term for a wide set of agents heavily invested in the same assets. It is a way

of thinking of the dialing up or down of the extent of overlap in portfolios. The effect of crowding

was manifest in the “Quant Quake” of 2007, when a number of leveraged hedge funds using the

same quantitative strategy were forced to exit similar positions at the same time (Khandani and

Lo (2011)). Crowding in a trade can increase the number of forced sellers and attract attention

from strategic sellers that enter the market in anticipation of the effect of crowding (Stein (2009);

Brunnermeier and Pedersen (2009)). This was famously explained by a principal at Long-Term

Capital Management shortly after its failure (Lowenstein (2000), p. 156-157): “The hurricane is

not more or less likely to hit because more hurricane insurance has been written. In the financial

markets this is not true. The more people write financial insurance, the more likely it is that a

disaster will happen, because the people who know you have sold the insurance can make that

disaster happen.”

As expected, the effects of shock on the agents’ capital and on price will be greater, the greater

the amount of crowding. We can see in Figure 12 the effect of crowded trades by varying the asset

allocation from this benchmark for a given pricing shock, and comparing it to the results shown

above, which are based on an equal allocation between Asset 1 and Asset 2 for Hedge Fund 1. In

Figure 12 we have Hedge Fund 2 hold 50 percent of its allocation in Asset 2 and see the effect of

varying the proportion of the remaining 50 percent allocation held in Asset 1 versus Asset 3. In

this analysis, we have Asset 2 suffer the shock. As would be expected, a high allocation in Asset 1

versus Asset 3 leads to a larger price effect for Asset 1 and Asset 2, and a larger drop in capital for

Hedge Fund 1 and Hedge Fund 2. However, as Hedge Fund 2 transfers its allocation from Asset 3

to Asset 1, the sensitivity to the allocations of Hedge Fund 2 affects both firms, though by different

amounts.

The greater the overall concentration in the shocked asset, the greater the effect will be to those

who are holding that asset. A higher allocation in Asset 1 versus Asset 3 leads to a larger price

effect for Asset 1 and a larger drop in capital for Hedge Fund 1.

30

Figure 12: The Effect of Crowded Trades Due to Varying Asset Allocations During a Pricing Shock


6 Evaluation of Regulatory Risk Measures under Crisis

A wide range of measures have been proposed to address market and financial system risk

and a relatively small subset has been implemented by regulators. In this section, we assess key

regulatory risk measures used to impose risk constraints on the largest U.S. banks in light of the

dynamics revealed by the agent-based model during fire sale events. These measures are used for

three types of risk constraints: capital, stress, and funding liquidity.

6.1 Impact on Capital

VaR is computed by calculating the returns of the current portfolio over a past period and then

computing the standard deviation of those returns. The VaR measure is typically then taken to

be the two- or three-standard deviations of returns. Of course, the relevance of this risk measure

depends on how well the distributions of future returns are reflected by the returns used in the

sample.

Figure 13 presents the results of introducing a one-time shock to one of the assets held by a

hedge fund, showing the continuing downward path for the fund’s capital due to the subsequent

contagion and cascade. Figure 13a shows the envelope of paths for the hedge fund’s capital over

1,000 simulations. The solid red line is the average across the paths, and the dotted lines are the 5th

and 95th percentiles. The distribution manifests a marked skew. Figure 13b shows the distribution

of changes in capital over time. The skew is also apparent in this figure, as is the fat tail for the

31

Figure 13: Capital of Hedge Fund 1 (HF1) after a 15 Percent Shock to Asset 1 for 1,000 Runs ofthe Simulation

Note: The solid red line is the mean of the paths, the dotted lines are the 5th and 95th percentiles.Source: Authors’ model.

drop in capital; the first percentile pulls away from the fifth percentile during the period of severe

drop.

We can express the results with a VaR measure, but it differs from the traditional VaR in

several respects. First, the conventional VaR measure is symmetric but here, unsurprisingly, there

is asymmetry. Second, the time period matters; the variability of the paths is high during the

early periods, but over a longer time the effect dissipates. And, notably, these results suggest a

two-tiered response to the shock. While most of the realizations of the model depict a capital loss of

30 percent or less, a distinct group shows much greater losses in post-shock capital. This highlights

a complexity to the distribution in the extreme tail.

6.2 Stress Testing

The failure of regulators to anticipate the events of 2007-09 led to supervisory risk assessments

adding stress testing of the largest U.S. financial institutions. The Federal Reserve’s Supervisory

Capital Assessment Program (SCAP) in 2009 evolved into the Comprehensive Capital Analysis and

Review (CCAR) in 2011 (Federal Reserve Board 2013a, 2013b). CCAR has since been combined

with the Dodd-Frank Consumer Protection and Wall Street Reform Act stress testing (DFAST)

requirements as a tool for U.S. bank supervision. On the international front, the Basel Committee

on Banking Supervision (2010) lays out principles for stress testing.

32

The stress tests estimate the effect of specified shocks on the loans and assets held by the banks.

But, as pointed out by Bookstaber et al. (2014), the tests do not consider possible second-round

impacts, such as idiosyncratic increases in bank funding costs related to deterioration in capital

adequacy or declines in liquidity. Once our model has shown the credit and trading losses at a

bank, we must ask questions such as: What happens next? What are second-round effects of one

bank’s stress on other banks? What impacts does a stress event have on other parts of the financial

system? How do those events, in turn, alter the behavior of a bank? These questions relate to the

dynamics of the process, the interconnections, and the health of the transformations within the

financial system.

Table 4 illustrates how our agent-based model can provide insight by showing the dynamic

impact of the stress to the entire system, and thereby serve as a tool for extending stress tests to

capture the overall effect of the stress scenarios. The table shows the progression of one simulation

run of the agent-based model. Each period in the progression is depicted by a network showing

which agents (nodes) influence other agents. The networks are depicted as an output of the model,

and the network structure changes period-by-period as the environment changes due to the agents’

actions and as the agents adapt accordingly. For this example, the shock does not have far to go

before it embroils the system; it reverberates through the system, demonstrating the contagion and

cascades typical of the fire sales that this model seeks to address before running its course in six

periods.5

In Table 4, the dark outline for the nodes shows the agents’ initial size (in this case we assume

all of the agents have the same starting capital and all initial prices are identical), The shrinking of

the colored area within the nodes is proportional to the decline in capital in the case of the hedge

funds and bank/dealers, the reduction in funding for the cash provider, and the drop in prices in

the case of the assets. If the color within a node disappears, that agent has defaulted.6

5The parameter values used in this section are the same as used in Section 4.6Each edge in the network denotes the relational impact of one node, i, on another, j, based on the relationship

that exists in the agent-based model, normalized by running the simulation a number of times with variations on eachvariable. The width of the edge shows the cumulative effect of the transmission with respect to t periods and the nruns of the simulation, and the color of the edge in the figure shows the intensity of the interaction in the currentperiod; a darker color means greater intensity or change in the system relative to other runs and periods observed.

33

6.3 Funding Liquidity Coverage Constraints

The third area of regulatory focus for establishing risk constraints is in short-term funding

liquidity, the ability of a bank to fund short-term liabilities with liquid assets. The primary risk

measure for this is the liquidity coverage ratio (LCR) as described in Basel Committee on Banking

Supervision (2013). We can evaluate the dynamic implications of shocks to short-term funding

liquidity using the same methods as we have above for stress testing in two ways. First, a given

shock will propagate through funding and credit channels to affect the funding liquidity and the

LCR, and this will be seen in the simulation. Second, we can impose a shock to the funding

liquidity, and see how that initial shock creates a cascade for funding liquidity, as well as how it

moves out to affect the markets and the agents.

The agent-based modeling framework can posit a range of shock origination as shown in Table

5. These include price shocks, as employed above, and shocks to funding through the cash provider,

to redemptions through the hedge funds, and funding liquidity and related credit effects through

the bank/dealers. For all, we can show the propagation of the initial shock.

34

Table 4: A Multi-Period Illustration of Interaction Between Agents Starting with a Shock to Asset1 (A1), then Providing Snapshots for Periods 2, 4, and 6.

Network Graph of Base Model Description of Events

Period 0 The market is in an equilibrium state where theBank/Dealer 1 and Hedge Fund 1 hold Asset 1,they are directly affected by the shock. CashProvider 1 is also affected because the value ofcollateral declines. In a static stress test, theanalysis ends at this point.

Period 2 Bank/Dealer 1 and Hedge Fund 1 decrease theirpositions in both Asset 1 and Asset 2, result-ing in a drop in Asset 2. This affects otheragents with holdings in Asset 2, in particu-lar, Bank/Dealer 2 and Hedge Fund 2. CashProvider 1 is affected because it holds collateralin Asset 2 as well as in Asset 1.

Period 4 The propagation from the shock leads to adefault of Bank/Dealer 1 and Hedge Fund 1.Credit exposure that Bank/Dealer 2 has toBank/Dealer 1 spreads problems through thecredit channel. The drop in Asset 2 affectsHedge Fund 2, and its forced sales spread theshock to A3. Note that no entities holding theshocked asset also hold Asset 3. Cash Provider1 markedly reduces its funding due to the dropin the value of its collateral.

Period 6 Funding in the system is eventuallyall but shut off, and both hedge funds andBank/Dealer 1 default. Asset 2 ultimately suf-fers a greater price drop than Asset 1, which wasthe asset originally shocked.

Note: The thickness of the edges indicates the cumulative effect on, and the coloring within the agent symbolsindicates the total value of price in the case of assets, capital in the case of the bank/dealers (BD) and hedge funds(HF), and funding in the case of the cash provider (CP). The darker the coloring of the edge, the more recent theeffect.Source: Author’s model.

35

Table 5: Examples of the Initial Effect of Types of Shocks

Price Shock Funding Shock

Liquidity / Credit Shock Redemption Shock

Note: Price shocks initially affect hedge funds and bank/dealers holding the asset, as well as the cash providerholding the asset as collateral. A funding shock passes from the cash provider through the bank/dealer to the finalfunding users; a credit shock pass from the agent under credit stress to counterparties and providers of funding; anda redemption shock affects the assets held by the agent facing redemptions.Source: Author’s model.

36

7 Conclusion

This paper contributes an agent-based model that gives a broad view of the transformations and

dynamic interactions in the financial system. Our model provides an avenue toward highlighting

and monitoring key crisis dynamics such as fire sales and funding runs. Using a map of funding and

collateral flows, the model links these flows to asset markets, providing a structure for examining

the effect of the individual firms’ actions on each other.

This study integrates several related literatures into a multi-agent framework that incorporates

the major market participants in the U.S. asset and funding markets. By extending the Cifuentes

et al. (2005) model and integrating the behavior of market participants on both the funding and

borrowing sides, we demonstrate how stresses on these firms can cause pricing consequences and

feedback effects which are not Gaussian distributed. By comparing the results of our model to var-

ious traditional risk measures, we show the limitation of these measures in capturing the outcomes

caused by vulnerabilities in the financial system.

This study demonstrates the importance of capturing various interconnected, network-like re-

lationships among the market functions, which when stressed can cause reverberations across the

financial system. Previous studies have shown that feedback cycles are integral to explaining how

the credit crises in 2008 unfolded (Brunnermeier and Pedersen (2009); Tasca and Battiston (2016)).

By integrating market asset price correlations through overlapping portfolios with funding networks,

our model generates these same feedback cycles. While the model presented in this paper is more

stylized than required for central bank stress testing, it provides an existence proof of a prototype

for macroprudential, stress testing. As such, this study represents a critical step toward creating

an operational model for integrating stress testing across firms.

37

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Appendix

Table 6: Model Variable Glossary

Bm Price elasticity of demand for asset m

φCW Global parameter that governs the impact of Bank/Dealer k going belowLiqRatioMin on its CW k

φHC Global parameter that governs the impact of Bank/Dealer k going belowLiqRatioMin on its HCc,k

An Assets held by Bank/Dealer k or Hedge Fund n

AAllocationn Vector of % of assets m allocation for Bank/Dealer k or Hedge Fund n

ATargetn Target quantity of assets held by Bank/Dealer k or Hedge Fund n

C The number of Cash Provider in the model

CAn Collateral of Bank/Dealer k or Hedge Fund n

CAHFk Collateral of Hedge Funds using Bank/Dealer k

CAPBk Collateral of Prime Broker of Bank/Dealer k

CATDk Collateral of Trading Desk of Bank/Dealer k

Capn Capital of Bank/Dealer k or Hedge Fund n

CEK−1 Credit exposure of Bank/Dealer k to another Bank/Dealer K − 1

CETotalk Credit exposure of Bank/Dealer k to all the other Bank/Dealers

CWk Creditworthiness of Bank/Dealer k

EDSn Funding driven sales of Bank/Dealer k or Hedge Fund n

Fn Funding to Bank/Dealer k or Hedge Fund n

FPBk Funding to Prime Broker of Bank/Dealer k

F TDk Funding to Trading Desk of Bank/Dealer k

HCc,k The haircut Cash Provider c give to Bank/Dealer k

K Number of Bank/Dealers in the model

Lc,k Loan Cash Provider c gives to Bank/Dealer k

LMaxc,k Loan maximum of Cash Provider c for Bank/Dealer k

LTargetc,k Loan target of Cash Provider c for Bank/Dealer k

LevBuffern Leverage buffer of Bank/Dealer k or Hedge Fund n

LevCurrentn Current leverage of Bank/Dealer k or Hedge Fund n

LevMaxn Leverage maximum of Bank/Dealer k or Hedge Fund n

LevTargetn Leverage target of Bank/Dealer k or Hedge Fund n

LevBufferRaten Percent of LevMax

n that Bank/Dealer k or Hedge Fund n sets LevBuffern

LevTargetRaten Percent of LevBuffer

n that Bank/Dealer k or Hedge Fund n sets LevTargetn

Liqdebit Liquidity reserve debit

LiqRk Liquidity ratio of Bank/Dealer k

LiqRatioMink Liquidity ratio minimum of Bank/Dealer k

LiqRatioTargetk Liquidity target of Bank/Dealer k

M Number of assets in the model

N Number of Hedge Funds in the model

Nk The subset of N Hedge Funds that Prime Broker of Bank/Dealer k works

On,m(t)Sum of all normal orders for buying or selling assets by Bank/Dealer kor Hedge Fund n

Pm Price of asset m

PLm Previous day’s trading profit/loss accounting for asset m

PRm Price return for asset m

PRRm Random price movement which is N(0,m)

Qn,m Quantity of asset m held by Bank/Dealer k or Hedge Fund n

QMaxk Quantity of assets that a Bank/Dealer k can sell in a single period

t The current period of the model

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Table 7: Model Parameters

LevTarget 0.85Adrian and Shin (2013) that leverage targets tend tobe close to the maximum leverage level.

HC(0) 0.13 Price return for asset m.

LiqR 0.3The levels specified for the liquidity coverage ratio inBasel Committee on Banking Supervision (2013).

Bm

10 basispoints per$10 billion

Greenwood et al. (2015) use a market impact of 10basis points per $10 billion of liquidation.

P (0) 100 Author’s Choice

Capk(0), Capn(0) 10 Million Author’s Choice

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An Agent-based Model for Financial Vulnerability

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