Rama Cont, University of Oxford


Deleveraging by financial institutions in response to losses may lead to contagion of losses across institutions with common asset holdings. Unlike direct contagion via counterparty exposures, this channel of contagion - which we call indirect contagion - is mediated through market prices and does not require bilateral exposures or relations. We show nevertheless that indirect contagion in the financial system may be modeled as a contagion process on an auxiliary network defined in terms of 'liquidity weighted portfolio overlaps' and we study various properties of this network using data from EU banks. Exposure to price-mediated contagion leads to the concept of indirect exposure to an asset class, as a consequence of which the risk exposure of a portfolio strongly depends on the asset holdings of large institutions in the network. We propose a systemic stress testing methodology for evaluating this risk exposure and construct a simple indicator of bank-level exposure to indirect contagion – the Indirect Contagion Index – based on the analysis of liquidity-weighted overlaps across bank portfolios. This indicator is shown to be strongly correlated with bank losses due to deleveraging and may be used to quantify the contribution of a financial institution to price-mediated contagion.  
This is joint work with Eric Schaanning (European Systemic Risk Board).

Tuesday, February 5th, 2019
11:00 AM - 12:30 PM
1011 Evans Hall

[1] Rama Cont, Eric F Schaanning (2016) Fire Sales, Indirect Contagion and Systemic Stress Testing. https://ssrn.com/abstract=2541114
[2] Rama Cont, Eric F Schaanning (2017) Monitoring Indirect Contagion.  https://ssrn.com/abstract=3195174

Credits and Thanks to the Consortium for Data Analytics in Risk @ Berkeley.

My Seminar Notes/Outline:

Bank stress tests have become an essential component of bank supervision.

Stress tests assume ‘passive’ behavior by banks, which is a fundamental flaw.

“Stress tests conducted by bank supervisors still lack a genuine macro-prudential component” .. “ endogenous reactions to initial stress.. loss amplification mechanisms and feedback effects” are missing [BCBS 2015]

Financial institutions subject to portfolio constraints (capital, liquidity, leverage constraints) unwind positions when faced with large losses

Question: Does the bank have enough capital to withstand a given shock?
Result: Comes down to solvency and illiquidity.

Initial shock to assets -> cycle of [ deleveraging -> market impact -> mark to market losses -> deleveraging]

Assumption: we assign linear weights to the ordering of categories by liquidity of assets (higher weight to liquid assets, lower weight to illiquid assets). This models sale of liquid assets first before the illiquid assets.

Loss amplification from portfolio deleveraging

1 – Portfolio holdings of financial institutions by asset class: N institutions, K illiquid asset classes, M marketable asset classes -> N x ( M + K ) portfolio matrix (network)

2 – Portfolio constraints: capital ratio, leverage ratio, liquidity ratio, … -> range of admissible portfolios (“safety zone”)

3 – Reaction : of bank when its portfolio exits the admissible region (deleveraging / rebalancing)

4 – Market impact : market prices react to portfolio rebalancing

5 – Mark-to-market accounting: transmits market impact to all institutions -> may lead to feedback if market losses are large (loss contagion works here; transmission of losses occurs through common holdings)

[all linear constraints; if we use variance, it’d still be convex]

We want to quantify risk weights, using projections.

Leverage ratio of \i <= \lambda_max
Capital ratio of \i = RWA(i) / C^{i} <= \lambda_max

(where RWA(i) = risk weighted average)

Observation of deleveraging: when portfolio constraints are breached following a loss in asset values, financial institutions deleverage their portfolio by selling some assets in order to comply with the portfolio constraint

If following a loss L^I in asset values, leveraging of bank \i exceeds constraint \lambda, bank deleverages by selling a proportion \Gamma^I \in [0,1] of assets in order to restore a leverage ratio. If we reach the set constraint for loss threshold, we don’t sell; but if we don’t, we sell a proportion.

Market impact is linear(ized) \psi_\mu(x) = x / D_{\mu} (where D_{\mu} is market depth)

Mark-to-market loss of \i resulting from fire sales is based on \Omega_{ij} , the “liquidity weighted overlap” between portfolios \i and \j

=>  Loss contagion = contagion process on network defined by [\Omega_{ij}]

Result of application to EU data: we see that largest “liquidity weighted overlap” occur between the largest banks, which means that they hold relatively similar portfolios.

-          A stress scenario is defined by a vector \epsilon \in [0,1]^K whose components \epsilon_k are the percentage shocks to asset class k

-          Initial/Direct loss of portfolio

-          We consider the BA stress scenarios used in the actual EU 2016 stress test and modulate the shock sizes \epsilon_k from 0% to 20%

-          Examples of stress scenarios

o   Spanish residential and commercial real estate losses

o   Northern Europe residential losses

o   Southern Europe commercial real estate losses

o   Eastern Europe commercial real estate losses

-          Our model allows to distinguish between failures due to insolvency (negative equity) and failures due to illiquidity (zero liquid assets)

Indirect exposures

Consider two institutions (A) and (B).

  • A and B hold a common financial asset (say, gov bonds). A holds an illiquid asset (‘subprime’) that B does not hold. Notional exposure of B to ‘subprime’ is zero.
  • However, in the event of a large loss in ‘subprime’ assets, A may be forced to sell some of its bonds, pushing down their market price, resulting in a market loss for B (there is an indirect contagion when someone else holds an asset you do and sells).
  • So, B experiences a loss following a large shock to ‘subprime’ assets: B has an (indirect) exposure to an asset it does not hold!
  • Magnitude of this indirect exposure is directly linked to the overlap between B and institutions holding this asset
  • Institutions with large holdings will be …

(Total loss) = (Direct loss) + (Indirect loss through contagion)

Being in a financial systemic network, we have to consider indirect losses, else face large unexpected indirect losses

Regulator can run these stress tests to a particular bank to let it know its exposure to risk, but cannot release to competitors.

Monitoring exposure to fire sales

Price mediated contagion can be modeled as a contagion process on a network whose nodes are financial institutions and whose links are weighted with liquidity weighted overlaps.

Eigenvalue is highest for rank 1  network matrix, and goes down rapidly for rank = 2,3,4, …

This means that we can essentially model the entire network by a single portfolio (very bad).

Define: Indirect Contagion Index (ICI) of a financial institution \i as its component U_i in the (normalized) principal index.

We currently look at direct exposures to measure inter-connectedness, but these are very small (already hedged) compared to indirect exposures.

We take ICI (indirect contagion index) as a measure of exposure to fire sales loss [regression of log(F Loss) on log(ICI) for a given % shock at estimated market depth.

-          This gives R^2 = 0.89 for 13$%

First round loss affects the most, and less (but still affected) by the subsequent rounds of losses.


CAPM tells us everyone should hold the same portfolio, but we see from this perspective that diversification and diversity are different. Having diversification pushes portfolios to being similar (of course, banks have similar business structures), but in terms of contagion, this is the worst-case situation.

So, from the example that HSBC does not hold loans to Spanish loans to Spanish households, this shows our failure to truly follow the CAPM. Our model shows the two extremes are both bad (no diversification and too much/complete diversification).


Thus we should have regulation show indirect indirect losses.

Response from regulators (to this presentation): Already know these results, just increase the % shock threshold.

However, we see that indirect contagion effects cannot be mimicked by scaling up micro shocks.

-          Scaling up the macro shocks can replicate the average bank loss but not the cross-sectional distribution of losses across banks.

Equate total losses and compare scaling approach for loss with contagion and without contagion. We see that the distribution is not the same for each. So we should expect biased results, such as an overestimate for big banks, and an underestimate for small banks. This will not correctly localize risk in the system.