EFFICIENCY AND STABILITY OF A FINANCIAL ARCHITECTURE WITHTOO-INTERCONNECTED-TO-FAIL INSTITUTIONS

MICHAEL GOFMAN, UW-MADISON

August 28, 2014

• Study efficiency-stability trade-off for different financial architectures.

Implication for the desired structure of the financial system

Implications for the costs and benefits of too-interconnected-to-fail banks and whether they are systemically important

Implications for understanding the relationship between contagion and diversification of banks

Comparative statics on a calibrated network by holding the density constant and decreasing heterogeneity across banks in the number of counterparties

Use a model with endogenous exposures between banks to compute market efficiency before and after contagion

Objectives

Trading Model:

Mapping from endowments to equilibrium allocations for any possible network of trading relationships

The Proposed Framework

Financial Architecture

Unobservable:

Network of trades:- Density- Max in-degree- Max out-degree- Diameter- Size

Prices, profits, volume

Efficiency

Unobservable:

Observable:

Financial Architecture

Price-setting mechanism: bargaining, auctions.

Financial Architecture – Network of Trading Relationships

Distribution of endowment and valuations shocks

Stability

Illustration of the Model

1Initial allocation:E(1)=1

V(1)=0.3 V(2)=0

Privatevalue: V(5)=0.6

V(4)=1Feasiblefirst-bestallocation

V(3)=0

2 3 4

5

Valuation: P(5)=0.6

P(1)=0.525 P(2)=0.5625 P(3)=0.75 P(4)=1

Welfare loss = 1-0.6=0.4Surplus loss =welfare loss/first-best surplus = 0.4/(1-0.3)=0.57

,𝐵𝑖=1−0.5

𝑁 (𝑖 ,𝑔)

Model Fit: Visualization

Equilibrium daily network of trades in the model. Only one third of all trading relationships are equilibrium trades.

Network of trades in the Fed funds market on September 29, 2006 Source: Bech and Atalay (2010)

Model Data

Equilibrium Network of Trades: Model vs. Data

* Data Source: “The Topology of the Federal Funds Market” Bech and Atalay , Physica A, 2010

3 parameters to match 5 moments using SMM, 5 std. dev. (not targeted) also match well.

Efficiency Before and After Contagion

• Failure of the most interconnected bank triggers failure of counterparties with exposure above 15%.

• Exposure of bank A to bank B = loans from A to B / all loans by A.

Average Cascade Size from Failure of the Most Interconnected Banks

• Between 30% to 55% of banks fail due to endogenous contagion.

• The number of bank failures is non-monotonic.

Comparative Statics with Six Banks

Contagion Scenario with Cumulative Losses (Preliminary)

• Cascade is triggered by failure of the most interconnected bank

• A bank fails if exposure to all banks failed in the past is above 15%.

20 40 60 80 100 120 140 1600

200

400

600

800

1000

Maximum Number of Counterparties

Number of failed banks

• Efficiency is as important as stability but it is frequently omitted in policy discussions and is rarely quantified.

• Bridging the gap between theory and empirics is important for financial regulation. To compute efficiency we need to use some trading model, the calculation is more reliable if the model can also match the data.

• Using a trading model to compute endogenous exposures between banks is important for studying contagion risk.

• To understand the costs and benefits if too-interconnected-to-fail banks the comparative statics should be with respect to the variance of the degree distribution, holding the mean of the distribution constant.

Final Remarks

• Cumulative contagion: a bank fails if exposure to all banks failed in the past is above a threshold.

• Add counterparty risk to the trading model.

• In addition to the dynamical allocation in the network of trading relationships, allow for non-iid shocks and study trading when traders anticipate they will receive position/negative shocks in the future. Might improve the fit of the model even further.

• Strategic network formation to narrow down what counterfactual network would form under regulation that puts constrains on banks.

Model Limitations and Future Work