Discussion of Centrality-based Capital Allocations and Bailout Funds Alter, Craig, and Raupach (2014) Alireza Tahbaz-Salehi

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1 Discussio of Cetrality-based Capital Allocatios ad Bailout Fuds Alter, Craig, ad Raupach (2014) Alireza Tahbaz-Salehi Columbia Busiess School Aual Iteratioal Joural of Cetral Bakig Research Coferece Federal Reserve Bak of Philadelphia September 2014

2 Fiacial Networks Much recet iterest i the relatioship betwee systemic risk ad etwork effects, maily a cosequece of the Fiacial Crisis. Large body of recet, theoretical works direct cotractual likages fire-sales ad pecuiary exteralities etc. Sure, the models are theoretically ice, but are they relevat? Almost o quatitive/empirical aalysis.

3 This Paper Uses a very rich dataset to fill this void Extracts the iterbak etwork of the Germa bakig system A fairly elaborate model of baks balace sheets, exogeous shocks, ad the cotagio mechaism Mai Questio: whether policies that rely o etwork statistics ca improve stability of the system as a whole. Simulate the extet of cotagio uder differet policies Tax itercoectivity through capital charges (ex ate policy) (what I will focus o) A bailout fud based o etwork statistics (ex post policy)

4 Theoretical Framework (Simplified) istitutios/baks Baks have outside ad iterbak liabilities ad assets. The fiacial etwork captures the extet of iterbak liabilities. j i y ij Each bak holds some capital k i. Depositors ad other creditors are seior to iterbak creditors (v i ). Baks are subject to exogeous shocks to their assets ɛ real i.

5 Cotagio Mechaism If a bak defaults, its creditors get paid o a pro rata basis. The total out-paymet of bak i is equal to { { } } x i = max mi π ij x j + k i v i ɛi real, y ji, 0. where π ij = y ij / r=1 y rj. Solutio Cocept: the vector of iterbak paymets x = (x 1,..., x ) that solves the above system of equatios. Alteratively, if Li IB = y ji x i : { { Li IB = mi max π ij Lj IB + v i + ɛ real i k i, 0 } }, y ji

6 Cotagio Mechaism If a bak defaults, its creditors get paid o a pro rata basis. The total out-paymet of bak i is equal to { { } } x i = max mi π ij x j + k i v i ɛi real, y ji, 0. where π ij = y ij / r=1 y rj. Solutio Cocept: the vector of iterbak paymets x = (x 1,..., x ) that solves the above system of equatios. Alteratively, if Li IB = y ji x i : { { Li IB = mi max π ij Lj IB + v i + ɛ real i k i, 0 } }, y ji

7 Cotagio Mechaism Shocks propagate over the iterbak likages. (a variat of the model of Eiseberg ad Noe, 2001) If a bak defaults, there is a bakruptcy costs of C i proportioal to the bak s size. Total deadweight social loss: L agg = C i 1{i defaults} i=1 Set capital requiremets to miimize E[L agg ].

8 Network Cetralities Set capital requiremets based ot oly o baks idividual riskiess (VaR), but also some widely used etwork statistics of the baks. Cetrality of bak i: c i : R + R + Examples: the size of i s total iterbak assets c i = y ij eigevector cetrality: c is the eigevector of the liabilities matrix c i = y ji c j.

9 Network Cetralities Set capital requiremets based ot oly o baks idividual riskiess (VaR), but also some widely used etwork statistics of the baks. Cetrality of bak i: c i : R + R + Examples: the size of i s total iterbak assets c i = y ij eigevector cetrality: c is the eigevector of the liabilities matrix c i = y ji c j.

10 Network-Based Capital Requiremets Set capital requiremets based o cetralities ad a o-etwork bechmark: k i = βk VaR i + (1 β) Choose β such that L agg is miimized. ( c i c j ) kj VaR The ratioale beig that shocks to more cetral baks would propagate more.

11 Mai Results: Capital Requiremets Settig capital requiremets based o total assets leads to the most improvemet. Aside from the size of total assets, capital requiremets based o Opsahl cetrality provide the best performace.

12 Commets First Observatio: capital rules based o size outperform all other cetrality measures. However, size is hardwired ito the performace measure: Larger baks are assumed to have a higher bakruptcy cost. Not surprisig that the capital allocatios best o size domiate all other metrics.

13 Commet: What is the Right Network Statistic? The paper relies o a specific structural model of iterbak cotagio. So why ot rely o the etwork statistic that is implied by the structural model? I fact, off-the-shelf measures ca be misleadig i idetifyig systemically importat fiacial istitutios.

14 A Simple Liear Ecoomy Suppose that spillovers are liear: Li IB = π ij Lj IB + ɛi real. Total losses: Lagg IB = Li IB. i=1 I such a ecoomy: dl agg dɛ j = eigevector cetrality of bak j

15 Network Statistics Eigevector cetrality is the correct otio for systemic importace of a fiacial istitutio if iteractios/spillovers are liear. (or at least, whe the iteractios are smooth, so that ca be liearly approximated). This may ot geeralize to a ecoomy with o-smooth iteractios: debt cotracts bakruptcy costs etc.

16 No-Smooth Iteractios: Debt Cotracts Cosider a ecoomy i which all baks are of equal sizes: (idetical iterbak assets ad liabilities) y ij = y ji = y. All baks have idetical eigevalue cetralities. Also, suppose that baks are liked via stadard debt cotracts (as i the curret paper): { Total losses: L IB i = mi y, max { 0, π ij Lj IB + ɛ real i L agg = C 1{i defaults} i=1 k }}

17 Network Statistics Harmoic distace of bak i from bak j m ij = 1 + π ik m kj. k =j Propositio (Acemoglu et al., 2014) Suppose bak j is hit with a large eough shock. The, bak i defaults if ad oly if m ij m for some m. Despite the fact that all baks have the same eigevector cetrality, weighted out-degree, weighted i-degree, Boacich cetrality,...

18 Network Statistics Implicatio: A bak is systemically more importat the shorter the harmoic distaces of other baks to it are. Ituitio: with liear iteractios, positive ad egative shocks propagate symmetrically, but ot if the iteractios are ot smooth. More importatly: the correct otio of cetrality should come from the structural model of etwork iteractios.

19 Commet: Equilibrium Multiplicity Itroducig bakruptcy costs: suppose that there is a drop i the value of a bak s assets if it defaults: { { }} Li IB = mi y, max 0, π ij Lj IB + ɛi real + C 1{i defaults} k Because of the discotiuity, the ecoomy may have multiple equilibria. The paper focuses o the equilibrium with the miimum losses.

20 Commet: Equilibrium Multiplicity The set of systemically importat baks may deped o the equilibrium selected. I the best eq. baks o the left are more systemically importat. I the worst eq. baks o the right are more systemically importat. Optimal capital requiremets may be sesitive to the equilibrium selected.

21 Summary Very importat ad relevat work: May theoretical studies, but almost o quatitative aalyses of the mechaisms studied i the literature The paper fills a importat void. Mai commet: the proper etwork statistic/momet should be a cosequece of the structural model of iterbak spillovers. Off-the-shelf etwork statistics ca be misleadig. Equilibrium multiplicity would make the picture more complicated.