Networks n Fnance and Marketng I Prof. Dr. Danng Hu Department of Informatcs Unversty of Zurch Nov 26th, 2012
Outlne n Introducton: Networks n Fnance n Stock Correlaton Networks n Stock Ownershp Networks n Board Drector Networks n Bank Networks n Ref Book: The Network Challenge: Strategy, Proft, and Rsk n an Interlnked World, Paul R. Klendorfer, Yoram J Wnd, Robert E. Gunther 2
Introducton: Networks n Fnance n Networks that are based on relatonshps n Fnance doman: Stock correlatons Stock ownershps Board of Drectors Inter-bank Market/Transactons/Payments NOT Network n economcs (e.g., supply chan networks) n The most complex system s human behavor! In fnancal markets, stock prce movements are largely nfluenced by behavors of dfferent tradng partes (human bengs). n Econophyscs ams to understand the tradng behavors by modelng the prce statstcal propertes of a stock through a model of agents tradng t.
4 Modelng Market Rsk: Stock Correlaton Networks Based on Modern Portfolo Theory, the market rsk of a portfolo of stocks can be calculated as the sum of the co-varance of each stock pars return of an ndvdual stock s calculated as r ( τ ) = ln P( τ ) ln P( τ 1) The correlaton between the returns of and j can be calculated as ρ j = r r j r r j ( r 2 2 r )( r 2 2 j r ) j The lnk dstance between stock and j can be calculated as d = 2 (1 ρ,, j j )
Correlaton based mnmal spannng trees of real data from daly stock returns of 1071 stocks for the 12- year perod 1987-1998 (3030 tradng days). The node colour s based on Standard Industral Classfcaton system. G. Bonanno, G. C., F. Lllo, R. Mantegna.PRE E 68 046130 (2003).
Stock Ownershp Networks Garlaschell et al. Physca A, 350 491 (2005).
Board Drector Network Multple Interlock Bpartte Network: two dfferent knd of nodes lnks between dfferent groups. Projecton Lnk vertces of the same group Weght Consder Weght! Varous, see Ref n Battston et al. EPJB, 350 491 (2005).
Interbank Payment/Loan Networks De Mas et al. In preparaton.
Fnancal Network Analyss n Fnancal Networks Analyss can help In dstngushng behavors of dfferent markets In vsualzng mportant features as the chan of control In testng the valdty of market models n Many of these fnancal networks are scale-free networks. Thus dfferent network models can be tested aganst such emprcal fnancal networks.
Case I: The Small-World of Investng n Socal Networks on Informaton Transfer n Stock Market connectons between mutual fund managers and corporate board members va shared educaton networks. academc nsttutons attended for both undergraduate and graduate degrees as our network measure n The major fndngs are portfolo managers place larger bets on frms they are connected to through ther network perform sgnfcantly better on these holdngs relatve to ther non-connected holdngs. (7.8% per year) postve returns concentrated on news announcements
Case II: Network Analyss of Bank Systemc Rsk In a bankng system, systemc rsk s the rsk of contagous bank falures that leads to the system-wde breakdown. A close call: 2008 fnancal tsunam Two major sources: nterbank payment and correlated fnancal portfolos Correlated rsk exposures n banks fnancal asset portfolos: X Y Z Banks A B C Interbank payments Fgure.5. An example of contagous bank falures 11
Research Questons and Desgn Research Questons: How to predct contagous bank falures n a gven crss scenaro? Whch banks to nject captal frst to stop contagon n a gven scenaro? We propose a Network Approach to Rsk Management (NARM) A Network Model of Systemc rsk Systemc Rsk Estmaton Algorthm Fnancal Crss Smulaton Model correlated portfolo lnks (Fnancal prncples) Predct contagous bank falures Smulated economc shocks The network model of systemc rsk Hgh systemc rsk scenaros Model nterbank payment lnks (Network prncples) Recommend banks for captal njecton 12 Smulated captal njecton
Modelng Systemc Rsk (Fnancal Prncples ) Based on Modern Portfolo Theory, the systemc rsk a bank contrbutes to the bankng system from correlated portfolos: j L calculated as G() = w w j σ σ j ρ j proxy of rsk from correlated portfolos: return covarance wth lnked banks We then construct the correlated portfolo lnks between and j by calculatng ρ j = r r j r r j ( r 2 2 r )( r 2 2 j r ) j ρ j > 0.5 Interbank clearng payment vector: p * = F + N d j= 1 π 0 j p * j + e f f f d F > F * p + F + (.e., s ablty to pay). N j= 1 + N j= 1 π N j j= 1 π j p π * j p j * j + e p * j + e + e d < 0 13 0
Modelng Systemc Rsk (Network Prncples) Correlatve Rank-In-Network Prncple (CRINP): The mportance of a node depends on the number of s ncomng lnks the mportance of the nodes that lnks to Nodes use lnks to transmt ther nfluences/recogntons to others; such recogntons n turn buld up the mportance of lnked nodes. Ctaton mpact factor, Webpage rankng (e.g., Google s PageRank) Systemc rsk n bankng systems Hyperlnk-Induced Topc Search (HITS) Algorthm 14 Authorty score estmates the mportance of a web page p Au( p) = n =1 Hub() Hub score estmates the nfluences of page p s outgong lnks n Hub( p) = Au() =1
Research Desgn BI Algorthm Development A Network Model of Systemc rsk Model correlated portfolo lnks (Fnancal prncples) Systemc Rsk Estmaton Algorthm Predct contagous bank falures Fnancal Crss Smulaton Smulated economc shocks The network model of systemc rsk Hgh systemc rsk scenaros Model nterbank payment lnks (Network prncples) Recommend banks for captal njecton Smulated captal njecton 15 15
Lnk-Aware Systemc Estmaton of Rsks (LASER) Algorthm Based on HITS, we ntegrated MPT-based systemc rsk and CRINP by teratvely calculatng Authorty score of bank measures the relatve systemc rsk receves from ts lnked banks: j A Au = G( j) u U O j O u Hub j Hub score of measures the relatve systemc rsk bank contrbutes to ts lnked banks: j C Hub = G( j) v V I j I v Au j G() = j L w w j σ σ j ρ j represents the systemc rsk orgnatng from the correlated fnancal portfolos O j O u # I & j % $ I ( v ' models the mpacts of dfferent amounts of payments
Research Desgn A Smulaton-based Evaluaton Experment A Network Model of Systemc rsk Model correlated portfolo lnks (Fnancal prncples) Systemc Rsk Estmaton Algorthm Predct contagous bank falures Fnancal Crss Smulaton Smulated economc shocks The network model of systemc rsk Hgh systemc rsk scenaros Model nterbank payment lnks (Network prncples) Recommend banks for captal njecton Smulated captal njecton 17 17
A Smulaton-based Evaluaton Experment: Dataset Federal Depost Insurance Corporaton (FDIC) dataset: quarterly reports of major U.S. banks condton and ncome balance sheets, ncome statements, and other supervsory data Tme Span No. of Quarters No. of Reportng Banks No. of Reports Average number of reportng banks per quarter 2001-2010 38 7,822 281,401 7,405 Smulated nterbank payments for each scenaro based on emprcal fndngs on the Fed Wre network topology (Soramäk 2007) densty (0.30%), average path length (2.62), average degree (15.2), etc. quarterly statstcs of U.S. Fed wre Interbank settlement servce. http://www.federalreserve.gov/paymentsystems/fedfunds_qtr.htm 18
γ β < 1.4, ranges from 4.9% to 12.5%. β 1.5, γ ncreases drastcally. β =1.7, γ = 54%, System-wde breakdown Results: Average Bank Falure Rates Average Bank Falure Rate γ 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Average Bank Falure Rates of Generated Scenaros at Dfferent Shock Rates 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Shock Rate β The U.S. bankng system can sustan mld smulated economc shocks untl the shock rate β 1.5. focusng on 1.9 β 1.5 19
Results: Predctng Contagous Bank Falures LASER Authorty score outperforms other benchmark methods Captal Adequacy Rato (CAR) 20
Results: Determne Captal Injecton Prorty LASER Hub score outperforms other benchmark methods n stoppng further contagous falures. 21
Applcatons: Stress Testng n Bankng Systems NARM (LASER and the smulaton methods) can be mplemented as stress testng nformaton systems. Intended users: Early warnng on possble contagous bank falures Decson support n Balout polcy makng Fgure.6. Screenshots of an prototype for NARM 22