1. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A AA 1

2.  Traditional Banking  Role of banks 2  Originate & distribute  Securitization  Pooling  Tranching  Insuring (CDS)  Dual purpose  Tradable asset  Collateral feeds repo market for levering  Channel funds Long-run repaymentProspect of selling off Maturity transformation Retail fundingWholesale funding (money market funds, repo partners, conduits, SIVs, …) Info-insensitive securities Demand depositsABCP, MTN, overnight repos, securities lending Demand deposits AL Loans (long- term) Equity ABCP/MTN AAA Loans (long- term) Equity BBB … SIV/Conduit

3. Changing banking landscape  Traditional Banking  Role of banks 3  Originate & distribute  Securitization  Pooling  Tranching  Insuring (CDS)  Dual purpose  Tradable asset  Collateral feeds repo market for levering  Channel funds Long-run repaymentProspect of selling off Maturity transformation Retail fundingWholesale funding (money market funds, repo partners, conduits, SIVs, …) Info-insensitive securities Demand depositsABCP, MTN, overnight repos, securities lending Demand deposits AL Loans (long- term) Equity ABCP/MTN AAA Loans (long- term) Equity BBB … SIV/Conduit

4. Two questions  Why is reaction so sharp?  Liquidity spirals (non-linear dynamics due to adverse feedback loop)  Real economic effects  macro model with financial sector (w/ Sannikov)  Too much leverage and maturity mismatch?  Identify and measure externalities (risk spillovers rather risk of a bank in isolation)  CoVaR (w/ Adrian) 4 ABS issuance Source: JPMorgan

5. Overview  Theory (with Sannikov)  Spirals: Non-linear adverse feedback loops + volatility effects  Externalities  Implementation (with Adrian)  CoVaR: measuring systemic risk contribution/externalities  One method: Quantile regressions  Addressing procyclicalites due to spirals 5

6. Brunnermeier-Sannikov (new) Entrepreneurs  Needs financing  Start projects (trees with payoff a t K t )  da t / a t =g dt +σ dZ t  capital depreciates  investment 6 Financial Experts  Monitoring (growth of a t )  Securitizes “trees” to expand investment Households  Provide financing DEBTDEBT EQU ITY AL outside inside Optimal dynamic contract direct financing a t grows slower

7. Role of financial experts in the economy: Entrepreneurs 7 Financial Experts Households Securitize investments and sell products to households Direct financing Provide funding more efficiently than direct lending Both entrepreneurs and households benefit from the financial sector

8. Model setup - overview Entrepreneurs  Needs financing  Start projects (trees with payoff a t K t )  da t / a t =g dt +σ dZ t  capital depreciates  investment 8 Financial Experts  Monitoring (growth of a t )  Securitizes “trees” to expand investment Households  Provide financing DEBTDEBT EQU ITY AL outside inside Optimal dynamic contract pσppσp

9. Model setup - overview Entrepreneurs  Needs financing  Start projects (trees with payoff a t K t )  da t / a t =g dt +σ dZ t  capital depreciates  investment 9 Financial Experts  Monitoring (growth of a t )  Securitizes “trees” to expand investment Households  Provide financing DEBTDEBT EQU ITY AL outside inside Optimal dynamic contract direct financing a t grows slower

10. Model setup: production of output and capital  Production of output (numeraire) (apples) : Y t = a t K t, where da t =  a t dZ t  Note everything will be scale invariant w.r.t. Y t  Production of capital K t (trees) : dK t = (Φ(I t /Y t ) -  ) K t dt,  Investment-ratio I t /Y t depends on  y t ν t price of capital (value of asset/tree)  i.e. ν t = price-earnings ratio dν t =  t ν dt+  t ν dZ t (price of a tree in terms of apples divided by y t )  max i {ν t a t K t Φ(i t /y t ) – i t } supply of capital: κ(ν t )K t 10

11. Financing of capital  All agents  risk neutral (for now)  common discount rate of   Direct financing through households (fraction 1-ψ t )  Growth of a is zero  ν t ≥ 1/(  +  )  Break even for HH 1-(  +  )ν t +  t ν +  t ν = 0 (HH)  Indirect financing through financial experts (fraction ψ)  Growth of a is g at cost b per y da t = ga t dt+  a t dZ t  Reduced form for better resource allocation (monitor, service mortgage, channel continuation funding)  ν t ≤ (1-b)/(  +  -g) 11 Capital appreciation earnings financing cost

12. Financing friction – optimal contracting  Expert’s incentive problem  effort choice, y t are non-contractable, but asset value ν t y t is  Incentive (“skin in the game”) constraint:  t gν t - b  0   t = b/(gν t )  Evolution of experts balance sheet  Asset side – long maturity d(ν t y t ) = y t (  t ν +(g -  )ν t +  t ν )dt + y t (  ν t +  t ν )dZ t  Liability side 1.Debt 1.Debt – overnight maturity 2.Outside equity 2.Outside equity: 1-  t 3.Inside equity 3.Inside equity dn t =  n t + y t [(1-b-(  +  -g)ν t +  t ν +  t ν )dt +  t (  ν t +  t ν ) dZ t ] 12

13. Competitive equilibrium  State variable:  t = N t /Y t d  t = …. (from Ito)  N t is aggregate wealth (net-worth) of financial experts  Y t is aggregate output (scale-invariant)  Solve in terms of  P/E ratio: ν t = ν(  t )  Expert i’s value function: f t n t = f(  t )n t  Fraction of indirect investment: ψ(  t ) ≤ 1  Expert i’s Bellman equation  n t f t dt = max y E[d(n t f t )] = max y {(  n t +y[1-b-(  +  -g)ν t +  t ν +  t ν ]) f t +n t μ t f +  t f y  t (  ν t +  t ν )} dt  FOC: [1-b-(  +  -g)ν t +  t ν +  t ν ] +  t f  t (  ν t +  t ν ) = 0 (FS)  Household  FOC: 1-(  +  )ν t +  t ν +  t ν =(<) 0 (HH) 13 precautionary motive =μ t n =σ t n

14. Competitive equilibrium  State variable:  t = N t /Y t d  t = …. (from Ito)  N t is aggregate wealth (net-worth) of financial experts  Y t is aggregate output (scale-invariant)  Solve in terms of  P/E ratio: ν t = ν(  t )  Expert i’s value function: f t n t = f(  t )n t  Fraction of indirect investment: ψ ≤ 1  Expert i’s Bellman equation  n t f t dt = max y E[d(n t f t )] = max y {(  n t +y[1-b-(  +  -g)ν t +  t ν +  t ν ]) f t +n t μ t f +  t f y  t (  ν t +  t ν )} dt  FOC: [1-b-(  +  -g)ν t +  t ν +   t ν ] +  t f  t (  ν t +  t ν ) = 0 (FS)  Household  FOC: 1-(  +  )ν t +  t ν +  t ν = 0 (HH) 14 precautionary motive =μ t n =σ t n 1 2 3

15. Competitive equilibrium  State variable:  t = N t /Y t d  t = …. (from Ito)  N t is aggregate wealth (net-worth) of financial experts  Y t is aggregate output (scale-invariant)  Solve in terms of  P/E ratio: ν t = ν(  t )  Expert i’s value function: f t n t = f(  t )n t  Fraction of indirect investment: ψ ≤ 1  Expert i’s Bellman equation  n t f t dt = max y E[d(n t f t )] = max y {(  n t +y[1-b-(  +  -g)ν t +  t ν +  t ν ]) f t +n t μ t f +  t f y  t (  ν t +  t ν )} dt  FOC: [1-b-(  +  -g)ν t +  t ν +   t ν ] +  t f  t (  ν t +  t ν ) = 0 (FS)  Household  FOC: 1-(  +  )ν t +  t ν +  t ν = 0 (HH) 15 precautionary motive =μ t n =σ t n 1 2 3 1 2 3

16. Function of experts’ networth/GDP 16 Marginal value of a $ Leverage P/E ratio GDP growth

17. Results 1: Non-linear dynamics - spirals  Fact 1: financial sector  increases growth but  may also increase volatility  Fact 2: Loss spiral  price is more volatile, as experts approach regime when they fire- sale assets  Fact 3: “Outside-equity spiral”  t = b/(gν t )  for low ν t, fraction of outside equity shrinks (difficult to raise because agency problem gets worse)  Fact 4: Leverage spiral  Leverage: [v(  t )ψ t –  t ]/[v(  t )ψ t ] 1. Internal: Own risk management for ψ t <1 2. External: Margin/haircuts spiral (see Brunnermeier-Pedersen, 09) 17

18. Introducing margin/haircut constraint  Level of debt is limited by  Incentive constraint (in aggregate) +haircut/margin constraint  Spirit: asset can only be sold with a delay  Haircut is multiple of price volatility h(  ν t +  t ν )/ ν t  Main changes  price-earning ratios go down  price volatility  goes up as long as haircuts don't binding (especially near the point where haircuts start binding)  goes down when haircuts bind  Experts value function rises (externalities – later)  Internal risk management is enforced Fear of haircut constraint becomes binding 18

19. Vol. and leverage with haircut constraints 19

20. Graphs with haircut constraints (red) 20

21. Graphs with haircut constraints (red) 21

22. Graphs with haircut constraints (red) 22

23. Results 2: Externalities – welfare  “Too much” leverage/maturity-mismatch due to externalities?  Financial regulation should focus on externalities  Within the financial sector  Between financial sector and real economy (entrepreneurs)  Two forms of inefficiencies:  Inefficient (pecuniary) externalities – regulatory correction for an instant  Dynamic externality - commitment problem within an institution 23

24. Result 2: Externalities – welfare  Focus within financial sector  Effect of one expert’s choice of y on value function of everybody: f(  ) (1-b+(  +  -g)ν t +  t ν +  t ν ) + f’(  ) σ t η  t (  p t +  t ν ) - f’(  )  2 g + (f’(  )  + f(  )) ψ t (d  t ν /dψ t +  d  t ν /dψ t ) + f’(  )  [1-b+(  +  -g)ν t +  t ν +  t ν ] + [f’’(  )  + f’(  )]  t   t (  ν t +  t p ) + [f’’(  )  + 2f’(  )]  t  ψ t  t d  t ν /dψ t. 24

25. Results 2: Externalities – welfare  Focus within financial sector  Effect of one expert’s choice of y on value function of everybody: f(  ) (1-b+(  +  -g)ν t +  t ν +  t ν ) + f’(  ) σ t η  t (  p t +  t ν ) - f’(  )  2 g + (f’(  )  + f(  )) ψ t (d  t ν /dψ t +  d  t ν /dψ t ) + f’(  )  [1-b+(  +  -g)ν t +  t ν +  t ν ] + [f’’(  )  + f’(  )]  t   t (  ν t +  t p ) + [f’’(  )  + 2f’(  )]  t  ψ t  t d  t ν /dψ t. 25 Affects the drift of η, and impacts other experts Affects the volatility of η, and impacts other experts Affects economic growth, and impacts other experts Zero in individual expert’s FOC

26. On externalities – welfare analysis  Focus within financial sector  Effect of one expert’s choice of y on value function of everybody: f(  ) (1-b+(  +  -g)ν t +  t ν +  t ν ) + f’(  ) σ t η  t (  p t +  t ν ) - f’(  )  2 g + (f’(  )  + f(  )) ψ t (d  t ν /dψ t +  d  t ν /dψ t ) + f’(  )  [1-b+(  +  -g)ν t +  t ν +  t ν ] + [f’’(  )  + f’(  )]  t   t (  ν t +  t p ) + [f’’(  )  + 2f’(  )]  t  ψ t  t d  t ν /dψ t. 26 (+) economic growth good for experts Zero in individual expert’s FOC Effect on value of other expert’s assets, through prices (-) profit causes η to grow, which hurts other experts (+) effect on expected value of cash(-) effect on expected value of assets Fire-sale externality

27. Externalities 27

28. Related Literature  End borrowers’ financing frictions  Bernanke-Gertler-(Gilchrist), …, Mishkin  Kiyotaki-Moore  Financial sector’s frictions – liquidity spirals  Brunnermeier-Pedersen  Diamond-Dybvig, Allen-Gale, …  He-Krishnamurthy  Dynamic contracting  DeMarzo-Fishman-Sannikov, … 28

29. Differences to Bernanke-Gertler-Gilchrist BGG 1. “small” aggregate shocks around steady state idiosyncratic shocks are essential  Default and associated costly state verification is more likely 2. Asset prices are driven by default (verification cost) due to idiosyncratic risk 3. Expert’s rent is always zero (?)  No incentive to keep “dry powder” (liquidity) … (No Bellman equ.) 4. Countercyclical leverage  Entrepreneur take on same position after drop in networth  Leverage increases after drop in net- worth 5. Debt vs. Equity 6. No fire-sale externality 29 BruSan 1. Focus on (large) aggregate shocks (idiosyncratic shocks not essential) (no restriction to steady state) 2. Asset price drops due to fire sales 3. Expert’s rent depends on state  t  Incentive to keep “dry powder” (liquidity) … 4. Procyclical leverage  Experts reduce position after drop in networth  Liquidity spirals 5. Securitization (debt, inside + outside equity) 6. Fire-sale externality (rationale for regulation)

30. Differences to Kiyotaki-Moore KM – (Kiyotaki version) 1. Zero-prob. temporary shock  Persistent (dynamic loss spiral)  Amplified through collateral value 2. Non- vs. productive (leveraged) sector 3. Dual role of durable asset 1. Production 2. Collateral 4. Exogenous contract  One period contract  Debt is limited by collateral value 5. Durable asset doesn’t depreciates (capital, fully) 30 BruSan 1. Permanent TFP shocks  Margin/haircut spiral (leverage)  Loss spiral 2. Investment through leveraged financial sector 3. Dual role of durable asset 1. Production 2. Securitization 4. Optimal contract  Dynamic contract  Debt is limited due idiosyncratic risk and costly state verification 5. δ-depreciation rate

31. Differences to He-Krishnamurthy He-Krishnamurthy 1. Endowment economy  GDP growth is exogenously fixed  No physical investment 2. No direct investment in risky asset by households  Limited participation model 3. Contracting  Only short-run relationship (t to t+dt)  Fraction of return, fee  Asset composition (risky vs. risk-free) is not contractable  Non-effort lowers return by xdt  x is exogenous,not linked to fundamental  Private benefit from shirking  No benchmarking 4. Pricing Implications  When experts wealth declines, their market power increases, and so does their fee  Price impact depends on assumption that household have larger discount rate than experts 5. Procyclical Leverage 6. In H-K calibration paper 1. No fee, households are rationed in their investment 2. As expert wealth approaches 0, interest rate can go to –∞ 3. Heterogeneous labor income for newborns of lD t 4. Non-log utility function 31 BruSan 1. Production economy  GDP growth depends on net-wealth  Physical investment 2. Direct investments by all households 3. Contracting  (Potential) long-run relationship  Fraction of return, fee, size of asset pool  Effort increases fundamental growth to gdt  Monetary benefit from shirking  No benchmarking 4. Pricing Implication  Price drop with state variable 5. Countercyclcial Leverage  Entrepreneur take on same position after drop in networth  Leverage increases after drop in net-worth

32. Conclusion  Incorporate financial sector in macromodel  Higher growth  Higher volatility  Main insights:  Adverse feedback loops  Externalities (rationale for financial regulation)  Within financial sector  Toward the real economy 32

33. Macro-prudential regulation  Externalities – “stability is a public good”  Fire-sale externality Fire-sales depress prices also for others  Volatility: Precautionary hoarding  uncertainty about future funding  …  Network externality: Hiding owns’ commitment  Uncertainty for counterparties (of counterparties …)  Countercyclical regulation – counteract spirals  Regulation strict during booms  Lean against credit bubbles  Incorporate funding structure 33

34. Overview  Theory (with Sannikov)  Spirals: Non-linear adverse feedback loops  Externalities  Implementation (with Adrian)  CoVaR: measuring systemic risk contribution/externalities  One method: Quantile regressions  Addressing procyclicalites due to spirals 34

35. “CoVaR” with Tobias Adrian  Systemic risk measure  Capture externalities and contribution to systemic risk  “Clone property”  Splitting one institution to 10 identical clones (which perfectly comove with each other) does not reduce systemic risk  Contrast to current regulation  focus on risk in isolation, VaR  incentive to hang on to others, become big, interconnected  procyclical  Amplify non-linearities even further 35 VaR 1%

36. Who should be regulated?  “Clone Property”  Split individually systemic institution i in 10 identical clones c: CoVaR i = 10 CoVaR c 36 groupexamplesmacro-prudentialmicro-prudential “individually systemic” International banks (national champions) Yes “systemic as part of a herd” Leveraged hedge funds YesNo non-systemic largePension fundsN0Yes “tinies”unleveredN0No

37. CoVaR – systemic risk measure  VaR q i is implicitly defined as quantile  CoVaR q j|i is the VaR conditional on institute i (index) is in distress (at it’s VaR level)  ΔCoVaR q j|i = CoVaR q j|i – VaR q j  Various conditionings? (direction matters!)  Contribution ΔCoVaR  Q1: Which institutions contribute (in a non-causal sense)  VaR system | institution i in distress  Exposure ΔCoVaR  Q2: Which institutions are most exposed if there is a systemic crisis?  VaR i | system in distress  Network ΔCoVaR  VaR of institution j conditional on i in non-causal sense! q-prob. event

38. Network CoVaR  conditional on origin of arrow 38 270 70 118 247 57 108 116 50 357 133 116 72 67 72 122 49 50 76 564 68

39. Overview  Theory (with Sannikov)  Spirals: Non-linear adverse feedback loops  Externalities  Implementation – CoVaR (with Adrian)  CoVaR: measuring systemic risk contribution/externalities  One method: Quantile regressions  Addressing procyclicalites due to spirals 39

40. Quantile Regressions: A Refresher  OLS Regression: min sum of squared residuals  Predicted value:  Quantile Regression: min weighted absolute values  Predicted value: 40 Note out (non-traditional) sign convention!

41. Quantile Regression: A Refresher 41

42. Financial Intermediary Data  Publicly traded financial intermediaries 1986-2008  Commercial bank, security broker-dealers, insurance companies, real estate companies, etc.  Weekly market equity data from CRSP  Quarterly balance sheet data from COMPUSTAT  CDS and option data of top 10 US banks, daily 2004-2008 42

43. Change in total asset value X i t  Change in total asset value (detrended)  where  A t + = market equity * leverage ratios  “detrend factor” 43

44. 44 VariableMeanStd. Dev.MinMaxObservations Returnsoverall0.2755.92-2430.042420.38N = 47895 between1.07-4.402.98n = 44 within55.91-2431.342419.08T-bar = 1088 Portfolio VaRoverall-105.59128.35-1547.03237.35N = 47895 between110.07-366.58-3.45n = 44 within71.16-1433.60493.51T-bar = 1088 Delta CoVaRoverall-500.76523.62-4956.012285.65N = 47895 between361.39-1262.44278.14n = 44 within383.75-4488.662533.57T-bar = 1088 Summary Statistics of Risk Measures OLD

45. ΔCoVaR vs. VaR  VaR and ¢ CoVaR relationship is very weak  Data up to 12/06 45

46. Overview  Theory (with Sannikov)  Spirals: Non-linear adverse feedback loops  Externalities  Implementation – CoVaR (with Adrian)  CoVaR: measuring systemic risk contribution/externalities  One method: Quantile regressions  Addressing procyclicalites due to spirals  Step 1: Time-varying CoVaRs  Step 2: Predict CoVaR using institution characteristics  Balance sheet variables (leverage, maturity mismatch, + interdependence, …)  Market variables (CDS, implied vol.,…) 46

47. Overview  Measuring Systemic Risk Contribution  One Method: Quantile Regressions  CoVaR vs. VaR  Addressing Procyclicality  Step 1: Time-varying CoVaRs  Step 2: Predict CoVaR using institution characteristics  Balance sheet variables (leverage, maturity mismatch, + interdependence, …)  Market variables (CDS, implied vol.,…) 47

48. Step 1: Time-varying CoVaR  Control for macro factors, M t interpretation  VIX Level“Volatility”  3 month yield  Repo – 3 month Treasury“Flight to Liquidity”  Moody’s BAA – 10 year Treasury“Credit indicator”  10Year – 3 month Treasury“Business Cycle”  Real estate index “Housing”  Equity market risk  Obtain Panel data of CoVaR  Next step: Relate to institution specific (panel) data 48

49. Step 1: Time-varying ΔCoVaR  Derive time-varying VaR t  For institution i:  For financial system:  Derive time-varying CoVaR t  ΔCoVaR t = CoVaR t - VaR t 49

50. Table 2: Average Exposures to Risk Factors 50

51. Table 1: Summary Statistic 51

52. Time-varying VaR 52

53. Time-varying VaR and ΔCoVaR 53

54. Step 2a: Portfolios Sorted on Characteristics  Institutional characteristics matter  … but individual financial institutions have changed the nature of their business over time  Form decile portfolios, each quarter, according to previous quarter’s data: 1. Leverage 2. Maturity mismatch 3. Size 4. Book-to-Market  Add 4 industry portfolios 1. Banks 2. Security broker-dealers 3. Insurance companies 4. Real estate companies 54

55. Table 3A: ΔCoVaR Forecasts by Characteristics Cross-section, Portfolios, 1% 55

56. Discussion of Table 3A  At 2-year horizon, all characteristics are significant  Leverage, maturity mismatch, size are positive related to systemic risk contribution  Higher book-to-market indicates less systemic risk  Two effects 1.Closeness to default boundary 2.Riskiness of assets  Latter effect seems to dominate 56

57. Table 3B: ΔCoVaR Forecasts by Characteristics Cross-section, 2 years 57

58. Discussion of Table 3B  Coefficients get larger further out in the tail, indicating more $-value of assets at risk in the tail  Coefficients appear significant, as before  In addition to including time effects as in Tables 3, we are adding fixed effects in Table 4  Shows the extent to which changes to future systemic risk can be forecasted over time 58

59. Table 4: ΔCoVaR Forecasts by Characteristics Time Series/Cross Section, Portfolios, 1% 59 Timing of tail risk is harder to forecast than cross-section contribution

60. Step 2b: Forecasting with Market Variables  CDS spread and equity implied volatility for 10 largest US commercial and investment banks (from Bloomberg)  Betas:  Extract principal component from CDS spread changes/implied vol changes within each quarter from daily data  Regress each CDS spread change/ implied vol change on first principal component 60

61. Table 6: ΔCoVaR Forecasts by Market Variables Cross Section, Portfolios, 1% 61 short data-span (2004-2008)!

62. Extension to our Analysis  Co-Expected Shortfall (“Co-ES”)  Advantage: coherent risk measure  Disadvantage: any estimate “in” the tail is very noise  Inclusion of additional information  derivative positions  off-balance sheet exposure  Crowdedness measure  Interdependence measures  Bank supervision information 62

63. Countercyclical Regulation  When market is relaxed Strict Laddered Response  Step 1: supervision enhanced  Step 2: forbidden to pay out dividends  See connection to debt-overhang problem)  Step 3: No Bonus for CEOs  Step 4: Recapitalization within two months + debt/equity swap  When market is strict Relax regulatory requirement 63

64.  Causal risk spill over effects  Non-causal 64 A B Adverse feedback loop - amplification ABC

65. Shock Amplifier vs. Absorber OLD 65 INSTITUTIONS VaR_index COEFFICIENT1 Year1.5 Years1 Year1.5 Years Fitted CoVaR_contrib (lag)4.46**6.43*** (1.91)(1.95) Resid CoVaR_contrib (lag)0.500.52 (0.40)(0.41) Fitted CoVaR_exp (lag)0.750.51 (1.42)(1.34) Resid CoVaR_exp (lag)2.94***3.95*** (0.57)(0.54) VaR_index (lag)0.30**0.13-1.25***-1.96*** (0.12) (0.33)(0.32)

66. What type of charge?  Capital charge  Strictly binding  Might stifle competition  Pigouvian tax + government insurance  Generates revenue  In times of crisis it is cheap to issue government debt  very salient  Private insurance scheme  (Kashap, Rajan & Stein, 2008 + NYU report)  Requires lots of regulation 66

67. Conclusion  Theory  Liquidity spirals - non-linear dynamics  Externalities  Macro-prudential regulation  Focus on externalities  Measure for systemic risk is needed, e.g. CoVaR  Countercyclical regulation  Find variables that predict average future CoVaR  Forward-looking measures, spreads, …  Also,  VaR measure is not sufficient – incorrect focus  Quantile regressions are simple and efficient way to calculate CoVaR 67