Weak & Strong Systemic Fragility

1. Weak & Strong Systemic Fragility Casper G. de Vries Erasmus University Rotterdam & Tinbergen Institute

2. Contents • Current Credit Crisis • Fat Tails • Multivariate Fat Tails • Systemic Risk Measure • Bank Networks • Hedge Fund Application • Estimation • Conclusion

3. Banks & Systemic Risk A Reality Check

4. Current Crisis Aspects • History: Savings glut & Low interest produced Credit binge big time • Basel I stimulates Conduits formation to shift mortgages off-balance & repackaging of risk • Interest rate tightening triggers mortgage failures; Basel II 2008 start brings on-balance fears • Asymmetric information about conduits, non-market over the counter instruments, turns money market into market for lemons

5. Two Crucial Crisis Features • I/ Asymmetric Information • II/ Interconnectedness of Banks and other Vehicles

6. I/ The Asymmetric Information Problem • The Old Lady meets the Old Maid, or … Payoff if win: W Probability to win: 3/4 Payoff if loose: -L Probability to loose: 1/4 Willingness to play if not dealt the old maid if: 3/4W-1/4L>0 Thus play if: W/L>1/3

7. The Old Lady meets the Old Maid Probability to win: 3/4 Payoff if win: W autarky Payoff if loose: -L Probability to loose: 1/4 Willingness to play if not dealt the old maid if: 3/4W-1/4L>0 Subprime woes lead to risk reassessment such that L increased and: W/L<1/3

8. II/ Bank Network System Banks are highly interconnected: directly • Syndicated Loans • Conduits • Interbank Money Market indirectly • Macro interest rate risk • Macro gdp risk

11. Fat versus Normal:2 Features • Univariate: More than normal outliers along the axes • Multivariate: Extremes occur jointly along the diagonal, systemic risk is of higher order than if normal (market speak: market stress increases correlation)

12. Basel Motivation • Systemic Risk of banks is important due to the externality to the entire economy • Motive for Basle Accords & why banks are stronger regulated than insurers (Solvency) • Surprise is micro orientation of Basle II, rather than macro approach • Improper information to supervisor; overregulation or too little?

13. Fat Tails

18. Normal versus Fat Tail Normal Fat Ratios

19. Multivariate Fat Tails

21. Of Larger Order Than

22. Feller Theorem Consider two independent Pareto distributed random variables X and Y Their joint probability is

24. Of Equal Order as

25. Conclude • With linear dependence, as between portfolios and balance sheets, the probability of a joint failure is: • Of smaller order than the individual failure probabilities in case of the normal, hence systemic risk is unimportant • Of the same order in case of fat tails, hence systemic risk is important

26. Systemic Risk Measure

27. Systemic Risk Measure • Like marginal risk measure VaR • Desire a scale for measuring the potential Systemic Risk

28. Pr{Min>s} 1 + Pr{Min>s} / Pr{Max>s} = 1 + Pr{Max>s} Given that there is a bank failing, what is the probability the other bank fails as well?

29. Normal Zero Fat Tails Positive Answers Differ Radically Question: If bank exposures are linear in the risk factors, and banks have some of these factors in common, then what is the expected number of failures given that there is a failure? Note: to see something under normality, we need a finer risk measure like the Trace of the covariance matrix / the Tawn measure

31. Note Plus Shape + is due to the Outliers • Under normal, just get a Circular cloud

32. Consider Bank versus Market Neutral Hedge Fund • Bank is Long in both X and Y • Bank portfolio return X+Y • Hedge fund is long in X, short in Y • Hedge fund portfolio return X-Y

35. Systemic Risk Measure • Do not know where systemic failure sets in • Take limits • Evaluate in limit and extrapolate back • Construct Multivariate VaR, in terms of Failure Probability, rather than loss quantile • Conditional Failure Measure: • Given that one bank fails, Probability the other banks fail

36. Y Pr{Min>s} X 1 + Pr{Min>s} / Pr{Max>s} = 1 + Y Pr{Max>s} X Systemic Risk Measure:

37. (1-a)R+aQ Pr{Min>s} Normal Case aR+(1-a)Q 1 + Pr{Min>s} / Pr{Max>s} = 1 + (1-a)R+aQ Pr{Max>s} Q aR+(1-a)Q R = 1+ = 1 Q R

38. Ledford-Tawn measure Need fine measure in case of normality since Use instead

39. Portfolios composed of indepedent returns R and Q aR+(1-a)Q (1-a)R+aQ Q s/(1-a) R s/a (1-a)R+aQ=s

40. (1-a)R+aQ Pr{Min>s} Fat Tail Case aR+(1-a)Q 1 + Pr{Min>s} / Pr{Max>s} = 1 + (1-a)R+aQ Pr{Max>s} Q aR+(1-a)Q R = 1+ > 1 Q R

41. Systemic risk with fat tails Since numerator and denominator are of the same order in case of fat tails, the measure Is appropriate

42. Bank Network System • Syndicated Loans • Conduits • Interbank Money Market • 4 Banks with 4 Projects • Each Project Divisible into 4 Parts

43. Bank Networks Banks are circles. Arrows indicate transfer of –part of- project, loan etc. autarky Wheel 1 Wheel 2 Full Diversification Star Cycle

44. Bank Networks 1/2 1/4 Wheel 1 Wheel 2 autarky 1/4 1/4 1/4 1/4 1/4 1/4 1/4 Cycle Full Diversification Star

45. Systemic Risk, normal E=1, T=1/4 E=1, T=2/5 E=1, T=1/2 E=4, T=1 E=1, T=2/3 E=1, T=11/20

46. Systemic Risk, fat tails, =3 E=1 E=1+1/27 E=1+1 E=1+1/4 E=1+3 E=1+3/41

47. Conclude • Pattern of Systemic Risk under fat tails differs from normal based covariance intuition • Too much Diversification hurts Systemic Risk (slicing and dicing convexifies the exposures)

48. Banks & Hedge Funds application

49. Cross plot Insurers versus Banks