1. Financial crises, crisis spill-overs and the business cycle Stefan Straetmans, Maastricht university School of Business and Economics Risk Forum Paris, March 2015

2. Motivation and contribution Tail behavior - Univariate: fat tails (nonnormality) - Multivariate: tail dependence Features of the unconditional (time constant) df This paper: do they exhibit regime dependence? Extreme value analysis (EVT) presupposes a stationary unconditional (“long-term”) df → reconcilable with short-term regimes/states

3. M otivation and contribution (2) Tail indices, scalig constants, tail copula most likely not invariant over time.. Regime dependence may shed light on the determinants of tail fatness but careful: this is NOT a causality analysis Is there a way in between volatility and dependence modelling based on conditional df (multivariate GARCH, SV..) vs. “pure” EVT?

4. Motivation and contribution (3) Simplest way to introduce regime dependence that preserves unconditional stationarity of df: - mixture of Pareto tails (univariate EVT) - mixture of tail copula (multivariate EVT) In this paper: (exogenous) regime = business cycle We do find regime dependence for scaling constant, tail index and strength of tail dependence

5. Anticipating our results.... Recession-based downside asset tail risk highest for large variety of assets Recession-based bank linkages highest Stock-bond flight-to-quality dominates co-crashes during recessions; asymmetry much smaller in expansions Minimum variance portfolios are regime dependent; diversification meltdown in recessions

6. Univariate mixture model Survivor function as mixture of survivor functions: model survivor functions with Pareto tail:

7. Bivariate mixture model Survivor function as mixture: Tail copula 1-1 with joint survivor function: Mixture in survivor functions transfers to copula and tail copula:

8. Statistical relevance Regime dependence in tail fatness provides additional source of bias in tail index estimation Why? Pareto mixture is equivalent to higher order behavior which induces Hill bias Same should hold for multivariate mixtures and the strength of tail dependence (bias in extreme linkage measures)

9. Mixtures and higher order behavior n=2 states: n=3 states:

10. Economic relevance Short-term horizon risk managers probably interested to identify regime-dependent risk...but even financial regulators with long-term focus aim for countercyclical micro/macro prudential risk indicators Neglecting regime dependence potentially leads to too conservative capital requirements

11. Application: trading limits for bank traders Return series s>0 : maximum loss such that pension fund, bank does not become insolvent/illiquid s depends on actual solvency/liquidity position Maximum allowable investment I in risky position?

12. Previous evidence on regime dependence in tail behavior Only structural break analyses Univariate: breaks in tail index/tail quantiles? (scant) evidence limited to (emerging) currency returns (Koedijk et al. (1990, 1992), Straetmans et al. (2013)) Multivariate: breaks in tail copula: EMS forex return pairs (Straetmans (1998)) We adopt more complex subsample partitioning

13. Crisis and crisis spillover indicators Downside tail risk: tail index/probs/quantiles - individual assets and portfolios Bivariate co-crash probability - tail-β as bivariate co-movement indicator - compare co-crash vs. Flight-to-Quality probs Conditional expected number of co-crashes Multivariate co-crash probability Estimate on full, recession, expansion sample

14. Tail probs/tail quantiles Use marginal quantile estimator that exploits fat tails: Use Hill statistic for α Inverse of estimator renders “extreme” Value-at-Risk estimate for given p:

15. Co-crash tail probability

16. Alternative extreme comovement measures Conditional expected number of co-extremes and (scaled) multivariate co-exceedance likelihood:

17. Note: co-crash probability as mixture

18. Data Monthly business cycle dummies (1985-2012) - US: NBER dating committee - GE, FR, UK, JP: Economic Cycle Research Institute (ECRI) DS Daily financial returns (1/2/1985-31/12/2012) - 16 US bank stocks, G-5 stock and (10-year) sovereign bond indices, commodities (oil, gold, silver), exchange rates

19. Bank tail risk: representative results (p=0.1%) BanksRecessionExpansionEquality tests BOA1.750.762.730.12-3.292.51 BB&T2.370.303.130.09-1.982.79 NYMellon1.940.463.260.10-3.892.60 Comerica1.920.492.850.10-2.912.62 Huntington1.820.842.700.12-2.892.67 JP Morgan2.160.403.230.11-2.962.70 Keycorp1.800.692.810.11-3.302.59 North. Trust2.090.342.920.10-2.422.52 Wells Fargo2.040.453.290.09-3.542.79

20. General stock and bond tail risk (indices) RecessionExpansionEquality tests Stocks US2.020.202.960.06-2.802.40 GE2.510.102.800.07-0.891.53 UK2.460.102.730.06-0.831.99 FR2.440.132.940.07-1.362.00 JP2.880.092.630.080.750.88 Bonds US2.690.043.360.02-1.552.02 GE2.250.033.180.02-2.911.43 UK3.150.023.120.020.100.05 FR2.630.023.080.02-1.150.65 JP2.180.032.270.03-0.310.12

21. Forex and commodities RecessionExpansionEquality tests Forex US$/uk£2.470.063.160.03-1.762.09 US$/JPY2.180.113.350.04-3.182.39 US$/SFR2.210.083.460.03-3.302.35 Commodities Oil2.230.323.290.12-2.852.43 Silver2.030.242.540.13-1.571.53 Gold2.350.132.880.06-1.442.24

22. Bank linkages: MES and tail-β BankRecessionExpansionEquality tests ρρ BOA0.740.140.910.630.040.811.665.87 BB&T0.620.080.830.460.030.623.173.10 NY Mellon0.580.080.780.540.030.730.722.74 Comerica0.660.090.850.560.030.722.114.78 Huntington0.580.140.710.480.030.621.994.99 JP Morgan0.730.090.890.580.040.802.755.33 Keycorp0.690.130.800.540.030.743.083.42 North. Trust0.620.070.780.510.030.652.064.21 Wells Fargo0.740.110.920.510.030.753.884.61

23. Multivariate systemic risk results

24. Bank tail risk and systemic risk Consistent with fundamentals-based banking crises literature Incidence of banking panics increases during recessions cf. Gorton (1988) How to make it countercyclical? Turn it around... Macro prudential regulation: use recession (expansion) SR indicators to assess true expansion (recession) SR

25. Co-crash vs. Flight-to-quality

26. Stock/bond co-crashes vs. Flight-to- quality probabilities Full sampleRecessionExpansion ρρρ US0.0700.225-0.0960.0680.295-0.2520.0860.176-0.051 GE0.0500.180-0.1070.0390.195-0.1850.0480.196-0.080 UK0.0550.165-0.0660.0420.366-0.2880.076 0.021 FR0.0600.1000.0010.0830.188-0.2410.0650.0970.048 JP0.0600.090-0.0680.0110.092-0.1510.1060.099-0.030

27. Minimum tail risk portfolios Form 2-asset portfolio with pairs of DJ stocks Minimum variance portfolio: Minimum Value-at-Risk portfolio for low p- value:

28. DJ Correlations and the business cycle DJ Stock pairsCorrelations Full samplerecessionexpansion ExxonMobil/Wal Mart0.330.430.32 Wall Mart/P&G0.370.570.34 PG/J&J0.470.630.45 JJ/GE0.440.470.44 GE/JP Morgan0.560.630.53 JP Morgan/Pfizer0.340.450.32

29. Minimum Variance and tail risk portfolios DJ Stock pairsFull samplerecessionexpansion Minimum Variance results wMVw w Exxon/WalMart0.60.0130.410.0180.640.013 Wall Mart/P&G0.400.0140.330.0170.400.013 P&G/J&J0.450.0130.360.0150.460.013 J&J/JP Morgan0.830.01410.0160.740.013 Minimum tail risk results wqwqwq Exxon/WalMart0.590.0780.410.0950.630.074 Wall Mart/P&G0.310.0840.450.0960.300.080 P&G/J&J0.520.0780.280.0800.540.075 J&J/JP Morgan0.780.0930.930.0890.740.089

30. Diversification of portfolio tail risk: summary Tactical asset allocation: if your aim is to avoid extreme portfolio returns you have to invest differently during recessions Diversification meltdown during recessions: higher correlation, higher (minimized) portfolio variance and portfolio tail risk (VaR) Portfolio allocation w for minimum tail risk portfolios strongly differs from minimum variance portfolios

31. Extensions/avenues for future research Regime-dependence of left-right tail asymmetry →to be expected to be much more severe during recessions Allowing for thin and fat tails (Generalized EVD) Alternatives for the business cycle? Borio’s financial cycle Endgenous regime determination, more thzn two regimes...