Financial crises, crisis spill-overs and the business cycle

Stefan Straetmans, Maastricht university School of Business and Economics

Risk Forum Paris, March 2015

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

Motivation 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?

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

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

Univariate mixture model

Survivor function as mixture of survivor functions:

model survivor functions with Pareto tail:

ying!slowly var also

1with

1

21

21

21

12

2

21

xL

xLxxLxL

xxLxXP

xxLxxLxXP

xFxFxF 21 1111

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:

yxFyxFyxF ,11,1,1 21

tvQtuQFtvul t 211

0 ,1lim,

vulvulvul ,1,, 21

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)

Mixtures and higher order behavior

n=2 states:

n=3 states:

122 11

21

xxxF

etc.

11 231332121

321

xxxxF

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

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?

estimator quantile extreme 1

/Pr1Pr

1

pFx

xsIpxIXIpxFxX

p

pppp

niX i ,,1

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

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

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:

1

/1

, ,ˆ

np

pn

mXx nmp

xlarge ,ˆ,

xXn

mxXP nm

Co-crash tail probability

(1992) Huang followingestimator 1,1ˆ

copula" tail"or function" dependence tailstable" :1,1

"-tail" is

1,12

or 2

2

22

22112211

l

l

CPXX

l

pQXP

pQXpQXPppQXpQXPCP

XYM

XY

Alternative extreme comovement measures

Conditional expected number of co-extremes and (scaled) multivariate co-exceedance likelihood:

p

pQXpQXpQXP

pQXpQXpQXpQXPP

l

N

ppl

NpE

NNii

jjNNiiN

,...,,...,

,...,,...,

1,...,1,...,1

11

111

Note: co-crash probability as mixture

21

21

21

1

1,1211,12

1,111,1-2

1,12

XYX

XY

CPCP

ll

ll

lCP

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

Bank tail risk: representative results (p=0.1%)

Banks Recession Expansion Equality tests

BOA 1.75 0.76 2.73 0.12 -3.29 2.51

BB&T 2.37 0.30 3.13 0.09 -1.98 2.79

NYMellon 1.94 0.46 3.26 0.10 -3.89 2.60

Comerica 1.92 0.49 2.85 0.10 -2.91 2.62

Huntington 1.82 0.84 2.70 0.12 -2.89 2.67

JP Morgan 2.16 0.40 3.23 0.11 -2.96 2.70

Keycorp 1.80 0.69 2.81 0.11 -3.30 2.59

North. Trust 2.09 0.34 2.92 0.10 -2.42 2.52

Wells Fargo 2.04 0.45 3.29 0.09 -3.54 2.79

ER ER qq

R Rq E Eq

General stock and bond tail risk (indices)

Recession Expansion Equality tests

Stocks

US 2.02 0.20 2.96 0.06 -2.80 2.40

GE 2.51 0.10 2.80 0.07 -0.89 1.53

UK 2.46 0.10 2.73 0.06 -0.83 1.99

FR 2.44 0.13 2.94 0.07 -1.36 2.00

JP 2.88 0.09 2.63 0.08 0.75 0.88

Bonds

US 2.69 0.04 3.36 0.02 -1.55 2.02

GE 2.25 0.03 3.18 0.02 -2.91 1.43

UK 3.15 0.02 3.12 0.02 0.10 0.05

FR 2.63 0.02 3.08 0.02 -1.15 0.65

JP 2.18 0.03 2.27 0.03 -0.31 0.12

R Rq E Eq ER ER qq

Forex and commodities Recession Expansion Equality tests

Forex

US$/uk£ 2.47 0.06 3.16 0.03 -1.76 2.09

US$/JPY 2.18 0.11 3.35 0.04 -3.18 2.39

US$/SFR 2.21 0.08 3.46 0.03 -3.30 2.35

Commodities

Oil 2.23 0.32 3.29 0.12 -2.85 2.43

Silver 2.03 0.24 2.54 0.13 -1.57 1.53

Gold 2.35 0.13 2.88 0.06 -1.44 2.24

R Rq E Eq ER ER qq

Bank linkages: MES and tail-β Bank Recession Expansion Equality tests

ρ ρ

BOA 0.74 0.14 0.91 0.63 0.04 0.81 1.66 5.87

BB&T 0.62 0.08 0.83 0.46 0.03 0.62 3.17 3.10

NY Mellon 0.58 0.08 0.78 0.54 0.03 0.73 0.72 2.74

Comerica 0.66 0.09 0.85 0.56 0.03 0.72 2.11 4.78

Huntington 0.58 0.14 0.71 0.48 0.03 0.62 1.99 4.99

JP Morgan 0.73 0.09 0.89 0.58 0.04 0.80 2.75 5.33

Keycorp 0.69 0.13 0.80 0.54 0.03 0.74 3.08 3.42

North. Trust 0.62 0.07 0.78 0.51 0.03 0.65 2.06 4.21

Wells Fargo 0.74 0.11 0.92 0.51 0.03 0.75 3.88 4.61

ER ER MESMES R E

RMES EMES

Multivariate systemic risk results

109.0 053.2 :Expansion

319.0 676.3 :Recession

139.0 558.2 :sample Full

16E1

banks 16N

MULEE

MULRR

MUL

PE

PE

PE

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

Co-crash vs. Flight-to-quality

%05.0

1

:quadrant 2nd

11

:quadrant 3rd

return bond

returnstock

p

pQSpQBPCP

pQSpQBPCP

B

S

SBFTQ

SBCO

Stock/bond co-crashes vs. Flight-to- quality probabilities

Full sample Recession Expansion

ρ ρ ρ

US 0.070 0.225 -0.096 0.068 0.295 -0.252 0.086 0.176 -0.051

GE 0.050 0.180 -0.107 0.039 0.195 -0.185 0.048 0.196 -0.080

UK 0.055 0.165 -0.066 0.042 0.366 -0.288 0.076 0.076 0.021

FR 0.060 0.100 0.001 0.083 0.188 -0.241 0.065 0.097 0.048

JP 0.060 0.090 -0.068 0.011 0.092 -0.151 0.106 0.099 -0.030

COP FTQP COP FTQP COP FTQP

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:

21 1 RwwRRp

2122

21

2122

2

MVw

/1

,ˆ min

pn

mwRwq nmp

w

DJ Correlations and the business cycle

DJ Stock pairs Correlations

Full sample recession expansion

ExxonMobil/Wal Mart 0.33 0.43 0.32

Wall Mart/P&G 0.37 0.57 0.34

PG/J&J 0.47 0.63 0.45

JJ/GE 0.44 0.47 0.44

GE/JP Morgan 0.56 0.63 0.53

JP Morgan/Pfizer 0.34 0.45 0.32

Minimum Variance and tail risk portfolios

DJ Stock pairs Full sample recession expansion

Minimum Variance results

w MV w MV w MV

Exxon/WalMart 0.6 0.013 0.41 0.018 0.64 0.013

Wall Mart/P&G 0.40 0.014 0.33 0.017 0.40 0.013

P&G/J&J 0.45 0.013 0.36 0.015 0.46 0.013

J&J/JP Morgan 0.83 0.014 1 0.016 0.74 0.013

Minimum tail risk results

w q w q w q

Exxon/WalMart 0.59 0.078 0.41 0.095 0.63 0.074

Wall Mart/P&G 0.31 0.084 0.45 0.096 0.30 0.080

P&G/J&J 0.52 0.078 0.28 0.080 0.54 0.075

J&J/JP Morgan 0.78 0.093 0.93 0.089 0.74 0.089

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

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...