EXTREME DOWNSIDE RISK AND FINANCIAL CRISIS. Richard D. F. Harris, Linh H. Nguyen, Evarist Stoja Paris, March 2015

Transcription

1 EXTREME DOWNSIDE RISK AND FINANCIAL CRISIS Richard D. F. Harris, Linh H. Nguyen, Evarist Stoja Paris, March 2015

2 Motivation & Background Investors are crash averse, giving rise to extreme downside risk premium Systematic risk: Systematic skewness: Kraus and Litzenberger (JF, 1976), Harvey and Siddique (JF, 2000) Systematic kurtosis: Dittmar (JF, 2002), Guidolin and Timmermann (RFS, 2008) Systematic higher moments: Chung et al. (JB, 2006) Systematic tail risk: Ruenzi and Weigert (working paper, 2013) Idiosyncratic risk: Idiosyncratic skewness: Mitton and Vorkink (RFS, 2007), Conrad et al. (JF, 2013) Idiosyncratic tail risk: Huang et al. (JBF, 2012) Market level analysis: Bali et al. (JFQA, 2009), Bollerslev and Todorov (JF, 2011) Main challenge: leverage and volatility feedback effects (Black, 1976; Campbell and Hentschel, JFE 1992)

3 Research objective & methodology Investigate the behaviours of the extreme downside risk return relationship in different market conditions, especially in distress periods? Methodology: Bali et al. (JFQA, 2009) framework Markov-switching mechanism

4 Bali et al. (JFQA, 2009) (BDL) framework Regression framework: R t+1 = α + βe t VaR t+1 + γx t + ε t+1 Extreme downside risk measures E t VaR t+1 Historic VaR t : nonparametric (worst return of estimation period) or Skewed Student-t parametric Next period Expected value from AR(p) process of Historic VaR t Estimation period: 1 month to 6 months Other control variables: Macro variables: Detrended RFR, Change in Term structure Risk premium, Change in Credit Risk premium, Dividend yield; Lagged market excess return R t ; Dummy for Oct 1987;

5 Markov-switching-incorporated BDL framework First-order Markov process and two regimes: R t+1 = α St+1 + β St+1 E t VaR t+1 + γ St+1 X t + ε St+1 t+1 Where 2 ε St t~n 0, σ St S t = 1, if state 1 occurs at time t 2, if state 2 occurs at time t The nature of the two states is represented in σ St, where a high level of σ St implies the turbulent state and the other one is for normal state.

6 Data Market return: value weighted CRSP all stock index Risk free rate: 1 month Treasury Bill from Kenneth R. French Online Data Library Term structure Risk premium: 10 year Treasury Note yield (The Board of Governors of the Federal Reserve System database) 1 month Treasury Bill Credit Risk premium: MOODY s BAA corporate bond yield MOODY s AAA corporate bond yield (The Board of Governors of Federal Reserve System database) Dividend yield: Fama and French (JFE, 1988) method using the distribution-included value-weighted CRSP index return and the distribution-excluded one (CRSP database) Additional macro variables: Industrial production (The Board of Governors of the Federal Reserve System database) Monetary base M2 (The Board of Governors of the Federal Reserve System database) Inflation (The Bureau of Labor Statistics database) Oil price (The Bureau of Labor Statistics database) Time period: July 1962 Jun 2013

7 Empirical Results: The distress period inconsistency State Const Et(VaRt+1) Lagged return RFD DTRP DCRP DY Raw Nonparametric VaR State variance Expected Duration (0.199) (5.934) (-0.273) (-2.740) (0.170) (1.442) (-0.134) (-1.467) (-2.318) (-0.217) (-0.754) (-3.258) (1.634) (1.595) Raw Skewed Student-t VaR (-0.239) (5.777) (-0.355) (-2.506) (0.273) (1.508) (-0.122) (-1.514) (-2.822) (-0.150) (-0.877) (-3.358) (1.825) (1.840)

8 Empirical Results: The distress period inconsistency State Const Et(VaRt+1) Lagged return RFD DTRP DCRP DY AR4 Nonparametric VaR State variance Expected Duration (-2.464) (6.068) (-3.622) (-3.113) (-2.822) (2.758) (1.841) (-0.853) (-1.623) (1.327) (-1.179) (-1.354) (0.914) (0.614) AR4 Skewed Student-t VaR (-2.013) (6.109) (-1.609) (-2.777) (-0.066) (1.591) (0.090) (-0.780) (-1.732) (0.569) (-1.030) (-3.227) (1.605) (1.658)

9 Empirical Results: The distress period inconsistency Raw NonPara VaR AR4 NonPara VaR Raw Skewed Student-t VaR AR4 Skewed Student-t VaR Raw NonPara VaR AR4 NonPara VaR Raw Skewed Student-t VaR AR4 Skewed Student-t VaR Const E t (VaR t+1 ) Lagged return Dummy RFD DTRP DCRP DY Adjusted R^2 Panel A: Original period July December % (-1.529) (2.098) (1.030) (-4.625) (-2.500) (-2.349) (2.249) (1.592) % (-2.372) (2.790) (0.742) (-6.398) (-2.466) (-2.425) (2.118) (1.691) % (-1.475) (1.896) (0.996) (-4.871) (-2.525) (-2.360) (2.268) (1.546) % (-2.094) (2.386) (0.784) (-6.246) (-2.500) (-2.425) (2.136) (1.629) Panel B: New period January June % (-1.417) (-0.949) (0.442) (0.852) (-0.052) (-0.329) (1.803) % (-1.878) (0.277) (1.306) (1.332) (0.184) (-0.995) (1.983) % (-1.602) (-0.438) (0.762) (1.042) (0.065) (-0.664) (1.949) % (-2.012) (0.840) (1.398) (1.419) (0.254) (-1.303) (2.069)

10 The consistency is robust in modifications of BDL framework Additional state variables: IP growth (constructed under Chen et al., 1986 method); Change in nature logarithm of M2; Change in Inflation; Change in Oil price Significantly improve BDL framework in a consistent manner Could not solve the distress period problem

11 MS-BDL results using extended set of state variables Measure State Const Et(VaRt+1) Raw Nonparam AR4 Nonparam Raw Skewed Student-t AR4 Skewed Student-t Lagged Return RFD DTRP DCRP DY IPG MBG DIF DO State variance Expected Duration (-0.820) (5.130) (0.349) (-0.942) (0.937) (1.059) (-0.157) (2.927) (-0.852) (-1.722) (0.990) (-1.886) (-1.883) (-0.377) (-0.660) (-3.331) (2.929) (2.150) (2.662) (-0.882) (-0.531) (2.168) (-2.333) (5.233) (-1.108) (-0.629) (0.787) (1.370) (-0.225) (3.037) (-0.586) (-0.882) (0.092) (-2.076) (0.132) (0.601) (-1.336) (-3.089) (2.471) (2.239) (2.813) (-1.187) (-1.426) (2.693) (-0.883) (5.363) (0.722) (-0.544) (1.190) (1.041) (-0.547) (2.270) (-0.869) (-1.698) (0.614) (-1.959) (-1.549) (-0.324) (-1.075) (-3.176) (3.014) (2.368) (2.797) (-0.981) (-0.638) (2.205) (-2.013) (4.900) (-0.378) (0.067) (0.959) (0.600) (-0.963) (2.347) (-0.713) (-0.521) (-0.136) (-1.865) (-0.069) (0.576) (-1.502) (-2.848) (2.591) (2.789) (2.559) (-0.962) (-1.218) (2.705)

12 Sub-sample BDL results using extended set of state variables Tail risk measure Const Et(VaRt+1) Lagged Return Dummy RFD DTRP DCRP DY IPG MBG DIF DO Panel A: Original Period July December 2005 Adjusted R^2 Raw % NonPara VaR (-3.142) (3.409) (0.460) (-3.827) (-0.863) (-1.778) (2.796) (2.228) (5.657) (-1.214) (-1.206) (-0.087) AR % NonPara VaR (-4.526) (5.031) (-0.339) (-8.921) (-0.688) (-1.575) (3.224) (2.611) (6.199) (-1.364) (-1.128) (-0.202) Raw Skewed % Student-t VaR (-3.605) (3.855) (0.495) (-7.593) (-0.934) (-1.513) (3.321) (2.444) (6.084) (-1.388) (-1.038) (-0.185) AR4 Skewed % Student-t VaR (-4.763) (5.239) (-0.148) (-9.583) (-0.708) (-1.549) (3.187) (2.628) (6.209) (-1.465) (-0.993) (-0.312) Panel B: New Period January June 2013 Raw % NonPara VaR (0.256) (-1.294) (-1.004) (-1.560) (-2.062) (2.064) (0.367) (2.363) (-1.245) (-2.334) (4.262) AR % NonPara VaR (-0.411) (0.019) (-0.019) (-0.662) (-1.488) (1.717) (0.771) (1.886) (-1.214) (-2.669) (4.626) Raw Skewed % Student-t VaR (0.007) (-0.809) (-0.618) (-1.269) (-1.811) (1.956) (0.507) (2.284) (-1.256) (-2.417) (4.403) AR4 Skewed % Student-t VaR (-0.721) (0.504) (0.187) (-0.305) (-1.227) (1.587) (0.944) (1.724) (-1.192) (-2.647) (4.481)

13 The consistency is robust in modifications of BDL framework Accounting for non-iid return in risk measure estimation Ignoring non-iid phenomena of return (autocorrelation, volatility clustering) is inconsistent with the idea of extreme downside risk Location-scale model to estimate VaR when return is non-iid: AR(1)-GARCH(1,1) Skewed Student-t residual distribution Performance improved, but distress period problem still persists

14 MS-BDL results using Non-iid VaR measures Measure State Const Et(VaRt+1) Raw Skewed Student-t AR4 Skewed Student-t Lagged Return RFD DTRP DCRP DY IPG MBG DIF DO State variance Expected Duration (-2.631) (7.023) (-2.055) (-0.769) (0.783) (1.835) (0.289) (4.442) (-0.641) (-0.647) (0.074) (-2.924) (1.121) (0.860) (-1.086) (-3.078) (2.003) (2.599) (2.667) (-1.533) (-1.713) (2.951) (-3.622) (7.211) (-3.859) (-0.886) (-2.335) (2.056) (2.239) (3.873) (-0.634) (-0.938) (0.314) (-2.398) (0.538) (1.953) (-0.838) (-0.442) (1.788) (1.060) (4.117) (-1.072) (-1.700) (2.017)

15 Solutions for the problem: filtering out leverage and volatility feedback effects The fundamental reason for the distress period puzzle is the leverage and volatility feedback effects. Filtering these effect is the underlying rationale of the use of the expected risk measures instead of the realized ones in BDL framework. The underlying assumption in their framework is that these effects dissipate within one month. In turbulent periods, these effects take longer to dissipate, undermining the one period ahead expected measure in BDL framework Solution: Two period ahead expected measure (FOSA): E t VaR t+1 = φ 0 + φ 1 E t 1 VaR t + φ i VaR t i p i=2 E t 1 VaR t = φ 0 + φ i VaR t 1 i p i=1

16 Volatility clustering surge in turbulent period Clustering - no state variable Clustering - state variables at t Clustering - state variables at t +1 Clustering - state variables at t +2 Const Realized Variance Market return Dummy RFD DTRP DCRP DY IPG MBG DIF DO Adjusted R^ % (6.917) (3.380) % (4.098) (2.593) (-3.062) (-2.287) (-2.036) (-0.529) (-1.424) (-1.765) (-2.616) (0.517) (1.497) (-1.481) % (5.735) (2.315) (-2.951) (16.590) (-2.258) (-0.651) (1.374) (-2.799) (-3.777) (3.208) (-1.377) (-1.726) % (5.740) (3.704) (-2.243) (14.365) (-2.140) (0.955) (2.610) (-2.592) (-3.157) (1.607) (-1.410) (-1.483)

17 MS-BDL results using FOSA measures Measure State Const Et(VaRt+1) Lagged Return RFD DTRP DCRP DY IPG MBG DIF DO State variance Expected Duration IID Nonparam (-3.206) (6.144) (-4.184) (-1.928) (0.126) (2.543) (1.113) (0.777) (-0.999) (0.308) (-0.652) (-4.251) (3.152) (-0.704) (-1.072) (-2.454) (2.111) (2.460) (5.309) (-1.481) (-2.361) (4.307) IID Parametric (-2.411) (5.365) (-3.849) (-1.792) (0.281) (2.504) (0.890) (0.725) (-0.594) (0.210) (-0.551) Skewed-t (-3.912) (2.824) (-0.585) (-1.252) (-2.605) (1.920) (2.458) (5.123) (-1.633) (-2.407) (4.332) NIID Parametric (-2.062) (5.695) (-3.037) (-1.827) (0.868) (2.496) (-0.306) (2.225) (-0.244) (-0.293) (-0.263) Skewed-t (-3.774) (2.445) (0.119) (-0.456) (-3.100) (2.348) (2.933) (3.668) (-1.677) (-2.255) (3.554)

18 Economic interpretation of FOSA measures The leverage and volatility feedback effects ensure the asset pricing relationship of risk and return: in turbulent periods, assets need to have low concurrent returns in order to have high expected return corresponding with the expectation of the prolong uncertain period in the future. This is exactly what BDL framework captures: a significantly positive relationship between next month s market excess return (R t+1 ) and the corresponding tail risk expectation E t (VaR t+1 ). In distress periods, leverage and volatility feedback effects spread out, investors sell off dramatically over multiple periods, depressing the expected tail risk expected returns relationship. Therefore, it takes more than one period for this relationship to be realized. Specifically, in the context of our investigation, investors generally need to wait until period t+2 to be able to observe the relationship. Mathematically, in these distress times, we can capture a significantly positive relationship between R t+2 and E t (VaR t+2 ), which is the underlying rationale of our FOSA measures.

19 Robustness checks Asymmetric conditional volatility models in the locationscale filter: GJR GARCH, EGARCH Different VaR confidence levels: 1 percent, 2.5 percent, 5 percent Expected Tail Loss (Conditional VaR) risk measure Accounting for variance

20 Contribution & Conclusion Demonstrate the extents on which the exploration of the extreme downside risk-return state-based relationship could be improved by developing on the original BDL framework. Propose and prove the cause of the distress context puzzle to be the work of the leverage and volatility feedback effects. Propose a simple effective modification to the risk measure to overcome this challenge, which could be regarded as an illustration of the underlying mechanism on how tail risk is factored into expected returns.

21 THANK YOU!