Short-selling constraints and stock-return volatility: empirical evidence from the German stock market

Transcription

1 Short-selling constraints and stock-return volatility: empirical evidence from the German stock market Martin Bohl, Gerrit Reher, Bernd Wilfling Westfälische Wilhelms-Universität Münster Contents 1. Introduction 2. A general Markov-Switching GARCH framework 3. Empirical analysis 4. Concluding remarks 1

2 1. Introduction General setting: During the financial crisis 2008/2009 and the Greek crisis 2009/2010 several countries imposed limitations on shortselling activities Officially announced objectives of these limitations: displacement of short-sellers prevention of further declines in stock prices stabilization of stock prices 2

3 Effects of short-selling constraints: Governments, regulators and the media blame short-sellers for reinforcing stock-market downturns By contrast, empirical researchers mostly find distortions of short-selling restrictions on market efficiency (Bris et al., 2007; Journal of Finance) liquidity (Boehmer and Wu, 2009; Working Paper, Texas A&M) pricing of stocks (Boehmer et al., 2008; Journal of Finance) Several event studies on the effects of short-selling restrictions on stock-market volatility 3

4 Topic of this presentation: Short-selling restrictions and stock-return volatility in Germany during the financial crisis Our conjecture: Short-selling constraints limit the investors ability to find the fundamental stock price short-selling bans may contribute to a destabilization of stock prices during periods of market downturns and may even exaggerate stock-price declines short-selling bans are likely to be counterproductive 4

5 Structure of presentation: Econometric techniques for analyzing volatility single-regime GARCH models Markov-switching GARCH models (Reher and Wilfling, 2011; CQE-Working Paper 17/2011) Empirical implementation application to German stock-market data analysis of the (de)stabilizing effects of short-selling constraints (economic results) 5

6 2. A general Markov-switching GARCH framework Single-regime GARCH models: [I] Basic GARCH model formally introduced by Bollerslev (1986, Journal of Econometrics) Capturing empirically relevant heteroscedastic features in financial time-series data (e.g. volatility clustering) A multitude of extensions of the basic GARCH model to cover distinct asymmetries in the volatility structure (e.g the leverage effect) 6

7 Single-regime GARCH models: [II] Hentschel (1995, Journal of Financial Economics) presents a parametric family of GARCH models nesting the most popular GARCH specifications µ ν b c Model Reference free Exponential GARCH Nelson (1991) c 1 Threshold GARCH Zakoian (1994) 1 1 free c 1 Absolute Value GARCH Hentschel (1995) Basic GARCH Bollerslev (1986) 2 2 free 0 Nonlinear-asymmetric GARCH Engle and Ng (1993) free GJR GARCH Glosten et al. (1993) free µ 0 0 Nonlinear ARCH Higgins, Bera (1992) free µ 0 c 1 Asymmetric power ARCH Ding et al. (1993) Note: Table compiled from Hentschel (1995, Table 1). 7

8 Markov-switching models: Designed to capture discrete mean and volatility shifts in the DGP of a time series Phases with constant mean and volatility structures are called (Markov-)regimes of the DGP Examples: Exchange-rate dynamics in the run-up to a currency union (Wilfling, 2009; Journal of International Money and Finance) Stock-price dynamics during takeover bids (Gelman and Wilfling, 2009; Journal of Empirical Finance) Mean and volatility structures of a forward-looking asset price are affected by changing anticipations of market participants 8

9 Markov-switching GARCH modeling: Econometrically demanding due to a problem known as path dependence Gray (1996, Journal of Financial Economics) constructs a Markov-switching framework for Bollerslev s basic GARCH model circumventing the problem of path dependence Klaassen (2002, Empirical Economics) refines this methodology with respect to statistical inference Our innovation: We combine the Gray-Klaassen Markov-switching framework with Hentschel s (single-regime) parametric GARCH family (Reher and Wilfling, 2011; CQE-Working Paper 17/2011) 9

10 Econometric advantage: Rich Markov-switching framework with complex GARCH specifications of different functional forms across two Markovregimes µ i ν i b i c i Model free Exponential GARCH c i 1 Threshold GARCH 1 1 free c i 1 Absolute Value GARCH Basic GARCH 2 2 free 0 Nonlinear-asymmetric GARCH free GJR GARCH free µ i 0 0 Nonlinear ARCH free µ i 0 c i 1 Asymmetric power ARCH 10

11 Model setup: Our two-regime Markov-switching GARCH framework consists of 3 components: a mean equation for the stock-return process {r t } a (conditional) volatility equation for {r t } a specification of the dynamics of the unobservable Markovregime process {S t } 11

12 Mean equation: (i = 1, 2 denotes the Markov-regimes) r t+1 = λ i + γ i h i,t + h i,t ɛ t+1 with λ i, γ i : regime-specific parameters h i,t : regime-specific (conditional) variance-processes (GARCH-in-Mean) {ɛ t }: i.i.d. N(0, 1) random variables 12

13 Statistical implication: Conditional return distribution can be written as the mixture r t+1 φ t with N(λ 1 + γ 1 h 1,t, h 1,t ) with probability p 1,t N(λ 2 + γ 2 h 2,t, h 2,t ) with probability (1 p 1,t ) φ(t) the information set as of date t p 1,t Pr{S t = 1 φ t } the ex-ante probability of being in regime 1 on date t 13

14 Volatility equation: ( hi,t ) µi 1 µ i = ω i + α i with ( f i (x) = x b i c i (x b i ) h (i) t 1 ) µi f ν i i (δ(i) t ) + β i h (i) t 1 : aggregated past conditional variances δ t (i) : aggregated shock terms ( h (i) t 1) µi 1 µ i, ν i : parameters determining the GARCH specification (basic GARCH, EGARCH, TGARCH,...) ω i, α i, β i : regime-specific parameters µ i 14

15 Markov-regime process {S t }: Time-varying transition probabilities: Pr ( ) S t = 1 S t 1 = 1, r t = Pt Pr ( ) S t = 2 S t 1 = 1, r t = 1 Pt Pr ( ) S t = 1 S t 1 = 2, r t = 1 Qt Pr ( ) S t = 2 S t 1 = 2, r t = Qt with P t = Φ(d 1 + e 1 r t ) Q t = Φ(d 2 + e 2 r t ) (Φ( ) is the cdf of the standard normal distribution) 15

16 Likelihood function: L(Θ) = f(r t,..., r 1 ; Θ) = T t=1 (Θ vector containing all model parameters) f(r t r t 1 ; Θ) Log-likelihood function: log[l(θ)] = = T t=1 T t=1 log [ f(r t r t 1 ; Θ) ] log 2 j=1 f(r t S t 1 = j, r t 1 ; Θ) p j,t 1 16

17 Maximum likelihood estimation: All components of the log-likelihood function have recursive structures Implementation in MATLAB Numerical optimization using the BFGS algorithm yields estimates of all model parameters ex-ante regime-1 probabilities Pr{S t = 1 φ t } smoothed regime-1 probabilities Pr{S t = 1 φ T } 17

18 3. Empirical analysis Institutional background: September 19, 2008: BaFin announced prohibition of naked short sales of the shares of 11 (financial) stocks prolongation in 3 steps until January 31, 2010 (343 trading days) May 18, 2010: BaFin reinstalled the restriction until March 31, 2011 (except for Hypo Real Estate) 18

19 Focus of the analysis: Short-selling constraints and stock-return volatility Modus operandi: Construction of an index representing 10 (out of 11) restricted enterprises (our sample group) Construction of an index for a control group consisting of all DAX30 enterprises not in the sample group excluding Volkswagen (due to takeover speculation) Sampling period: January 2, 2006 June 23, 2010 (1136 trading days) 19

20 Daily index returns for the sample and the control group 20

21 Estimation framework: Estimation of Markov-switching EGARCH-TGARCH and TGARCH-TGARCH specifications Mean equation: r t+1 = λ + h i,t ɛ t+1 (non-switching constant, no GARCH-in-Mean) Markov-regime process with constant transition probabilities: Pr ( S t = 1 S t 1 = 1 ) = π 1 Pr ( S t = 2 S t 1 = 1 ) = 1 π 1 Pr ( S t = 1 S t 1 = 2 ) = 1 π 2 Pr ( S t = 2 S t 1 = 2 ) = π 2 21

22 Table 1 Estimates of EGARCH-TGARCH and the TGARCH-TGARCH model for the sample group and the control group Sample group Control group Sample group Control group EGARCH- EGARCH- TGARCH- TGARCH- TGARCH TGARCH TGARCH TGARCH µ µ ν ν λ (0.0015) (0.0067) (0.0001) (0.0015) ω (0.0012) (0.0234) (0.0000) (0.0002) ω (0.0010) (0.0010) (0.0000) (0.0004) α (0.0014) (0.0171) (0.0002) (0.0006) α (0.0050) (0.0420) (0.0003) (0.0041) β (0.0000) (0.0000) (0.0023) (0.0134) β (0.0559) (0.0214) (0.0040) (0.0491) π (0.0001) (0.0238) (0.0000) (0.0001) π (0.0001) (0.0299) (0.0000) (0.0053) c (0.0009) (0.0444) (0.0027) (0.0721) c (0.1598) (0.3074) (0.0035) (0.0202) Volatility persistence in regime 1 Volatility persistence in regime 2 Notes: Estimates for parameters from the Eqs. (1) to (10). Standard errors are in parentheses., and denote statistical significance at 10, 5 and 1% levels, respectively.

23 Volatility persistence in GARCH models: Measure of the persistence of volatility shocks The higher the volatility persistence the longer it takes until a volatility shock dies out Volatility persistence can be computed from the parameters in the volatility equation If the regime-specific volatility persistence equals 1 then the unconditional variance in that regime gets infinitely large High (low) regime-specific volatility persistence indicates low (high) variance stability in that regime 23

24 Volatility-persistence results: For both groups: volatility persistence in regime 1 is larger than in regime 2 regime 1 is the unstable (high) volatility regime regime 2 is the stable (low) volatility regime In the sample group a switch from regime 2 to regime 1 entails a larger increase in volatility persistence than in the control group potential indication of a variance-destabilizing effect (to be interpreted with caution) 24

25 Conditional variances and regime-1 probabilities for the EGARCH-TGARCH specification 25

26 Graphical results: The overall level of the conditional variances of the sample group is higher than in the control group no overwhelming stabilizing effect of the constraints The sample group exhibits a second substantial variance peak in spring 2009 while the control group does not This variance peak is associated with a switch from the lowvolatility regime 2 to the high-volatility regime 1 Interestingly, this regime switch happened exactly on that day when the BaFin announced a prolongation of the phase of short-selling restrictions (indication of a destabilizing effect) 26

27 4. Concluding Remarks 1. Econometric modeling: Development of a unifying Markov-switching GARCH framework to estimate complex GARCH equations of distinct functional forms across two Markov-regimes Application to two stock-return indices from the German stock market an index representing a group of enterprises subject to naked short-selling constraints an index for a control group 27

28 2. Results: The switches in the volatility regimes appear to primarily stem from the financial crisis rather than from the imposition of the short-selling constraints However: no overwhelming volatility-stabilizing effect of (naked) shortselling constraints (Weak) evidence that short-selling restrictions may have a destabilizing effect 28

29 Thank you for your attention! 29