Leverage and Asymmetric Volatility: The Firm Level Evidence

Transcription

1 Leverage and Asymmetric Volatility: The Firm Level Evidence Presented by Stefano Mazzotta Kennesaw State University joint work with Jan Ericsson, McGill University and Xiao Huang, Kennesaw State University

2 Outline Introduction Asymmetric volatility and leverage The panel data model Time varying risk premium and leverage Empirical results Conclusion

3 Two explanations of asymmetric volatility: Leverage effect (e.g. Black (1976) Christie (1982)): Stock price Leverage Risk Volatility Time-varying risk premium, (e.g. French et al. (1987) Campbell and Hentschel (1992), Bekaert and Wu (2) Persistent volatility Required rate of return Stock price

4 Leverage and volatility The traditional leverage effect argument states that as stock prices drop, increased leverage pushes up the equity volatility for a given asset volatility (business risk). This is the spirit of the test in Christie (1982). But from a firm s perspective, the choice of leverage and volatility is a joint one, at least in the medium to long term. Leverage will depend on volatility and vice versa. Thus a two way relationship needs to be modeled

5 The leverage effect revisited We ask what can be learnt By reconsidering the leverage effect at the individual firm level in the presence of an alternative explanation (time varying risk premia) By allowing leverage and volatility to influence each other in a two-way system Captures also long term effects.

6 Our contributions A panel vector autoregression (PVAR) approach to study the dynamics of leverage, volatility, and risk premium jointly Control firm level heterogeneity We find leverage effect is more important than volatility feedback effect and it accumulates over the time Volatility feedback exists but does not reinforce over the time.

7 The data CRSP quarterly database COMPUSTAT daily database merged using the identifiers CUSIP, and CNUM. Sample period: ,861 firm-quarter observations The debt is computed as the sum of total liabilities (data54) and preferred stock (data55). Equity is computed as the product of common shares outstanding (data61) and price at the end of the quarter (data14). The leverage variable QR it is the ratio of debt over equity at time t for firm i. Quartiles are obtained based on the average QR it. We consider firms with QR>1 outliers and eliminate them.

8 Empirics Leverage: QR it =Debt/Equityforfirm i at time t Realized volatility: σ it = q PQ h=1 r2 ith Risk premium: r it = P Q h=1 r m,t 1,h P Q h=1 r2 m,t 1,h P Q h=1 [r i,t 1,hr m,t 1,h ] where Q = number of days in each quarter r it = return of stock i in excess of T-Bill r mt = market return in excess of T-Bill

9 Stats: QR Panel 1: All Sample Q1 Q2 Q3 Q4 All Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera E E+12 Probability Observations Panel 2: No Outliers Q1 Q2 Q3 Q4 All Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera E E+8 Probability Observations

10 Figure 1. Cross Sectional Average QR, with +/- One Standard Deviation Bands..7 Q1 2. Q All Q3 Q

11 Stats: Realized Volatility No Outliers Q1 Q2 Q3 Q4 All Mean Median Maximum Minimum..... Std. Dev Skewness Kurtosis Jarque-Bera E E+6 Probability Observations

12 Figure 2. Cross Sectional Average Realized Volatility, with +/- One Standard Deviation Bands. 2.8 Q1 2.8 Q All Q3 2.8 Q

13 Stats: CAPM required returns No Outliers Q1 Q2 Q3 Q4 All Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Observations

14 The PVAR model w it = α i + Φw i,t 1 + ε it w it = QR it σ it r it, α i = α i1 α i2 α i3, Φ = φ 11 φ 12 φ 13 φ 21 φ 22 φ 23 φ 31 φ 32 φ 33 ε i,t i.i.d. v (, Ω ε )andω ε = i =1,,N and t =1,,T. σ ε11 σ ε21 σ ε22 σ ε31 σ ε32 σ ε11

15 Pesaran s QMLE Estimation Take first differences The log likelihood function is w it = Φ w i,t 1 + ε it mn(t 1) l(θ) = 2 log (2π) N 2 log Σ η 1 2 NX i=1 η iσ 1 η η i where θ =(φ 11, φ 12, φ 13, φ 21, φ 22, φ 23, φ 32, φ 31, φ 33, ω 11, ω 21, ω 31, ω 22, ω 32, ω 33 ) Ω ε = ω 2 11 ω 11 ω 21 ω 11 ω 31 ω 11 ω 21 ω ω 2 22 ω 21 ω 31 + ω 22 ω 32 ω 11 ω 31 ω 21 ω 31 + ω 22 ω 32 ω ω ω 2 33

16 Trivariate PVAR QR i,t = φ 11 QR i,t 1 + φ 12 σ i,t 1 + φ 13 r i,t 1 + ε it1 σ it = φ 21 QR i,t 1 + φ 22 σ i,t 1 + φ 23 r i,t 1 + ε it2 r i,t = φ 31 QR i,t 1 + φ 32 σ i,t 1 + φ 33 r i,t 1 + ε it3 Trivariate Panel VAR. No outliers. Q 1 t-stats Q 2 t-stats Q 3 t-stats Q 4 t-stats All t-stats φ 1, φ 1, φ 1, φ 2, φ 2, φ 2, φ 3, φ 3, φ 3, ω 1, ω 2, ω 3, ω 2, ω 3, ω 3,

17 Main results ˆφ 21 gives a much larger leverage effect compared to estimates in previous research. ˆφ 21 and ˆφ 12 show leverage effect accumulates. ˆφ 32 confirms volatility feedback ˆφ 32 and ˆφ 23 show volatility feedback does not accumulate.

18 Wald Test H o : φ 13, φ 23, φ 31, φ 32, φ 33 are jointly = Quartile Q1 Q2 Q3 Q4 All Wald statistics p-val.....

19 Contemporaneous Correlations Q1 t-stats Q2 t-stats ρ(qr, σ) ρ(r, σ) ρ(qr, r) Q3 t-stats Q4 t-stats All t-stats ρ(qr, σ) ρ(r, σ) ρ(qr, r)

20 Contemporanous Correlation ρ (QR, σ) > contemporaneous leverage effect ρ ( r, σ) < no contemporaneous volatility feedback

21 Impulse response function AshockfromQR affects QR, σ and r persistently. Volatility shock affects leverage when leverage ratio is high. Shock from required return affects all variables negatively.

22 .1 Shock to QR Shock to σ Shock to E[r].2 4 x Q x Q Q Q Figure 1 - Impulse response: Response to one std shock. Legend: * blue = QR; + green = σ; o red = E[r]

23 Cumulative Effects of one sdt shock to QR on σ Q Q Q Q4

24 Figure 4 Cumulative Effects of an Orthogonal Shock ( 1 s.d. of σ ) to σ on rbar 2 x x Q Q2 1 x x Q Q4

25 Concluding remarks We reconfirm the relationship between equity volatility and the debt ratio presented in Christie (1982) across the four leverage quartiles. Our main finding is that a dynamic set up is important to capture the cumulative leverage effect. Financial leverage is an economically more significant determinant of equity volatilities than previous work has documented, and its effect accumulates over time. The accumulation of the leverage effect over time renders it at least up to five times larger than previously thought. Our study suggests that past results may be due to not fully allowing for the endogenous nature of the relationship between capital structure and business risk.