‘Leverage Effect’ in country betas and volatilities?

Abstract

Leverage effect hypothesis predicts past returns to have a negative effect on equity riskiness. We document a surprising pattern: the effect of past returns on country index betas and volatilities turns into positive as past-return horizon is extended. Past 60-month returns have a significant positive effect, which provides a direct means of ruling out leverage hypothesis as an explanation of asymmetric volatility. The positive effect of distant-past returns is puzzling. It appears to be due to mean reversion in stock indexes and international investors’ trading patterns consistent with mean reversion.

Keywords:

• asymmetric volatility
• leverage effect
• country stock indexes
• country beta and volatility
• long-horizon mean reversion
• equity portfolio flows

JEL Classification:

• G15
• G12

Acknowledgement

We thank Duminda Kuruppuarachchi for helpful comments.

Notes

¹ Leverage is a decreasing function of past equity returns (unless debt is zero or continuously rebalanced). Equity betas and volatilities are increasing in leverage. Thus, leverage effect induces a negative relation between riskiness and past returns (Black, 1976; Christie, 1982). Recall that equity leverage can be defined with respect to book equity or market equity. It is the market equity that is negatively related to past returns.

² Persistence in riskiness coupled with positive time-varying risk premiums leads to stock price decreases (increases) when equity riskiness is being revised upwards (downwards); see, for example, Campbell and Hentschel (1992).

³ The pattern seems undetected in related literatures (studies of asymmetric volatility, see footnote 7; studies of time-varying risk premia; studies on predicting country betas, e.g., Ülkü and Baker, 2014).

⁴ Another advantage of our sample period choice is that it provides a large cross-section as MSCI country indexes for emerging markets are available for only more recent periods.

⁵ The correlation between real returns and returns in excess of the risk-free rate is 0.98 or higher. We preferred real returns since reliable risk-free rate series were not available for some countries. US$ returns lead to similar conclusions.

⁶ Our results are similar regardless of the definition of volatility. We report results with the most basic definition, squared demeaned returns. Results with alternative definitions such as high−low range and standard deviation of daily returns in month t (available from the authors) are even stronger in pointing to the pattern documented in the article.

⁷ See Bouchaud et al. (2001), Figlewski and Wang (2000), Bollerslev et al. (2006) and Chen and Ghysels (2011).

⁸ Results for T<12 are available from the authors. As some studies report a significant ‘leverage effect’ in return volatilities, but not in betas (Braun et al., 1995; Bekaert and Wu, 2000), we report both. Table 1 shows that our results apply in both cases, with some difference in the timing of the sign change. Our conclusions in Tables 1–3 remain robust under various alternative adjustments for panel heteroscedasticity.

⁹ We also replicated the same estimation on Richards’ (1997) 1970–1995 sample period (available from the authors). While M(T)’s are usually insignificant in this period (consistent with Richards’ report), the same pattern holds consistently for both beta and volatility: β₂ gradually turns into positive and becomes significantly positive at T=60. Richards (1997) focuses on 36-month horizon, which is insignificant as it is in the middle of the range over which the sign change occurs.

¹⁰ We convert Standard & Poor’s ratings into a scale between 0–10 where 10 represents the lowest rating. Consequently, ‘ratings’ variable enters Equations 1 and 2 with a positive coefficient.

¹¹ The negative effect of short-horizon past returns is consistent with the volatility feedback story: good (bad) news decrease (increase) the riskiness of the equity, and near-past realized returns reflect revisions to expected returns.

¹² M(T)’s are positively correlated as their contents overlap. The correlation between M(12) and M(60) is +0.335, which does not pose risk of multicollinearity. However, the overlap obscures the strong negative correlation between distant-past returns and near-past returns.

¹³ We replicated the same analysis for S&P500 stocks (available from the authors). Unlike the international market-level case, the effect of M(T) remains negative up to T=48. Yet, returns between months 48 and 60 exert a significant positive effect on current beta and volatility. The difference is consistent with Aydemir et al.’s (2006) theoretical model that predicts stronger financial leverage effects at the individual stock level.

¹⁴ E[R_t∙R²_t]=0 for standard normal distribution. A negative relation between (demeaned) R_t and R²_t reflects negative skewness in return series. Thus, past returns can be used to predict conditional skewness. In Panel B of Table 2, we employ an approach along these lines.

¹⁵ The effect of R_i,t on current beta and volatility is captured by β₅ coefficients, which are significantly negative. In a univariate regression (not in the table), the relationship is highly significant with t = −4.48 in the beta regression and t = −8.41 in the volatility regression. These negative coefficients imply negative skewness. The effect of M(12) and M(60) on R_i,t’s effect on beta and volatility is captured by β₆ and β₇ coefficients, respectively. Positive β₆ indicates that when average returns over the past 12 months are high, the effect of current return shocks on current riskiness is less negative. Negative β₇ indicates that when average returns over the past 60 months are high, the effect of current return shocks on current riskiness is more negative. In other words, M(12) and M(60) exert significant effect on the conditional skewness of the return distribution: high M(12) makes conditional skewness less negative, and high M(60) makes it more negative.

¹⁶ These data are compiled at the destination market (for most countries, directly from the stock exchange); hence, they are not subject to biases from which TIC (US Treasury Capital International) data have been shown to suffer. Further details and summary statistics are presented in the online Appendix.

¹⁷ Our sample period captures recent times when such international strategies have become widespread. This may explain why the pattern has become more significant compared to Richards’ (1997) sample period. Yet, our results need to be confirmed on future data to make sure they were not driven by the specific periodicity of the two most recent global business cycles. Since our further results (available upon request) suggest stronger effects in the country-specific component, we think that the pattern documented in this article is more general than what can be attributed to two recent global cycles.