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«FLORIAN WEIGERT WORKING PAPERS ON FINANCE NO. 2013/25 SWISS INSTITUTE OF BANKING AND FINANCE (S/BF – HSG) OCTOBER 2012 THIS VERSION: MARCH 2013 In ...»

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IN SEARCH OF CUSHION? CRASH AVERSION AND THE

CROSS-SECTION OF EXPECTED STOCK RETURNS

WORLDWIDE

FLORIAN WEIGERT

WORKING PAPERS ON FINANCE NO. 2013/25

SWISS INSTITUTE OF BANKING AND FINANCE (S/BF – HSG)

OCTOBER 2012

THIS VERSION: MARCH 2013

In Search of Cushion? Crash Aversion and the

Cross-Section of Expected Stock Returns Worldwide ∗ Florian Weigert First Version: October 2012 This Version: March 2013 Abstract This paper examines whether investors receive a compensation for holding stocks with a strong sensitivity to extreme market downturns in a worldwide sample covering 40 different countries. I find that stocks with strong crash sensitivity earn higher average returns than stocks with weak crash sensitivity. The risk premium is particularly strong in countries that rank high on the individualism index developed by Hofstede (2001). My findings are consistent with the ‘cushion hypothesis’ by Weber and Hsee (1998) and Hsee and Weber (1999): Crash sensitivity is only marginally compensated in socially-collectivist countries where an investor’s social network serves as a cushion in the case of large financial losses. However, there exists a statistically and economically important premium in individualistic countries where investors personally bear the risk of large financial losses.

Keywords: Asset Pricing, Asymmetric Dependence, Copulas, Coskewness, Crash Aversion, Cultural Finance, Cushion Hypothesis, Downside Risk, Individualism, Tail Risk JEL Classification Numbers: C12, G01, G11, G12, G15, G17, F30.

∗ Florian Weigert is from the Chair of International Finance and CDSB at the University of Mannheim, Address: L9, 1-2, 68131 Mannheim, Germany, Telephone: ++49-621-181-1625, e-mail: weigert@bwl.unimannheim.de. The author thanks Stefan Ruenzi, Erik Theissen, and seminar participants at the University of Mannheim for their helpful comments. All errors are my own.

In Search of Cushion? Crash Aversion and the Cross-Section of Expected Stock Returns Worldwide Abstract This paper examines whether investors receive a compensation for holding stocks with a strong sensitivity to extreme market downturns in a worldwide sample covering 40 different countries. I find that stocks with strong crash sensitivity earn higher average returns than stocks with weak crash sensitivity. The risk premium is particularly strong in countries that rank high on the individualism index developed by Hofstede (2001). My findings are consistent with the ‘cushion hypothesis’ by Weber and Hsee (1998) and Hsee and Weber (1999): Crash sensitivity is only marginally compensated in socially-collectivist countries where an investor’s social network serves as a cushion in the case of large financial losses. However, there exists a statistically and economically important premium in individualistic countries where investors personally bear the risk of large financial losses.

Keywords: Asset Pricing, Asymmetric Dependence, Copulas, Coskewness, Crash Aversion, Cultural Finance, Cushion Hypothesis, Downside Risk, Individualism, Tail Risk JEL Classification Numbers: C12, G01, G11, G12, G15, G17, F30.

1 Introduction Since the pioneering work of Roy (1952), economists have recognized that individuals are aware of rare disaster events (e.g., stock market crashes) and take precautions to reduce their likelihood of being affected by such a catastrophe occurring. If agents derive disproportionately strong disutility from large financial losses, there should be a risk premium for the occurence of infrequent, yet heavy tail events (Rietz (1988)). Indeed, Gabaix (2012) shows that a time-varying rare disaster risk framework can explain several puzzles in macro-finance and Bollerslev and Todorov (2011) find that the compensation for rare events accounts for a large fraction of the U.S. equity risk premium.1 In addition to explaining the development of aggregate stock market returns, rare disasters and crash aversion are shown to have an impact on the pricing of individual stocks in the cross-section. Ruenzi and Weigert (2013) find that, in the U.S. setting, crash-sensitive stocks, i.e., stocks that are likely to perform particularly badly when the market crashes, earn significantly higher average returns than crash-insensitive stocks, i.e., stocks that offer some protection against market downturns.2 This finding is consistent with investors being particularly averse against suffering large financial losses during stock market crashes and thus requiring an additional return premium for holding such stocks.3 This paper examines the impact of investors’ crash aversion on the cross-sectional pricing of individual stocks worldwide. First, I investigate whether the premium for the crash sensitivity of a stock also holds out-of-sample across different international stock markets besides the United States. Second, I use differences in investor, firm, and market characteristics across countries to investigate the determinants of the crash sensitivity premium.

In particular, I examine whether the premium for a stock’s crash sensitivity is greater in those countries where investors are likely to exhibit a higher degree of aversion against large financial losses during market crashes.





However, these findings are not without dissension. Julliard and Ghosh (2012) document that it is unlikely that an equity premium puzzle of the same magnitude as the historical one would arise, if aggregate stock market returns are generated by a rare events distribution.

In related papers, Kelly (2012) and Cholette and Lu (2011) show that there exists a premium for stocks with heavy tail risk exposure. They document that stocks with high systematic tail risk exposure earn significantly higher expected returns than stocks with low systematic tail risk exposure.

Crash aversion is also documented in the empirical option pricing literature. Rubinstein (1994) and Bates (2008) find that instruments that offer protection against extreme market downturns (such as deep out-of-the-money puts) have high implied volatility and are relatively expensive.

Following the methodology of Ruenzi and Weigert (2013), I use copula methods based on extreme value theory to determine the crash sensitivity of a stock. Specifically, I capture the crash sensitivity of an individual stock based on the extreme dependence between the stock’s return and the market return in the lower left tail of their joint distribution (also called lower tail dependence, LTD).4 My empirical results indicate that a quintile portfolio consisting of stocks with the strongest LTD underperforms a quintile portfolio consisting of stocks with the weakest LTD by more than 8% on a monthly basis during periods of heavy market downturns. Consequently, from an equlilibrium perspective, investors who are sensitive to large losses during market crashes will require a premium for holding stocks with strong LTD in the long run.5 Investigating data from 40 countries, I find strong support for a LTD risk premium in the cross-section of average stock returns. In the pooled worldwide sample including U.S.

stocks (excluding U.S. stocks) from 1981 to 2011, top quintile LTD stocks outperform bottom quintile LTD stocks by 7.67% (6.16%) p.a. on average. The premium for LTD is positive and significant (at least at the 5% level) across all different geographical subsamples with a return spread between the strong LTD quintile portfolio and the weak LTD quintile portfolio ranging from 13.49% p.a. in America to 3.82% p.a. in Asia. Results from multivariate regression analyses reveal that the LTD premium cannot be explained by other risk- and firm characteristics, such as market beta (Sharpe (1964) and Lintner (1965)), size (Banz (1981)), book-to-market (Basu (1983)), liquidity (Amihud (2002)), momentum (Jegadeesh and Titman (1993)), idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang (2009)), and coskewness (Harvey and Siddique (2000)). Controlling for these variables, I find that an increase of one standard deviation in LTD is associated with an increase of average returns by 3.03% (2.18%) p.a. based on the worldwide sample including the U.S. (excluding the U.S.).

Although LTD has a strong positive impact on average stock returns both in the pooled When focusing on joint extreme events of stock returns, the linear correlation is not the appropriate dependence concept. The linear correlation cannot capture joint extreme events if the underlying bivariate distribution is non-normal (see Embrechts, McNeil, and Straumann (2002)).

Similar to the calculation of LTD, I also capture the extreme dependence between the stock’s return and the market return in the upper right tail of their joint distribution (upper tail dependence, UTD). Stocks with strong UTD realize their highest payoffs in times of stock market booms, i.e. have high upside potential.

Following the theoretical framework of Ang, Chen, and Xing (2006), investors are willing to hold stocks with high upside potential at a discount.

worldwide sample as well as in all geographical subsamples, there still exist large differences in the magnitude of the premium across countries. Separate examinations of each stock market reveal that the impact of LTD on average stock returns is significantly positive at the 10% level (5% level, 1% level) in 18 (15, 8) of the 40 countries. The largest return spreads between the top quintile LTD portfolio and the bottom quintile LTD portfolio are found in the U.S. (14.64% p.a.), Australia (12.79% p.a.), and the Netherlands (11.22% p.a.). Although not statistically significant, negative LTD premiums (i.e., LTD discounts) are found in China (-5.30% p.a.), South Korea (-3.46% p.a.), Taiwan (-3.05% p.a.), and the Philippines (-0.29% p.a.). Hence, these results lead to the question of how the magnitude of the LTD premium is related to country-specific differences in investor, firm, and market characteristics.

I regress the average country-specific LTD premium on a number of potential determinants that are known to vary across countries. The magnitude of the LTD premium is possibly related to cultural variables (as in Chui, Titman, and Wei (2010)), differences in religion and language (as in Stulz and Williamson (2003)), macroeconomic fundamentals and aggregate stock market characteristics, country-wide differences in accounting standards and variables proxying for investor protection (LaPorta, Lopez-De-Silanes, Shleifer, and Vishny (1998) and LaPorta, Lopez-De-Silanes, and Shleifer (2006)), as well as differences in a country’s stock market integration (Bekaert, Hodrick, and Zhang (2009)), government social spending, and investor characteristics. My explorative investigation reveals a surprising result: Crosscountry differences in the LTD premium are most strongly correlated with differences in one cultural variable, the Hofstede (2001) individualism dimension.6 How can one explain this empirical finding? My main hypothesis is that the premium for a stock’s LTD is higher (lower) in those countries where local investors are likely to exhibit a higher (lower) degree of crash aversion.7 Experimental studies in psychology and Hofstede (2001) studies work-related values around the world with reported data from 88,000 IBM employees in 76 countries over the time period from 1967 to 1973. According to his classification, cultures differ in their emphasis on five dimensions: individualism, masculinity, power distance, uncertainty avoidance, and long-term orientation. His model provides scales from 0 to 100 for each dimension for a total of 76 countries, and each country has a position on each scale or index, relative to other countries. Countries with a score on the high side of the individualism dimension represent a society where people look after themselves and their immediate family only. In contrast, countries with a score on the low side of this dimension, i.e., collectivistic countries, represent a society where people belong to in-groups that look after them in exchange for loyalty.

I implicitly assume that most stocks in a country are held by local investors and that local investors hold a disproportional amount of their wealth in domestic assets. French and Poterba (1991) find strong management (such as Weber and Hsee (1998) and Hsee and Weber (1999)) indicate that there exists a strong connection between financial risk taking of individuals and their cultural background. In particular, they find that individuals in individualistic countries tend to be more risk-averse in financial decisions than individuals in collectivistic countries.8 This result is explained in terms of a cushion hypothesis. The strong social network among individuals in a collectivistic country (such as China) allows for the joint development of mechanisms to hedge against financial risk. In particular, the tightly-knit society, and the increased awareness of family and friends, provides help if an individual suffers from a large financial loss (i.e., individuals are ’cushioned’ if they fall). Conversely, this financial ’insurance’ from the social network is not readily available to individuals in individualistic societies (such as the U.S.). Consequently, investors in individualistic countries are expected to require a higher premium for a stock’s LTD than investors in collectivistic countries.9 I find that the LTD premium is significantly higher in individualistic countries than in collectivistic countries.10 The return spread between the top quintile LTD portfolio and the bottom quintile LTD portfolio in those countries with individualism indexes in the top 20% (bottom 20 %) is 12.68% (-0.13%) p.a. Hence, the yearly returns on a long minus short LTD portfolio are more than 12.81% higher in those countries with individualism indexes in the top 20% than in those countries with individualism indexes in the bottom 20%. The positive relationship between the LTD premium and individualism is stable to a battery of different robustness checks, such as different portfolio sorting procedures, the use of a different individualism measure from the GLOBE study (see House, Hanges, Javidan, Dorfman, and Gupta (2004)), and different sample sizes.



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