Leverage causes fat tails and clustered volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called ‘value investing’, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage, i.e. borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times, funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds is fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset, this can cause substantial losses. This in turn leads to clustered volatility: before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power-law tails, which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on ‘irrational behavior’, such as trend following. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility becomes high, making these extreme fluctuations even worse.     

Stock Market Crashes and the Performance of Circuit Breakers: Empirical Evidence

This study examines the behavior of a small stock market with circuit breakers and with a one-hour preauction order imbalance disclosure, during the October 1987 crash. The crash and its aftershocks lasted for a week and selling pressure was concentrated in higher beta, larger capitalization, and lower leverage firm stocks. Circuit breakers when implemented reduced the next-day opening order imbalance and the initial price loss; however, they had no effect on the long-run response. Some price overreaction and reversal phenomena also are documented.     

The Impulse of Stock Market Volatility and the Market Crash of October 1987

This paper employs the technique of variance decomposition and impulse response functions to examine the dynamic nature of stock market volatility relationships among six major countries during the pre, around, and post October 1987 crash period. During the period around the crash, the US stock market volatility explains much better the variations of the stock market volatility of Australia, Hong Kong, Japan, Singapore and the UK. Our findings clearly indicate that the crash originated in the US and then spread to other major stock markets.     

Non‐operating earnings and firm risk*

We find that non‐operating earnings reduce total earnings volatility, stock price volatility, idiosyncratic risk, and crash risk. The risk‐reducing effects of non‐operating earnings are higher than those of operating earnings for risk measures based on stock market data. Non‐operating earnings serve to mitigate risks among firms with operating losses, high financial leverage, high growth uncertainty, and low‐ability managers.     

Price volatility,international market links,and their implications for regulatory policies

Conclusions The October 1987 stock market crash spawned an abundance of research papers, as scholars attempted to explain what seemed at the time, and to some extent remains, an inexplicable event.Except for the period immediately around the crash, there is only meager evidence that international linkages across markets have become tighter over time. Yet the crash was worldwide in scope, and its similarity across countries was uncanny. Just on the face, this international similarity puts doubt to such explanations as particular macroeconomic events in one country, failure of a given country's market system, or simultaneous changes in underlying fundamentals (which were quite different across countries).Assigning the origination of the crash to one country cannot be entirely ruled out, however, because of the possibility of a non-fully revealing equilibrium contagion process of the type suggested by King and Wadhwani (1988). Such a process would allow a world-wide crash to begin by a particular news event or even by a market mistake in one country. Evidence in favor of this process is that international correlations of returns increased dramatically during the crash period. However, this increase is consistent with other explanations, such as transaction costs hindering international arbitrage except during periods of high volatility.Was the crash the bursting of a bubble? Some evidence seems to support this proposition: for example, in the majority of countries, the pre-crash period displayed significant serial dependence in stock returns, dependence that was definitely not present in the post-crash period. However, further work is necessary to ascertain whether this measured serial dependence is unusual relative to what one would have expected to find, even in a perfectly random process, by choosing a sample period that happened to culminate in a random peak. Ross (1987) shows that such ex post sample period selection will induce upward bias in estimates of serial dependence. Cross-country tests failed to detect this bias, but there are several ambiguities in the tests that will have to be resolved in future work.The crash is history. What implications, if any, does it have for regulatory policy? Is there evidence that popular regulations or rules would have mitigated the crash, or that they would decrease price volatility in general? There is very little evidence in favor of the efficacity of margin requirements, price limits, or transactions taxes. Despite a large number of empirical studies, no one has provided evidence that margin requirements have an impact on volatility. There has been at least one recent paper claiming the contrary, but a careful examination of its methods have uncovered enough problems to cast those results into doubt.As for price limits, there must be a very short-term impact on measured volatility, for the measured market price at a trading halt is likely to understate the direction of movement. Yet even for daily data, the cross-country evidence is slim that price limits reduce volatility, and there is no evidence at all that they work over periods as long as a week. In other words, trading halts caused by limits seem to have no effect on true volatility.Transaction taxes are inversely but insignificantly correlated with volatility across countries, and the effect is too questionable for taxes to be used with confidence as an effective policy instrument.     

DOES THE OCTOBER 1987 CRASH STRENGTHEN THE CO-MOVEMENTS AMONG NATIONAL STOCK MARKETS?

This study examines the effect of the October 1987 crash on the co-movements among national stock markets. Interrelationships among the price movements in different national stock markets are analyzed using correlation and exploratory factor analysis. The data on weekly returns of 12 national stock market indices over the period from August 1984 to December 1990 are used in both local-currency and U.S. dollar terms for the analysis. This study finds that national stock markets became more interrelated after the crash, and the strengthening co-movements among national stock markets continued for a longer period after the crash. In addition, it is shown that the co-movements among national stock markets were stronger when the U. S. stock market was more volatile. These results imply that after investors experienced the October crash, they tend to give more weight to international factors in making investment decisions after the crash than before.     

Stock volatility and the crash of '87

This article analyzes the behavior of stock return volatilityusing daily data from 1885 through 1988. The October 1987 stockmarket crash was unusual in many ways. October 19 was the largestpercentage change in market value in over 29,000 days. Stockvolatility jumped dramatically during and after the crash. Nevertheless,it returned to lower, more normal levels more quickly than pastexperience predicted. I use data on implied volatilities fromcall option prices and estimates of volatility from futurescontracts on stock indexes to confirm this result.     

财务重述、管理层权力与股价崩盘风险：来自中国证券市场的经验证据

股市震荡引发投资者和监管层对股价崩盘风险的关注。从财务重述背后所反映的财务信息质量低下和公司治理失效出发,探讨其对股价崩盘风险的影响,结合管理层权力这一影响组织行为和产出能力的代理人特征,探讨其对财务重述与股价崩盘风险之间关系的影响。研究结果表明：相比未发生财务重述的公司,发生了财务重述的公司的股价崩盘风险明显更高;进一步纳入代理人特征———管理层权力后,发现代理人的这一特征对上述关系有明显的促进作用。     

What Makes Circuit Breakers Attractive to Financial Markets? A Survey

After the stock market crash of October 1987, the Brady Report (1988) and several academic researchers suggested the imposition of "circuit breakers" to prevent the market from fluctuating excessively. Most financial markets in the world have imposed circuit breaker systems, in the form of price limits and trading halts, in an attempt to reduce excessive market volatility. Similar to any other regulations, circuit breakers have proponents and opponents. In this survey, we analyze the benefits and costs of each type of circuit breaker, provide existing theoretical models and predictions related to each type of circuit breaker, and present findings from empirical studies to justify or disqualify the existence of circuit breakers. In addition, we synthesize existing studies and offer directions for further research in this area.     

Does alternative data reduce stock price crash risk? Evidence from third-party online sales disclosure in China

This study empirically investigates the effect of releasing alternative data on firm-specific price crash risk. Using the public launch of a firm's third-party online sales data in a well-known Chinese financial database as an exogenous shock, we find that stock price crash risk significantly decreases with the disclosure of third-party online sales data. The results are robust to a series of endogeneity corrections and robustness checks. We also find that the reduction of stock price crash risk is due to the decrease in managers' bad news withholdings and the increase in the accuracy of market expectations. In addition, the negative association between third-party online sales disclosure and crash risk is more pronounced for firms with weaker external governance, higher earnings volatility, greater likelihood of sales manipulation, and lower book-to-market ratio. Our findings yield important implications for a comprehensive understanding of the information disclosure effect of online sales data in the capital market and the mechanisms to reduce stock price crash risk.     

股指期货是股灾的“幕后推手”吗——基于2015年股灾期间沪深300股指期货高频数据实证分析

选取2015年6月15日至8月26日股灾期间沪深300股指期货与沪深300指数5分钟高频数据,通过E-G两步协整检验、格兰杰因果检验、脉冲响应模型等,对股灾期间股指期货市场价格发现功能及波动溢出效应进行实证研究.结果表明:股灾期间沪深300股指期货仍具备价格发现功能,但存在对现货市场的单向波动溢出,具有一定的"助跌"效应.     

Stock market volatility and the crash of 1987: evidence from six emerging markets

This paper studies volatility, risk premia and the persistence of volatility in six emerging stock markets before and after the 1987 stock market crash. The empirical investigation is conducted by means of the GARCH in the mean model (GARCH-M) and monthly data from Argentina, Greece, India, Mexico, Thailand, and Zimbabwe between January of 1976 and August of 1994. Results indicate changes in the ARCH parameter, risk premia and persistence of volatility before and after the 1987 crash. But these noted changes are not uniform and depend upon the individual markets. Factors other than the 1987 crash may also be responsible for the changes.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

The microstructural foundations of leverage effect and rough volatility

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in this model some of the main features of market microstructure in the context of high frequency trading: high degree of endogeneity of market, no-arbitrage property, buying/selling asymmetry and presence of metaorders. We prove that when the first three of these stylized facts are considered within the framework of our microscopic model, it behaves in the long run as a Heston stochastic volatility model, where a leverage effect is generated. Adding the last property enables us to obtain a rough Heston model in the limit, exhibiting both leverage effect and rough volatility. Hence we show that at least part of the foundations of leverage effect and rough volatility can be found in the microstructure of the asset.     

Stock market volatility and equity returns: Evidence from a two-state Markov-switching model with regressors

This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra- and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the ‘rebound’ model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than short-horizon investors.     

MARKET TIMING ABILITY OF POOLED SUPERANNUATION FUNDS JANUARY 1981 TO DECEMBER 1987

The performance of pooled superannuation funds is analysed within a framework that recognises that risk management or ‘market timing’ is an important aspect of the fund manager's decision-making. Two broad appraoches to the issue of ‘market timing’ are adopted: first, the performance evaluation model developed by Henriksson and Merton [1981] which allows for return differentials to arise from both security selection and market timing; and second, the recursive residuals methodology of Brown, Durbin and Evans [1975] which identifies points in chronological time when the risks of the funds underwent a change. The results indicate that only 5 out of 16 funds had significant shifts in their risk over the period of the study, all of which occurred in late 1986 to early 1987. It follows that the usual Jensen measure of performance is inappropriate for these funds since one component of their performance is due to market timing activities. The return performance of these market timing activities is significantly negative for 15 to 16 funds indicating that their timing ability is perverse. To some extent this is an artifact of the market crash of October 1987 and that all funds had a positive exposure to equities. However, due to their asset allocation policies all funds are assigned significantly positive security selection performance.     

Modelling S&P 100 volatility: The information content of stock returns

Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of the daily volatility of the S&P 100 index from 1984 to 1998 shows there is some incremental volatility information in the returns from the 100 shares that define the index. This evidence is obtained from ARCH models that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Significant differences between estimated volatilities are found for various stock measures and sub-periods.     

A Note: Natural Generalization of Black-Scholes in the Presence of Skewness,Using Stable Processes

The Lognormal price model is generalized to the class of Log-Stable Processes, a family which possesses self-similarity properties usually only associated with the Lognormal, but which, more generally, can model negatively skewed distributions of return. This generalization appears to explain several discrepancies between the Black-Scholes Model and observed market phenomena, such as the variation of implied volatility of option price with exercise price and term to expiry, and the nonzero probability of bankruptcy or ‘crash’. It will be argued that the class of maximally negatively skewed Stable distributions (a class which, paradoxically, contains the normal) may be utilized to produce models which imply these phenomena naturally.     

Volatility Reversion and Correlation Structure of Returns in Major International Stock Markets

This paper investigates the stochastic behavior of weekly stock market returns in the U.S., Japan, and the U.K. during the period 1984 to 1994. The analysis is carried out using an augmented version of Bollerslev's [7] multivariate GARCH model with structural dummies to test for differences in the mean, volatility, and covariance structure of returns during the pre- and post-October 1987 crash periods. In addition, the paper explores the issue of the volatility reversion and time-varying behavior of correlation structure of returns in these markets. Mean-spillovers exist from the U.S. and Japan to the U.K. The magnitude of these spillovers is, however, low. Volatility spillovers exist from the U.S. and, to a lesser extent, from Japan to the U.K. Mean returns in all three markets and volatility in Japan and the U.K. are the same during the two periods, while volatility in the U.S. is lower during the post-crash period. With the exception of the correlation of returns between Japan and the U.K., which has doubled since the October 1987 crash, the remaining correlations are statistically similar during the two periods. Simulations performed indicate that volatility is reverting in the sense that, when it departs from its long-run equilibrium level, it tends to revert back to that level.     

The Crash of ʼ87: Was It Expected? The Evidence from Options Markets

Transactions prices of S&P 500 futures options over 1985-1987 are examined for evidence of expectations prior to October 1987 of an impending stock market crash. First, it is shown that out-of-the-money puts became unusually expensive during the year preceding the crash. Second, a model is derived for pricing American options on jump-diffusion processes with systematic jump risk. The jump-diffusion parameters implicit in options prices indicate that a crash was expected and that implicit distributions were negatively skewed during October 1986 to August 1987. Both approaches indicate no strong crash fears during the 2 months immediately preceding the crash.