Tail relation between return and volume

“It takes volumes to move prices” according to a famous Wall Street adage. But is that really true? This issue regarding the return-volume relationship in the stock market has been addressed in the paper written by François Longin and Giovanni Pagliardi from ESSEC Business School Paris (1).

Are stock market crashes driven by panic selling due to the release of bad news? Do investors behave as perfectly rational agents who correctly assess all the information at their disposal? Are they subject to behavioral biases that might in turn lead to dramatic market crashes when negative news spread into the market? If you are interested in such questions, you can find answers in Longin and Pagliardi’s paper, which provides a rigorous analysis regarding extreme events, their “why” and “how”.

In a nutshell, our paper shows that when moving towards the tails of the statistical distribution of returns, trading volumes and returns display low extreme correlation, meaning that a stock market crash or a stock market boom can be associated with both large and small volumes. Such a result has been found for the US stock market using daily data of the S&P 500 index from 1950 to 2015. The stylized fact is consistent with the economic model developed by Gennotte and Leland (2). Their model shows how a stock market crash can happen even without the release of relevant news. In a framework where asymmetric information among market participants plays a crucial role, investors can misinterpret automatic trading and positive feedback strategies as informed trades. Therefore, algo-trading and positive feedback automatic strategies, together with asymmetric information, turn out to be crucial aspects because of which the stock market may crash.

Our empirical analysis uses extreme value theory. We select extremes with the peaks-over-threshold method, focusing on large positive and negative returns. We then estimate the bivariate distribution of extremes by fitting a general Pareto distribution for each marginal distribution and a Gumbel copula to model the dependence as done in Longin and Solnik (3). The key variable of the model is the extreme correlation coefficient, which can be computed directly from the copula.

The authors show that the extreme correlation is much lower in the tails, and its behavior is pretty symmetric for both tails. Several robustness checks ensure the stability of the results. The extreme correlation in the tails is lower than the usual correlation, and the difference is statistically significant. With this result, the paper sheds light not only on the technical aspects related to the statistical relation between returns and volume, but most importantly on the type of trading activity during extreme events.

Market crashes, their impact and how to manage the latter are some of the most crucial and debated issues in the finance community, comprising not only academics but also practitioners and regulators. And, of course, everybody should be interested in extreme events. Market crashes impact our wealth and therefore our lives. Understanding them deeply represents wonderful knowledge but also turns out to be a very useful tool. This is the motivation of the paper and the great effort devoted by the authors to it. Enjoy the read!

To know more about the paper

Useful resources

(1) Longin F. and G. Pagliardi (2015) Tail relation between return and volume in the US stock market: an analysis based on extreme value theory Working paper, ESSEC Business School.

(2) Gennotte G. and H. Leland (1990) “Market Liquidity, Hedging, and Crashes” American Economic Review, 80, 999–1021.

(3) Longin F. and B. Solnik (2001) “Extreme Correlation of International Equity Markets” Journal of Finance, 56, 649–676.

About the author

The article was written in November 2015 by Giovanni Pagliardi (ESSEC Business School, PhD Program, 2013-2017).

Tail relation between return and volume