The behaviour of the distributions of stock returns: an analysis of the European market using the Pearson system of continuous probability distributions

Abstract

We employ the Pearson system of frequency curves to analyse the behaviour of unconditional daily return distributions for all the shares that constitute the STOXX Europe 600 index. Our results show that over finite time periods of analysis the distributions are adequately described as type IV. The occasional exceptions are linked strictly to extraordinary events that result in abnormal returns. They are more frequent if short time intervals are examined. When an infinite time of analysis is assumed, the results do not reject the hypothesis that the behaviour of stock returns is symmetrical and that it is of type VII, which is a special case of type IV that subsumes the Student's t and the Cauchy distributions and is easier to deal with in practice.

Keywords:

• Pearson system
• type IV
• type VII
• European equity market
• stock return distributions
• stock return behaviour
• financial modelling

JEL Classification::

• G11

Acknowledgements

The author gratefully appreciates the thoughtful comments of Prof. Massimo Bilancia, Prof. Maurizio Fanni, the participants at the IV International Risk Management Conference, the Editor and the Referees, which have led to an improved version of this article. All remaining deficiencies and shortcomings are my responsibility.

Notes

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² That is

³ The shares of an electrical engineering conglomerate plunged 61.8% on a compound basis in a day (96.3% on a continuous basis) after announcing that it was considering Chapter 11 bankruptcy protection for its US subsidiary. An insurance company and a bank were hit heavily by their sub-prime mortgage loan losses and thus lost 77.6% and 66.6%, respectively, on a compound basis in a single day (149.5% and 109.6%, respectively, on a continuous basis). A supermarket operator's shares fell 63.0% on a compound basis (99.5% on a continuous basis) on the day when a fraud at a US subsidiary and a board level accounting scandal were announced. A silicon chip designer's shares crashed 63.0% in a day on a compound basis (99.3% on a continuous basis) when it warned that its third-quarter profit would be only half the expected level and it admitted that the industry downturn had finally had an impact on the company. A pharmaceutical company's shares dropped 62.1% on a compound basis (96.9% on a continuous basis) on the day of the announcement of very disappointing results in the trial of a new drug. A biotech company announced the voluntary suspension of the marketing of a treatment for multiple sclerosis after two serious adverse events affected its patients, thus causing its shares to fall 68.0% in a single day on a compound basis (114.0% on a continuous basis). The shares of a real estate company that had suffered heavily in the property and financial markets crisis dropped 47.8% in a single day on a compound basis (65.1% on a continuous basis) when it became clear that it had suffered high cash outflows and that it would incur serious problems in completing its development pipeline. An electrical power company's shares gained 40.9% on a compound basis (34.3% on a continuous basis) on the day when, at the height of the dot.com boom, it announced its plans to expand into telecommunications. In all cases, the distributions are type IV if these abnormal daily returns are not taken into account.