Fat Tails in Small Sample

38 Pages Posted: 6 Jan 1998

See all articles by Ronald Huisman

Ronald Huisman

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)

Kees C. G. Koedijk

Tilburg University - Department of Finance

Clemens J.M. Kool

Utrecht University - School of Economics

Franz C. Palm

University of Maastricht - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: September 1997

Abstract

It is a well-known stylized fact that financial returns are non-normal and tend to have fat-tailed distributions. This paper presents a methodology that accurately estimates the degree of fat-tailedness, characterized by the tail-index, in small samples. We present a simple approach based on the Hill estimator. Our estimator is a weighted average of a set of Hill estimators, with weights obtained by using simple least squares techniques. The estimator produces unbiased estimates for the tail-index in small samples and we also provide appropriate standard errors. Using this estimator we produce tail-index estimates for returns on stocks and exchange rates that are close to estimates obtained from extremely large datasets. The results indicate that many documented conclusions about the tail behavior of financial series have over-estimated their fat-tailedness in small samples.

JEL Classification: C13, C40, G10, F31

Suggested Citation

Huisman, Ronald and Koedijk, Kees G. and Kool, Clemens J.M. and Palm, Franz C., Fat Tails in Small Sample (September 1997). Available at SSRN: https://ssrn.com/abstract=51141 or http://dx.doi.org/10.2139/ssrn.51141

Ronald Huisman (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

Kees G. Koedijk

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4663048 (Phone)
+31 13 4662052 (Fax)

Clemens J.M. Kool

Utrecht University - School of Economics ( email )

Kriekenpitplein 21-22
Adam Smith Building
Utrecht, 3584 EC
Netherlands

Franz C. Palm

University of Maastricht - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands
+31-(0)43-3883833 (Phone)
+31-(0)43-3258535 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.cesifo.de

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