What Likely Range of My Wealth Will Be?

20 Pages Posted: 19 Oct 2008 Last revised: 7 Feb 2009

See all articles by Raymond Kan

Raymond Kan

University of Toronto - Rotman School of Management

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School; China Academy of Financial Research (CAFR)

Date Written: February 6, 2009

Abstract

The median is often a better measure than the mean in evaluating the long-term value of a portfolio. However, the standard plug-in estimate of the median is too optimistic. It has a substantial upward bias that can easily exceed a factor of two. In this paper, we provide an unbiased forecast of the median of the long-term value of a portfolio. In addition, we also provide an unbiased forecast of an arbitrary percentile of the long-term portfolio value distribution. This allows us to construct the likely range of the long-term portfolio value for any given confidence level. Finally, we provide an unbiased forecast of the probability for the long-term portfolio value falling into a given interval. Our unbiased estimators provide a more accurate assessment of the long-term value of a portfolio than the traditional estimators, and are useful for long-term planning and investment.

Keywords: long-term investment, median, quantiles

JEL Classification: C22, C53, G11, G12

Suggested Citation

Kan, Raymond and Zhou, Guofu, What Likely Range of My Wealth Will Be? (February 6, 2009). Available at SSRN: https://ssrn.com/abstract=1285745 or http://dx.doi.org/10.2139/ssrn.1285745

Raymond Kan

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S3E6
Canada
416-978-4291 (Phone)
416-971-3048 (Fax)

Guofu Zhou (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

Washington University
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-6384 (Phone)
314-658-6359 (Fax)

HOME PAGE: http://apps.olin.wustl.edu/faculty/zhou/

China Academy of Financial Research (CAFR)

Shanghai Advanced Institute of Finance
Shanghai P.R.China, 200030
China

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