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What Likely Range of My Wealth Will Be?

Raymond Kan
University of Toronto - Joseph L. Rotman School of Management

Guofu Zhou
Washington University, St. Louis - John M. Olin School of Business

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 Classifications: C22, C53, G11, G12

Working Paper Series

Date posted: October 19, 2008 ; Last revised: February 07, 2009

Suggested Citation

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

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Contact Information

Guofu Zhou (Contact Author) Washington University, St. Louis - John M. Olin School of Business ( email ) Washington University Campus Box 1133 St. Louis, MO 63130-4899 United States 314-935-6384 (Phone) 314-658-6359 (Fax)
Raymond Kan University of Toronto - Joseph L. Rotman School of Management ( email ) 105 St. George Street Toronto, Ontario M5S 3E6 Canada 416-978-4291 (Phone) 416-971-3048 (Fax)