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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 SeriesDate posted: October 19, 2008 ; Last revised: February 07, 2009Suggested CitationContact Information
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