What Will the Likely Range of My Wealth Be?

Abstract

The median is often a better measure than the mean in evaluating a portfolio’s long-term value. The standard plug-in estimate of the median, however, is too optimistic. It has a substantial upward bias that can easily exceed a factor of 2. This article provides an unbiased forecast of the median of a portfolio’s long-term value. It also provides an unbiased forecast of an arbitrary percentile of a portfolio’s long-term value distribution, which enables the construction of the likely range of a portfolio’s long-term value for any given confidence level. The article offers an unbiased forecast of the probability of a portfolio’s long-term value falling within a given interval. The article’s unbiased estimators give a more accurate assessment of a portfolio’s long-term value than do traditional estimators and are useful for long-term planning and investment.

Keywords: Investment Theory, Portfolio Theory, Quantitative Tools, Econometric and Statistical Methods, Portfolio Management, Portfolio Construction, Rebalancing, and Implementation, Private Wealth Management, Investment Policy Formulation