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.