In traditional retirement, planning the annual investment return is assumed to be a constant number, such as 8.5 percent per annum. This number depends on the asset allocation and on assumptions about the returns of the different asset classes. The outcome of the computation is typically presented as the expected wealth values over the anticipated period of retirement.
The problem with this approach is that investment returns are neither known nor constant over time. While investing is about risk, retirement calculators presenting single scenarios treat risk either as a certainty, or at best, as a 50/50 proposition: 50/50 you will do better or worse than the expected outcome. Investing is not an exact science; no one knows the precise return of different asset classes over any given number of years. Investment returns are random variables, characterized by expected values (or averages), standard deviations, and, more generally, probability distributions. For this reason, projections of an investment program's possible results should also be expressed in terms of probabilities. For example:
There is a 95 percent chance you won't run out of money in retirement.
There is a 50 percent probability you will accumulate at least $3.1 million. There is a 25 percent chance you will have $5.2 million or more. But there is also a 10 percent chance you will have $400,000 or less.
To arrive at these types of conclusions it is necessary to use what are ...