Portfolio Survival Probability Simulator Calculator

Survival probability is the share of simulated futures in which a portfolio still holds a positive balance at the end of the spending horizon. Each of the two thousand trials grows the balance by a random lognormal annual return, then subtracts a withdrawal that is indexed upward by the inflation rate every year; a trial fails the first time the balance reaches zero. That inflation indexing is what makes the problem hard. A 40,000 dollar withdrawal against a one million dollar portfolio is a 4 percent initial rate, but at 3 percent inflation the same real spending demands roughly 97,000 dollars in year thirty and consumes about 1.9 million dollars cumulatively. The order of returns matters as much as their average, since losses early in retirement permanently shrink the base that later gains can compound. Planners generally treat survival probabilities of 85 to 95 percent as acceptable; a result of 100 percent usually signals spending far below what the assets could support rather than a well-tuned plan. The model has clear boundaries. Constant-dollar withdrawal is a rigid rule that real retirees do not follow, and dynamic approaches such as spending guardrails materially improve outcomes. Taxes, advisory fees, Social Security, annuity income and lumpy late-life medical costs are all absent. Independent lognormal returns exclude mean reversion and understate crash severity, and two thousand trials carry roughly a percentage point of sampling noise in the headline survival figure.

Before the mid-1990s, retirement projections typically applied an average return to a spending plan, an approach that quietly assumes returns arrive in a smooth and forgiving order. William P. Bengen, a California financial planner, tested that assumption against the record. His article Determining Withdrawal Rates Using Historical Data, published in the Journal of Financial Planning in October 1994, ran rolling thirty-year periods across decades of US stock and bond data and found that a first-year withdrawal near 4 percent, indexed to inflation thereafter, survived even the worst starting points, notably retirements beginning in the mid-1960s. He named that worst-case figure SAFEMAX. In 1998 Philip Cooley, Carl Hubbard and Daniel Walz of Trinity University published portfolio success rates across a grid of stock and bond allocations and time horizons in the AAII Journal. That work, universally called the Trinity study, both reinforced the 4 percent figure and popularised expressing results as a success rate rather than a single answer. Monte Carlo engines reached retail retirement software during the late 1990s and 2000s, letting planners sample random paths instead of replaying historical sequences. Later research by Wade Pfau, Michael Kitces and others questioned whether 4 percent transfers to low-yield environments or to non-US market histories, while Bengen himself revised his figure upward after broadening the asset mix.