Portfolio Survival Probability Simulator Calculator
Calculate growth with the Portfolio Survival Probability Simulator. Enter principal, rate, compounding frequency, and time to see total balance, interest
Calculator
Adjust values & calculateSurvival Curve (every 5 years)
Formula
Each simulation grows the portfolio using geometric Brownian motion (annual return = mu - 0.5*sigma^2 + sigma*Z) and subtracts inflation-adjusted withdrawals each year. A simulation succeeds if the portfolio value remains positive through the entire time horizon. The survival rate is the percentage of simulations that succeed out of thousands of trials.
Last reviewed: December 2025
Worked Examples
Example 1: Standard Retirement at 4% Withdrawal
Example 2: Conservative Early Retiree
Background & Theory
The Portfolio Survival Probability Simulator applies the following established principles and formulas. Statistics and probability provide the mathematical framework for drawing conclusions from data under uncertainty. The measures of central tendency describe where data cluster. The mean is the arithmetic average, computed as the sum of all values divided by the count. The median is the middle value of an ordered dataset, robust to extreme outliers. The mode is the most frequent value. Spread is quantified by variance, the average squared deviation from the mean, and by its square root, the standard deviation. For a sample, variance uses n minus one in the denominator to correct for bias in estimation. The normal distribution, defined by its mean and standard deviation, is the cornerstone of parametric statistics. Its bell-shaped probability density follows the formula f(x) = (1 / (sigma * sqrt(2*pi))) * exp(-0.5 * ((x - mu) / sigma)^2). The empirical rule states that approximately 68 percent of observations fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three. A z-score standardizes a data point by subtracting the mean and dividing by the standard deviation, expressing how many standard deviations an observation lies from the mean. In hypothesis testing, the p-value is the probability of observing a result at least as extreme as the one obtained, assuming the null hypothesis is true. Confidence intervals express the range within which the true population parameter falls with a specified probability, typically 95 percent. Correlation measures linear association between two variables, with Pearson's r ranging from negative one to positive one. Correlation does not imply causation. Linear regression fits a line of the form y = a + bx to minimize the sum of squared residuals. Bayes' theorem relates conditional probabilities: P(A|B) = P(B|A) * P(A) / P(B), allowing prior beliefs to be updated on new evidence. The law of large numbers guarantees that the sample mean converges to the population mean as sample size grows. The central limit theorem states that the distribution of sample means approaches normality regardless of the population distribution, provided the sample size is sufficiently large, typically 30 or more.
History
The history behind the Portfolio Survival Probability Simulator traces back through the following developments. The mathematical study of probability emerged in the 17th century from correspondence between Blaise Pascal and Pierre de Fermat in 1654. Their exchange, prompted by a gambling problem posed by the Chevalier de Mere, established the foundations of probability theory by calculating expected outcomes through systematic enumeration of cases. Jacob Bernoulli formalized the law of large numbers in his posthumously published Ars Conjectandi of 1713, proving rigorously that empirical frequencies converge to theoretical probabilities with increasing observations. His work laid the groundwork for inferential statistics by connecting mathematical probability to observed data. Carl Friedrich Gauss developed the method of least squares around 1795 while adjusting astronomical observations, and he recognized the bell-shaped error distribution that now bears his name. Pierre-Simon Laplace independently worked on the normal distribution and proved an early version of the central limit theorem around 1810, demonstrating why errors in measurement tend toward normality. The late 19th century saw statistics emerge as a distinct scientific discipline. Francis Galton introduced regression and correlation in the 1880s while studying heredity. Karl Pearson formalized these concepts, developed the chi-squared test, and founded the journal Biometrika in 1901, establishing statistics as a rigorous academic field. Ronald Fisher transformed statistical practice in the early 20th century. His 1925 book Statistical Methods for Research Workers introduced significance testing, analysis of variance, and the concept of the p-value as a decision threshold, establishing the framework still used in scientific research. Fisher and Jerzy Neyman engaged in a prolonged methodological dispute over the interpretation of hypothesis tests. The Bayesian approach, rooted in the 18th century work of Thomas Bayes and Laplace, was largely eclipsed by frequentist methods through much of the 20th century but experienced a revival after World War II and accelerated with computational advances. The late 20th and early 21st centuries brought statistics into every domain through big data, machine learning, and the routine availability of software capable of processing millions of observations.
Frequently Asked Questions
Formula
Survival Rate = Successful Simulations / Total Simulations x 100
Each simulation grows the portfolio using geometric Brownian motion (annual return = mu - 0.5*sigma^2 + sigma*Z) and subtracts inflation-adjusted withdrawals each year. A simulation succeeds if the portfolio value remains positive through the entire time horizon. The survival rate is the percentage of simulations that succeed out of thousands of trials.
Worked Examples
Example 1: Standard Retirement at 4% Withdrawal
Problem: A retiree has $1,000,000, withdraws $40,000/year (4% rule), expects 7% return with 12% volatility, 3% inflation, 30-year horizon.
Solution: Run 2,000 simulations with GBM model\nWithdrawal rate: 4.00%\nReal return: 7% - 3% = 4%\nYear 1 withdrawal: $40,000\nYear 30 withdrawal (inflation-adjusted): ~$97,000\nTotal withdrawn over 30 years: ~$1,902,000\nMedian final portfolio: ~$1,500,000\nSurvival probability: ~88%
Result: Survival Rate: ~88% | Median Final: ~$1.5M | 4% withdrawal rate
Example 2: Conservative Early Retiree
Problem: Early retiree at 50 with $2,000,000, withdraws $60,000/year (3%), expects 6% return, 10% volatility, 2.5% inflation, 40-year horizon.
Solution: Run 2,000 simulations\nWithdrawal rate: 3.00%\nReal return: 6% - 2.5% = 3.5%\nYear 1 withdrawal: $60,000\nYear 40 withdrawal: ~$160,000\nLower withdrawal rate increases survival\nSurvival probability: ~92%
Result: Survival Rate: ~92% | 3% withdrawal rate | 40-year horizon
Frequently Asked Questions
What is portfolio survival probability and why does it matter?
Portfolio survival probability measures the likelihood that your investment portfolio will sustain your planned withdrawals throughout your entire retirement or spending horizon without running out of money. This is the central question in retirement planning because running out of money in your 80s or 90s would be catastrophic with no ability to return to work. The simulation runs thousands of scenarios with varying market returns to determine what percentage of cases your portfolio survives the full period. A survival probability of 90% or higher is generally considered acceptable, while below 80% suggests you may need to reduce spending, increase savings, or adjust your investment strategy.
How does inflation affect portfolio survival?
Inflation erodes the purchasing power of your withdrawals, requiring you to increase the dollar amount withdrawn each year to maintain the same standard of living. If you withdraw $40,000 in year one and inflation averages 3%, you need $41,200 in year two, $42,436 in year three, and so on. By year 30, your annual withdrawal would be approximately $97,000 in nominal terms just to maintain the same purchasing power. This exponentially growing withdrawal demand is why inflation is called the silent killer of retirement plans. Even moderate 3% inflation doubles prices in 24 years. The simulator accounts for this by increasing annual withdrawals by your specified inflation rate each year.
What does the survival curve tell me that a single probability number does not?
The survival curve shows the probability of your portfolio surviving to each specific year, revealing the timing pattern of potential failures. A portfolio might have 85% overall survival probability, but the curve shows whether failures cluster early (suggesting the portfolio is fundamentally underfunded) or late (suggesting it works for most reasonable scenarios but struggles in extended horizons). If the curve drops steeply around years 20-25, you know that is your danger zone and can plan accordingly with backup strategies. The curve also helps with partial planning: even if 30-year survival is only 80%, the 20-year survival might be 95%, informing decisions about annuity purchases or other hedging strategies for later years.
How can I improve my portfolio survival probability?
Several strategies increase survival probability. First, reduce the withdrawal rate: dropping from 4% to 3.5% can increase survival from 80% to over 90%. Second, maintain a diversified portfolio with some equity exposure for growth, as all-bond portfolios actually fail more often due to inflation erosion. Third, implement dynamic withdrawal strategies that reduce spending in down markets. Fourth, delay Social Security to increase guaranteed income. Fifth, consider purchasing a partial annuity to cover essential expenses with guaranteed income. Sixth, maintain a cash reserve of 1-2 years of expenses to avoid selling stocks during downturns. Seventh, consider part-time work in early retirement years to reduce portfolio drawdowns during this critical sequence-of-returns risk period.
What is sequence of returns risk and how does it affect survival?
Sequence of returns risk is the danger that poor market performance occurs early in your withdrawal period when your portfolio is largest and most vulnerable. Two retirees can experience identical average returns over 30 years but have vastly different outcomes depending on the order of those returns. Bad early returns combined with withdrawals permanently deplete the portfolio base, leaving less capital to benefit from later good returns. This is why Monte Carlo simulation is superior to simple average-return calculations: it captures the variability in return sequences. The simulator reveals this through the range of outcomes: some paths succeed brilliantly while others with the same average return fail because the bad years came first.
Should I use nominal or real (inflation-adjusted) returns in this simulator?
This simulator is designed to use nominal returns with a separate inflation rate input, which is the more accurate approach. When you enter 7% expected return and 3% inflation, the simulator grows your portfolio at rates centered around 7% while simultaneously increasing your withdrawal amount by 3% annually. This correctly models the real-world dynamic where your portfolio earns nominal returns but your spending needs increase with inflation. If you instead used real returns (already inflation-adjusted) of 4%, you would set the inflation input to 0% and keep your withdrawal amount constant. Both approaches should produce similar results, but the nominal approach better captures the interaction between volatile nominal returns and steadily increasing inflation-adjusted spending.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy