Monte Carlo Simulation: How to Model Investment Outcomes and Probability

How Monte Carlo Simulation Works

A Monte Carlo simulation for retirement planning follows these steps. First, specify the portfolio's expected return and standard deviation based on its asset allocation. For a 60/40 portfolio, this might be 8% expected return and 12% standard deviation. Second, specify the initial portfolio value, annual withdrawals (adjusted for inflation), and time horizon. Third, generate 10,000 random scenarios by drawing annual returns from a normal distribution (or another distribution) with the specified mean and standard deviation. Fourth, calculate the ending portfolio value for each scenario. Fifth, calculate the probability of success: the percentage of scenarios where the portfolio did not run out of money before the end of the time horizon. The result is a probability distribution that shows the range of possible outcomes, from worst-case (market crashes and early depletion) to best-case (strong bull markets and portfolio growth). Most target-date funds and retirement calculators use Monte Carlo simulation to provide probability-based guidance. Asset allocation by age →

Key Inputs and Assumptions

The accuracy of a Monte Carlo simulation depends entirely on the quality of its inputs. The expected return assumption is the most important and most uncertain input — small changes in expected return produce large changes in success probability. A 60/40 portfolio assumed to return 8% will have a much higher success rate than one assumed to return 6%. Standard deviation determines the dispersion of outcomes — higher volatility means a wider range of possible results, with both better best-case and worse worst-case scenarios. The withdrawal rate is the most actionable input: reducing withdrawals from 5% to 4% dramatically increases success probability. Inflation assumptions matter for inflation-adjusted withdrawals. The time horizon is also critical — a 30-year retirement (age 65 to 95) has much lower success probability than a 25-year retirement at the same withdrawal rate. Most simulations also incorporate Social Security income, pension income, and other cash flows to produce a more realistic picture. The key principle: Monte Carlo outputs are only as good as the assumptions fed into them. Target date fund glide paths →

Interpreting Monte Carlo Results

A Monte Carlo simulation reports the probability of success, typically expressed as a percentage. A 90% success rate means the portfolio lasted the full time horizon in 9 out of 10 scenarios. Financial planners typically consider a success rate above 80-90% as acceptable, though conservative planners target 95% or higher. The simulation also provides percentile outcomes: the 10th percentile (worst case), 25th percentile (bad but not catastrophic), 50th percentile (median), 75th percentile (good), and 90th percentile (best case). The 10th percentile outcome is often the most important — it shows the worst-case scenario that still happens 10% of the time. If the 10th percentile portfolio value is zero at age 85, there is a 10% chance of running out of money before then. The median outcome (50th percentile) is what the typical scenario looks like, but planning should focus on the lower percentiles because running out of money late in life is catastrophic. Retirement income planning →

The 4% Rule and Monte Carlo Evidence

The famous 4% rule — withdraw 4% of the initial portfolio value in the first year of retirement, adjusted for inflation each year thereafter — was developed by financial advisor William Bengen in 1994 using historical data. Monte Carlo simulation provides modern support for this rule: with a 60/40 portfolio, a 4% withdrawal rate has approximately 90-95% probability of lasting 30 years under reasonable return assumptions. The 5% withdrawal rate drops the success rate to approximately 70-80%. The 6% withdrawal rate drops it further to 50-65%. However, Monte Carlo simulations also show that the 4% rule is not a guarantee — it fails in the worst historical scenarios (like retiring in 1966, just before the 1970s stagflation). The rule also depends on the current valuation environment: retiring when stock valuations are high (low expected returns) may require a lower initial withdrawal rate. Many planners now recommend 3-3.5% as a more conservative starting point for early retirees or those with longer time horizons. FIRE movement withdrawal strategies →

How many scenarios should a Monte Carlo simulation run?

Most financial Monte Carlo simulations run 10,000 to 100,000 scenarios. With 10,000 scenarios, the success probability is accurate to within approximately 1% for typical success rates. Running more scenarios (100,000 or 1,000,000) improves precision marginally but requires more computational power. The key is that the number of scenarios must be sufficient for the extreme percentiles (like the 1st or 5th percentile) to be stable. For most retirement planning purposes, 10,000 scenarios provides adequate precision. The quality of the random number generator also matters — use a high-quality generator like the Mersenne Twister rather than simple built-in random functions. The most important factor is not the number of scenarios but the quality of the assumptions about returns, volatility, and correlations. A simulation with 1 million scenarios and bad assumptions is still worthless.

What are the limitations of Monte Carlo simulation?

Monte Carlo simulation has several important limitations. It assumes that returns follow a specified statistical distribution (typically normal), but real financial returns have fat tails, skewness, and time-varying volatility that simple distributions do not capture. It assumes that the expected return and standard deviation are constant over the simulation period, but in reality these parameters change over time with market conditions and valuations. It typically assumes that annual returns are independent (each year's return does not affect the next), but markets exhibit momentum and mean-reversion that create serial correlation. It cannot predict black swan events — once-in-a-generation crises that are outside the range of historical experience. And perhaps most importantly, it assumes that future return distributions will resemble historical ones, which may not hold given changing economic conditions, interest rates, and market structures. Despite these limitations, Monte Carlo simulation remains the best available tool for probabilistic retirement planning. Market efficiency and its implications →

How does sequence-of-returns risk affect Monte Carlo results?

Sequence-of-returns risk is the reason Monte Carlo simulation is so important for retirement planning. Two retirees with the same average return can have very different outcomes depending on the order of returns. A retiree who experiences negative returns in the first few years of retirement (while withdrawing from a depleted portfolio) can deplete the portfolio entirely, even if later years have strong positive returns. Monte Carlo simulation captures this by generating thousands of different sequences — some with early bear markets, some with early bull markets — and showing the distribution of outcomes. The simulation makes it clear that early retirement returns are far more important than later returns, which is why gradual withdrawal strategies (like the guardrails approach or variable percentage withdrawal) can improve success rates by reducing withdrawals after poor early returns. Understanding sequence-of-returns risk →

Can Monte Carlo simulation be used beyond retirement planning?

Yes. Monte Carlo simulation is used throughout finance for a wide range of applications. In portfolio construction, it is used to model the range of possible portfolio outcomes under different asset allocations. In options pricing, the Monte Carlo method is a standard technique for pricing complex derivatives where closed-form solutions do not exist — particularly for path-dependent options like Asian options and barrier options. In risk management, Monte Carlo VaR (Value at Risk) is one of the three main VaR calculation methods, especially for portfolios with options and non-linear instruments. In corporate finance, Monte Carlo simulation is used for project valuation under uncertainty, merger model analysis, and capital budgeting with uncertain cash flows. In insurance, Monte Carlo methods are used to model claims distributions and determine premium pricing. The technique is broadly applicable to any situation where outcomes depend on uncertain inputs that can be described probabilistically. Monte Carlo VaR in risk management →

Related Resources