Monte Carlo simulation
What is Monte Carlo simulation?
Monte Carlo simulation generates many possible portfolio paths from a specified return and cash-flow model to examine the distribution of future outcomes.
Simulation outputs should identify data window, return model, resampling block, horizon, contributions, withdrawals, fees, tax, inflation, rebalancing, and number of paths. Users should see percentile paths and goal outcomes, not false precision. Results are conditional scenarios rather than probabilities guaranteed by the future.
Model risk should be explored by comparing block-bootstrap, parametric, and stress-based assumptions where appropriate.
Validation should reproduce selected paths and reconcile cash flows and allocations step by step. Simulations used in advice need governance for code, data, assumptions, change approval, testing, and communication, because a visually polished fan chart can conceal a material implementation error.
How it works
A model draws or resamples returns, applies allocation, rebalancing, contributions, withdrawals, fees, tax, and inflation, and repeats the process many times. Results can include ending wealth, drawdown, goal funding, depletion, and percentile paths. The simulation explores assumptions; it does not observe the actual future probability distribution.
Model choices
Parametric models specify means, volatility, correlation, and distributions. Historical bootstrap resamples observed periods, while block bootstrap preserves some volatility clustering and serial dependence. Regime, factor, and scenario models add other structure. Palance's block bootstrap can retain empirical features better than a simple normal model but remains limited by history.
Inputs and path dependence
Return assumptions, valuation, horizon, allocation, cash-flow timing, inflation, fees, tax, and rebalancing materially affect results. Withdrawals create sequence risk, and illiquid assets require cash-flow and valuation treatment. Correlation and volatility can change under stress. Small input changes can produce large differences over long compounding horizons.
Reading outputs
Median is not a forecast, and a 5th percentile is not a guaranteed worst case. Success probability depends on the chosen definition, such as never exhausting assets or funding essential spending. Report distribution of spending cuts and shortfall magnitude, not one percentage alone. Extreme events beyond model support remain possible.
Practical governance
Version data, methodology, random seed policy, assumptions, and scenario count; test convergence and sensitivity; compare with deterministic stress and historical episodes. Explain limitations in plain language. Avoid excessive decimal precision, optimizing to one model, or using past average return as certain expected return. Update when goals or evidence change without rewriting prior decisions.
Sources and further reading
- Risk Management: An Introduction, CFA Institute
- Understanding Investment Performance, FINRA