What is the Monte Carlo Simulation?
The Monte Carlo method is a statistical technique used to model uncertainty. Rather than projecting one fixed outcome, it runs dozens or, possibly, hundreds of simulations using random variations in investment returns, helping planners and clients visualize a range of possible outcomes. In Voyant, this simulation provides a more realistic representation of market volatility and its impact on a financial plan.
Why Monte Carlo is Valuable for Financial Planning
Traditional financial forecasts often assume fixed returns. This can be misleading, especially for long-term plans. Markets don’t behave in straight lines, and returns vary year to year. The Monte Carlo simulation captures this unpredictability by using randomized inputs, allowing planners to explore how a plan performs under dozens or, possibly, hundreds of different scenarios.
Voyant’s implementation of the Monte Carlo simulation takes this a step further by accounting for asset class correlations, maintaining account-level distinctions (rather than lumping everything into a single “portfolio”), and modeling each plan year-by-year. The result is a realistic, nuanced model of financial outcomes.
Step-by-Step: How Voyant Runs a Monte Carlo Simulation
Each simulation in Voyant runs through the following steps:
1. Gather Historical Market Data
Voyant uses historical data to define expected returns and standard deviations for a standard set of asset classes:
Cash / Money Market
Short-Term Bonds
Long-Term Bonds
Value Stocks
Growth Stocks
Foreign Stocks
Emerging Markets Stocks
These statistics form the foundation for generating future returns.
2. Model Asset Class Relationships
Voyant builds a correlation matrix to understand how different asset classes move relative to one another. For example:
A positive correlation means two assets tend to rise and fall together.
A negative correlation means one asset may rise when the other falls.
Zero correlation means no meaningful relationship.
This matrix helps simulate real-world diversification and portfolio behavior.
3. Generate Random Returns Using Cholesky Decomposition
To simulate market uncertainty while preserving asset relationships, Voyant applies a mathematical method called Cholesky decomposition to the correlation matrix. This enables the software to generate random, but correlated returns across asset classes for each year in the plan.
4. Calculate Portfolio Returns
For each year:
Voyant generates a random return for each asset class.
These returns are weighted based on the client’s specific asset allocation in each account (e.g., 60% Growth Stocks, 40% Bonds).
The result is a unique portfolio return for each account, every year.
This is done per account, not at the plan level. For example:
Account A may be 25% Long-Term Bonds and 75% Growth Stocks.
Account B may be 30% Bonds and 70% Growth.
Because these are similar, their results will likely move in tandem during a simulation, but they are not treated identically.
How the Simulation Determines Plan Success
Once the account returns are generated for a simulation year:
Account balances grow based on the calculated return.
Expenses are deducted according to the plan.
If a shortfall occurs (i.e., expenses can't be covered), that year is marked as unsuccessful.
A Simulation Trial Is:
Successful if all years in the plan are covered without shortfalls.
Unsuccessful if any year in the plan has a shortfall.
Final Probability of Success:
The simulation runs n trials ("dozens or, possibly, hundreds...").
Your plan’s probability of success =
(Number of successful trials) ÷ (Total number of trials)
This percentage gives both advisors and clients a tangible measure of plan durability.
Why Voyant’s Monte Carlo Is Unique
Unlike some tools that oversimplify by modeling one aggregate account, Voyant:
Models each financial account separately (e.g., 401(k), brokerage, annuities)
Reflects individual account tax rules and return patterns
Preserves asset allocation differences between accounts
Simulates correlated return behavior using modern portfolio theory
This leads to more realistic outcomes, both in terms of growth and drawdown strategies, and allows advisors to model complex client scenarios with confidence.
Summary
Monte Carlo simulation in Voyant is a powerful tool that provides:
A dynamic way to model investment risk and market uncertainty
Realistic projections based on historical data, asset class correlations, and personalized asset allocations
Account-level precision and planning flexibility
By using this approach, financial planners can better inform clients about potential risks, stress-test different strategies, and give clients greater confidence in their long-term financial future.
Note: While the underlying math involves a Cholesky decomposition, the key takeaway is that we randomize returns at the individual asset class level, not at the portfolio level. This means that asset class correlations are treated as statistical tendencies, not guarantees, allowing the simulation to account for unlikely but possible outcomes within a normal distribution. This approach differs from our Major Loss functionality, where portfolios are treated as single, discrete entities.
Monte Carlo Simulation in Voyant – FAQ
Q: What does Voyant's Monte Carlo simulation actually simulate?
A: Voyant simulates annual returns for each asset class over the entire planning horizon. These returns are randomly generated using historical return expectations, standard deviations, and asset class correlations. For each year of the plan, returns for each asset class are calculated and then combined based on the portfolio’s asset allocation to create a simulated portfolio return for that year.
Q: Can we supply our own simulations for each asset class instead of using Voyant’s internal Monte Carlo simulation?
A: This is not currently available in the standard version of Voyant, but it could be considered as a custom build for enterprise clients. If this capability is essential to your planning process, please contact us to discuss potential implementation options.
Q: I have asked the software to run 1,000 iterations but it has stopped the simulation at a lower number. Why is this occuring?
A: The Monte Carlo simulation is designed to 'time-out' after 15 minutes if it has not run the requested number of iterations. The software automatically stops the simulation just before that happens and gives you the information up to that point.
1,000 iterations is nearly always going to take a significant chunk of time, but exactly how long will, to a large extent, simply be a function of the complexity within the plan itself. I hope that helps.
Monte Carlo Training Video