Monte Carlo Simulation
Forecasting Methods
Linear Planning
Linear projections rely upon one set of assumptions and project one outcome. Although linear projections may be easy to understand, they do not account for the great degree of variability inherent in financial planning.
Historical simulation and Monte Carlo simulation are two methods used to simulate potential outcomes of unpredictable situations. They are both commonly used in financial planning to help you evaluate the uncertainty and risk around expected portfolio growth and portfolio survival based on withdrawals, and as a result assess your financial plan.
Historical simulation is a method that applies historical returns to simulate potential outcomes.
A Monte Carlo simulation may provide a wider range of potential outcomes than an historical simulation, as the future may hold risks as yet unexperienced and reflected in the historical data. As a result, a Monte Carlo simulation, in contrast to an historical simulation, allows for "what-if" analysis. It can be reassuring to know that the plan will be successful in a wider variety of potential scenarios than those provided by a linear or historic projection.
Overview of Monte Carlo
A Monte Carlo simulation is a statistical application which applies random simulations to an uncertain situation. The objective of a Monte Carlo Simulation is to assess the risk inherent in long term predictions and support informed decision making. It was named after the resort town Monaco, known for its casinos, since the element of chance is essential to the method, similar to a game of roulette.
A Monte Carlo simulation provides a range of possible outcomes and the probabilities or likelihood that they will occur. In financial planning it is often used to evaluate the probability that your portfolio will last and you will be able to achieve your financial goals. This allows you to make sound decisions about other elements in your plan such as spending, investment strategy, long term care planning, legacy planning and more.
How does Boldin Apply Monte Carlo to Your plan?
In our Monte Carlo Analysis, we apply a normal distribution to the your rates of return. We generate 1,000 random simulations and then randomize the values along a normal distribution each month of the simulation. We then divide the number of simulations where funds never run out by the total number of simulations, and reflect that number back to you.
The model infers a standard deviation from the rate of return for each account under the forecast assumption selected. It selects the standard deviation from a lookup chart, in which we’ve chosen values which loosely mirror the standard deviation of different asset classes. For example, a rate of return of 10% will result in a standard deviation associated with growth stocks.
FOR EXAMPLE:
The probability that your savings will last until your goal age of 90 is 87.00%.
The probability that your legacy goal of $100,000 will be achieved is 87.00%
This means that in 870 of the 1,000 simulations we ran, you were able to fund all of your projected expense and legacy goals.
Additional Detail
The Monte Carlo Analysis Chart shows the optimistic result (green line), the pessimistic result (red line), and various percentile markers from the Monte Carlo analysis (blue line and shading). The blue plot line represents the median portfolio value each year.
Percentiles
Each one of the 1,000 Monte Carlo "iterations" has a different curve over time. In order to make sense of this spread of 1,000 iterations, we use interquartile ranges to show the probability of ending up at a certain place. This helps you understand not just if your plan is likely to succeed, but how much you might have left under different scenarios.
50th percentile (median): Half of the simulations ended with a portfolio value above this amount, and half below. It’s the “middle” outcome.
10th percentile: 90% of the simulations ended with more than this amount; only 10% ended with less. This shows a “bad but not catastrophic” scenario.
90th percentile: Only 10% of simulations ended with more than this amount; this represents a very optimistic scenario.
The range between the 10th and 90th percentiles gives you a sense of the spread of possible outcomes, highlighting the uncertainty and volatility in your plan.
The deviation increases with higher return rates to represent increased risk and variability. If you have a higher growth rates in your plan, you’ll see greater variability, as represented by the blue shaded area. This reflects the increased volatility that can be inherent in a portfolio with an aggressive allocation. If you have lower growth rates in your plan, you’ll see less variability, or blue shaded area. This reflects the lower volatility that can be inherent in a portfolio with a more conservative allocation.
We also see a spread of results that starts off tight and predictable, and as we project further into the future, becomes more scattered and variable. This is in fact representative of the world we live in. As much as we may wish to have a crystal ball and know what will happen, the further out we plan, the more that can end up happening.
How can you use Monte Carlo to assess your plan and make informed decisions?
Due to the risk and unpredictability inherent in investing, precise long-term financial forecasting is impossible, and the Monte Carlo simulation can be an important to tool support robust planning.
You can test different strategies-such as varying your withdrawal rate, changing asset allocation, or adjusting your retirement age-to see how they affect your probability of success. This helps identify the most robust plan under a wide variety of possible futures and prepares you for less favorable market conditions.
Monte Carlo simulations empower you to make better decisions about how much to save, when to retire, and how to invest. This insight is crucial for refining your plan and making adjustments as conditions or goals change.
High Chance of Success
If your Monte Carlo consistently reflects a high degree of success - where perhaps 90% or more of simulations result in success - this indicates that you may have some flexibility in your spending above the expenses projected in your plan. As a result, you might breathe easy, or explore ways to increase expenses, charitable giving, or reduce investment risk (and associated return.)
Low Chance of Success
If your Monte Carlo reflects a poor degree of success - where perhaps 20% or more of simulations result in a poor outcome - this indicates that your plan might benefit from improvement. As a result, you might explore ways to save more, spend less, or change your investment strategy.
What other methods can you use to assess your plan and make informed decisions?
The Monte Carlo Analysis is just one of a variety of ways to evaluate your plan. We recommend measuring your progress towards your specific goals against a number of indicators including your Chance of Success, Net Worth, ability to meet your spending and legacy goals, and others.
NOTE: Balances of accounts that you have excluded from the Withdrawal Strategies are included in the analysis.