Monte Carlo Simulation
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.
So, 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. This allows you to make sound decisions about other elements in your plan such as spending, long term care planning, legacy planning and more.
How does NewRetirement apply Monte Carlo to your plan?
In our Monte Carlo Analysis, we apply a normal distribution to the expected asset return rates under the assumption lens you’ve applied to your plan (optimistic, average, or pessimistic). 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 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.
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.
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. The 50th percentile shows the "middle" result of the simulation, while the area between the 25th and 75th percentiles shows the middle 50% of outcomes. Lastly, our "Chance of Success" metric is based on the percentage of iterations in which the portfolio lasted through the longevity age(s).
In addition 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. We recommend you use the Monte Carlo simulation when making decisions about your portfolio allocation, your projected growth rates, and the viability of your plan.
We encourage you to assess your Monte Carlo results under your pessimistic, average, and optimistic assumptions in order to ensure that you have properly considered the uncertain future.
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.)
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 increase your asset returns (and associated risk.)
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, Income Score, Net Worth, ability to meet your spending and legacy goals, and others.