Monte Carlo & Historical Analysis

Before we begin this discussion, keep in mind that "Financial Analysis" is a big topic with an extensive body of literature dedicated to it. Our goal is to give you the basics and to understand how OnTrajectory can be used to shed light on your financial future.

The following topics will be covered in this Guide:

  1. “All models are wrong, but some are useful.”
  2. Portfolio Mix
  3. Factors Affecting Growth
  4. Running Monte Carlo and Historical Analyses
  5. Viewing Results
  6. Calculate Success % / Chance of Success

1. “All models are wrong, but some are useful.” – George Box

This quote should be kept in mind. We create models and run analysis to provide the outline of a picture, to validate broad assumptions — or to alert of potential danger. No matter how painstakingly detailed our assumptions, there are no guarantees the results will be accurate.

To give you the most complete view we can, OnTrajectory provides three different Analysis Strategies.

1. Average Growth — This is the default technique employed when setting up and configuring your Trajectory. It is dictated by the % Growth field for each Account. The advantage of this technique is that you can fine-tune your Trajectory and easily visualize the result of small changes over long periods of time.

2. Monte Carlo — This type of analysis provides the likelihood that the Trajectory you defined will be 'successful'. It is based on randomized historical data, which replaces the % Growth and Inflation set by you. The range of historical data can be set through the 'Analysis Options' pop-up, below:

MC Options

Unlike Average Growth analysis, which produces a single Trajectory line, Monte Carlo produces a range of results because multiple randomizations are calculated for every year of your Trajectory. See the section “Running Analysis” (below) for more information.

3. Historical — Like Monte Carlo, this type of analysis uses historical data. Unlike Monte Carlo, however, data is not chosen randomly, but rather sequentially. In other words, for Year 1 of your Trajectory data from 1928 is used, for Year 2 data from 1929 is used, etc. This a single line for each year in the range set through the 'Analysis Options' pop-up, below:

Historical Options

Since we calculate results for every available 'Start Year', we can display a success percentage. See the section “Running Analysis” (below) for more information.

2. Portfolio Mix

Above we stated for both Historical and Monte Carlo analysis, %Growth is based on historical data, but which particular data are we talking about — and is that data they applied?

The Portfolio Mix tab defines the percentage of each Investment Type (Stocks, Bonds, Cash) in your virtual portfolio for Historical and Monte Carlo analysis (shown below).

Portfolio Mix

Adjust the mix to your liking, but be careful. Although the default settings seem to take a very conservative approach, remember that in Monte Carlo analysis, all Accounts get identical rates-of-return for a particular year — this includes whatever funds you have in low-yield Accounts. Our default ratio is similar to those used by other Monte Carlo Simulators.

Growth data comes from a variety of sources:

3. Factors Affecting Growth

As you experiment with different year ranges and Portfolio Mixes, you will see how your Trajectory is affected by factors such as Variance Drain (overall lower returns produced by periods of high volatility) and Sequence Risk (long-term lower performance when market declines occur at the beginning of an investment period). We recommend using sites such as Investopedia to understand how various factors affect your investments.

4. Running Monte Carlo and Historical Analyses

When OnTrajectory runs Monte Carlo or Historical analyses, we take into account every Income, Expense and Account item you have defined — along with every RMD, drawdown, rollover, gain, tax or penalty calculated along the way. Every aspect used to render your personal Trajectory is recalculated for each individual Monte Carlo and Historical 'run'.

To initiate a Monte Carlo or Historical analysis, click the "Views Menu" Views Menu Icon

Analysis Menu

The 'Analysis Options' pop-up window is launched automatically when selecting either Monte Carlo or Historical view, or by selecting 'Monte Carlo and Historical Options' from the top of the Views Menu (shown above).

Analysis Options

To begin, click the Run Analysis button.

The image below shows an example of a Monte Carlo analysis.

Monte Carlo Results

Because we run multiple Monte Carlo cycles, multiple results are displayed. Your Average Growth Trajectory is displayed in orange, along with a "success" percentage. This percentage represents the number of simulated runs that that both stayed and ended above $0. In other words, for the example above, 84% of the simulated runs ended with a dollar amount > 0.

Optionally, you can also display the 'Median' Monte Carlo Trajectory (displayed in blue), meaning there are an equal number of Trajectories above and below it.

The image below shows an example of Historical analysis.

Historical Results

Since OnTrajectory runs analyses for every available 'Start Year', multiple lines and a success percentage are displayed. This percentage represents the number of Historical simulated runs that that both stayed and ended above $0.

The image below shows an example of Historical and Monte Carlo analyses run together.

Analyses Results

Notice that success percentages may vary based on the type of analysis performed. Being able to see all of this information in a single view creates a more complete picture of your possible financial futures, and it helps to validate your assumtions along the way.

5. Viewing Results

OnTrajectory provides a wealth of additional information at the completion of Monte Carlo / Historical Analysis. The Results tab on the Analysis Options pop-up displays the total amount for certain groups of results for every age/year of the simulation. Total amounts are shown for:

An example of Analysis Results is shown below:

Simulation Results

The Avg % Growth row displays the Average Growth Rate for all the years for the group represented by a particular column. Counterintuitively, these growth rates will not always go from smallest to largest. Based on the Sequence of Returns (as discussed above), the average of a group of returns could be higher for a group with worse results. For example, the Worst 10 % group could have a higher Average % Growth value than the Worst 25% group. Again, this is a result of growth rates occuring in a certain order where bad results at the begining of a run have a greater impact over the entire run.

The Average % Gowth field is extremely helpful to determine a reasonable % Growth value when defining an Account item in OnTrajectory.

6. Calculate Success % / Chance of Success

Confidence Check

The 'Calculate Success %' button automatically runs both a Historical and Monte Carlo analysis on your data (see above for how to run these separately). OnTrajectory then averages the results and displays two percentage values.

The first value, called 'Chance of Success', represents the number of simulated Trajectories that result in an end amount above 0. The second percentage is the number of Trajectories that result in an end amount at or above your Final Trajectory — it's displayed next to the Final Trajectory amount in parentheses.

Confidence Check

In other words, a 90% chance of success means that an ending amount above 0 was achieved in 90% of the Historical and Monte Carlo 'runs'. And 80% next to your Final Trajectory, means that in 80% of the runs, a number at or above your Final Trajectory was achieved. As you model your future, you will see that the Final Trajectory percentage is primarily sensitive to the "% Growth" values defined in your accounts. While the overall "Chance of Success" percentage is effected by your Income, Expenses and % Growth.

In addition, sections are color coded as follows:

Confidence Check

It is important to note that percentages are NO GUARANTEE of success in your investments, and successive runs may vary due to the random nature of Monte Carlo analysis — usually +/- 3%. Finally, NO information provided by OnTrajectory should be considered investing advice. All financial information is solely for educational purposes. Please see your own professional for personal investment advice.

In any case, we urge you to use OnTrajectory to experiment and learn. The more you understand and the better your assumptions, the more clear your financial future will become.