Before we begin this discussion, keep in mind that this type of analysis is a huge topic with an extensive body of literature (both popular and academic). Our goal is to cover the basics to help you understand how OnTrajectory can be used to shed light on and give you confidence in your financial future.

— George Box

This quote should ALWAYS be kept in mind. We create
models and run analysis to provide the **outline** of a picture,
to validate **broad** assumptions — or to alert us of **potential**
danger. No matter how painstakingly detailed our assumptions,
there are no guarantees the results will be 100% accurate.

To give you the most complete view we can, OnTrajectory provides three different strategies for modeling growth in your investments.

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 your
**Trajectory** will be defined as 'successful' (i.e. you didn't run out of cash).
It is based either on **randomized** historical data or data parameters that you define, which then replaces
**% Growth** and **Inflation**. The range of
data is set through **'Advanced Analysis'**,
as shown below:

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

3.
Historical — This type of analysis uses only
historical data. Unlike Monte Carlo, however, data is not chosen randomly, but rather ** sequentially**.
In other words, for

The year range is set through **'Advanced Analysis'**, as shown below:

Since we calculate results for every available year in the year range, we can produce a success percentage similar to that for Monte Carlo analysis. See the section Running Historical Analysis below for more information.

We provide two "modes" for viewing analysis results — **Basic** or **Advanced**. Both are
available from the **"Analyze and View"** menu located in the top right portion of the screen. The menu
is displayed below:

In **Basic Analysis Mode** selecting either "Monte Carol Analysis" or "Historical Analysis" automatically
turns off auto-saving and prompts you to "Click for Refresh."

Upon refreshing the chart, you will see two new shaded sections, a lighter one for **Median** results and a darker one for **10th Percentile** results:

**Median** shows the lower half of returns, meaning 50% of the returns are above the shaded area — another way to
look at is you have a 50% chance of doing better than that result. The **10th Percentile** region shows the "worst" 10% of returns, meaning you
have a 90% chance of doing "at least" that well. Although 90% sounds quite high, it means you have a 10% of being at or below the darker region, which when
performing long-term financial planning is about the minimum amount of safety you should plan on. We typically encourage folks to shoot for **at least
a 95% chance of success**.

In any case, **Basic Mode** is a quick and easy way to get high-level Monte Carlo or Historical results without having to configure
any other options or navigate through any other screens. If you are interested in configuring options or viewing richer results, read on
as we next describe **Advanced Analysis** for the remainder of this guide.

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

The **"Portfolio Mix / Management" ** tab defines the percentage of each
Investment Type (Stocks, Bonds, Cash) in your virtual
portfolio for when historical data is used
(as shown below).

Adjust the mix to your liking, ** but be careful**. Although the default settings
seem to take a very conservative approach, remember that
when using Historical data, all Accounts get identical
rates-of-return for a particular year — and this includes whatever funds
you have in low-yield accounts as well as excess income you may not have invested. Our default ratio
is similar to those used by other simulation tools.

The underlying data comes from a variety of sources:

**Stocks**— based on S&P 500 Index and MSCI US Broad Market Index,**Bonds**— based on S&P High-Grade Corporate Index and Lehman Aggregate Bond Index,**Cash**— based on Citigroup 3-Month Treasury Bill Index.**Inflation**— based on Consumer Price Index (CPI-U) compiled by the U.S. Bureau of Labor Statistics.

Finally, **"Mangement Expense Fee"** represents a burden to your growth rate based on fees you
may pay to an advisor or for other management costs. If populated, this percentage is subtracted to whatever growth rate
is used, regardless whether Historical or Parameterized input data is chosen.

As you experiment with different year ranges, portfolio
mixes, or input parameters — you will see how your Trajectory is affected by
factors such as
**Variance Drain** (i.e. overall lower returns produced
by periods of high volatility) and **Sequence Risk**
(i.e. 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 these and other various factors
affect your investments.

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

To initiate Monte Carlo analysis, click the
**"Analyze & View" button**

The following menu will appear on the right side of the screen:

The 'Analysis Options' window launches automatically when either the **Monte Carlo** or **Historical**
option is selected, which they are by default. You can also launch the Simulation Options window by clicking
'Advanced Analysis' from the top of the **Views Menu** (as shown above).

To begin, select either **"Historical Input Data"** or **"Parameterized Input Data"**.

As discussed above,
Historical Input Data simply draws randomly from a set of years as defined in the "Data From:" and "Data To:" fields.
Parameterized Input Data, on the other hand, allows you to set both an **Expected Return** (expected average annual return)
and **Expected Inflation** (expected average annual inflation) — as well as **Volatility** (standard deviation) for each.

Default values are populated as shown below, however you can change these at any time.

The following tables lists historical annualized returns and volatility for various time periods and portfolio mixes that may be used while running simulations ("Equity" is the S&P 500 Index and "Bond" is the Five Year Treasury Note):

From 1929 to 2018 | Annualized Return % | Annualized Volatility |
---|---|---|

100% Equity / 0% Bond | 10.2 | 18.6 |

80% Equity / 20% Bond | 9.5 | 14.8 |

60% Equity / 40% Bond | 8.6 | 11.2 |

40% Equity / 60% Bond | 7.6 | 7.9 |

From 1970 to 2018 | Annualized Return % | Annualized Volatility |
---|---|---|

100% Equity / 0% Bond | 10.5 | 15 |

80% Equity / 20% Bond | 10.1 | 12.1 |

60% Equity / 40% Bond | 9.5 | 9.4 |

40% Equity / 60% Bond | 8.8 | 7.0 |

From 2000 to 2018 | Annualized Return % | Annualized Volatility |
---|---|---|

100% Equity / 0% Bond | 5.6 | 14.4 |

80% Equity / 20% Bond | 5.8 | 11.0 |

60% Equity / 40% Bond | 5.7 | 7.9 |

40% Equity / 60% Bond | 5.5 | 5.2 |

*Above data is from the the "Returns" program, Dimensional Fund Advisors (DFA).

The image below shows results of a **Monte Carlo** analysis.

Because multiple Monte Carlo cycles are run, multiple results are displayed. Your Trajectory is displayed in orange, along with a "success" percentage. This percentage represents the number of simulated runs that ended above $0. In other words, for the example above, 84% of the simulated runs ended with some amount of money left over. In 16% of them, you ran out of cash.

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

The image below shows an example of **Historical** and **Monte Carlo** analyses run together, which
allows you to compare success percentages from both types of analysis.

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.

Just like Monte Carlo analysis, Historical analysis takes into account every Income, Expense and Account — along with every RMD, drawdown, rollover, gain, tax or penalty calculated along the way.

To initiate Monte Carlo analysis, click the
**"Analyze & View" button**

The following menu will appear on the right side of the screen:

The 'Analysis Options' window launches automatically when either the **Monte Carlo** or **Historical**
option is selected, which they are by default. You can also launch the Simulation Options window by clicking
'Advanced Analysis' from the top of the **Views Menu** (as shown above).

To begin, set the desired years in the "Data From:" and "Data To:" fields, and click **"Save Changes & Run Analysis"**

The image below shows an example of **Historical** analysis.

Since OnTrajectory runs analyses for every available 'Start Year' in the range, multiple lines and a success percentage are displayed. This percentage represents the number of Historical simulated runs that ended above $0. In other words, for the example above, 93% of the simulated runs ended with some amount of money left over. In 7% of them, you ran out of cash.

Lastly, you will see a single Historical run in a thick yellow line. This is the run that starts on the year in the "Data From:" field.

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:

- The
**Worst**run **Worst 10%****Worst 25%****Median 50%****Best 25%****Best 10%**- The
**Best**run **Success %**— the percentage of runs that stayed and ended greater than 0.

An example of **Analysis Results** is shown below:

The **CAGR %** row displays the **C**ompound **A**nnual **G**rowth **R**ate for the group
represented by a particular column. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment
value if you assume that the investment has been compounding over the time period. In a scenario where either the initial Trajectory balance or the ending
Trajectory balance is negative, it is not possible to compute **CAGR %** — you will see a blank entry to represent such an occurrence.

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
occurring in a certain order where bad results at the beginning of a run have a greater impact over the entire run.

The **CAGR %** and **Average % Growth** fields are extremely helpful to determine a reasonable **% Growth** value when defining an
Account item in OnTrajectory.

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.

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:

- Chance of Success — greater than or equal to 90%
- Chance of Success — between 50% and 90%
- Chance of Success — less than 50%
- All other sections — amount greater than 0
- All other sections — amount less than 0

**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.