## RENO Example 1 - Planning a Retirement Strategy

### Problem Statement:

In planning for your retirement, you normally invest a percentage of your income in "safe investments" (Bank) or in "riskier investments" (Stock Market). For this example, assume that you are choosing to invest some of your money in the bank and some in the stock market, and let’s say that NASDAQ is tied to the NASDAQ Composite Index.

First, you do your research on the two investment vehicles and determine the following:

• The interest from the bank investment follows a generalized gamma distribution with mean = 1.7406, standard deviation = 0.1141 and lambda = 4.3106.
• The profit from the NASDAQ investment follows a normal distribution with mean = 13 and standard deviation = 28.

Note that you can use the Weibull++ software to analyze data on average bank interest rates and NASDAQ annual returns to obtain the distribution and parameters for this analysis, as illustrated in the figures below.

View Weibull++ figures
+ + Using ReliaSoft Weibull++ software to analyze data on average bank interest rates and NASDAQ annual returns to obtain the distribution and parameters for the RENO analysis.

You will invest X% of your income per year for the next Y years. Assume that your current income is \$40,000 per year and, based on past history, your income will increase yearly by a percentage that is normally distributed with mean = 4 and standard deviation = 1.5.

You will put Z% of your investment money in the bank for the first year and the remainder in NASDAQ. Given the volatility of NASDAQ, the following strategy is applied for subsequent years:

• Any profits made in the stock market at the end of each year will be transferred into the savings account for safe keeping. Thus, the amount invested in NASDAQ will be restricted to the initial amount put in plus annual contributions and minus any losses.
• The amount invested in NASDAQ will not increase as your income increases every year. It will always be equal to the first year investment.

### Objectives

• Estimate your investment income over the next 20 years if you invest 5% of your yearly income with 50% going to savings.
• Compare your investment income after 20 years, varying the investment portion from 0% to 20% of your yearly income (with 50% going to savings).
• Compare your investment income after 20 years, varying the investment portion from 0% to 20% of your yearly income and varying the amount invested in savings from 0% to 100%.

### Define the Resources

Define models to describe the stock profit, bank interest and the yearly increase in your income, as shown next.
+ Note that even though the investments are measured in money, the Model Unit has been set to Hours. This is because RENO flowchart results are always given in terms of the system base unit (SBU), and resources that require you to define a unit (i.e., models) will have their values automatically converted to base units during simulation. Therefore, whenever you don't want RENO to convert the value obtained from a model resource, simply make sure the model uses a unit that is defined as equal to 1 SBU. See the application help file for more information.

For this example, whenever one of the models returns a value as "X hours," it should be read as "X dollars." If the model unit you are using is not equal to 1 SBU (choose File > Manage Repository > Unit Settings to confirm), you will need to change the model units before resimulating the flowchart.

Define the following variables:

• A variable to represent your yearly income (CurrentSalary)
• Three variables to represent the percentage invested in the bank (StocksPercent), the percentage of income invested (InvestmentPercent), and the number of years to be analyzed (Years). These variables will be varied during simulation.
• Five other variables that will be used to keep track of the values that are passed during simulation.
+ Define RENO static functions to calculate the following:

• The amount of money that will be invested (Current_Investment).
• The amount that will invested in the bank each year (Savings_Portion).
• The threshold (Savings_Threshold) that will be used to determine whether you earned money in the stock market during a given year (and will therefore move those earnings into the bank account).
+ ### Build the Flowchart

Construct the flowchart shown below.

+ In order to keep track of how the investment incomes accumulate over the years, this flowchart is looped through. The loop is created by using the following blocks:

• A flag marker called "Start" to mark the start of the loop.
• A reset block called "Reset" to force the flowchart to generate new values for the RENO static functions at the start of every loop.
• A counter block called "Years" to count the number of years.
• A conditional block to check whether the number of years is less than the specified number. If the condition is met, the investment strategy will be applied (i.e., profits made in the stock market are transferred to the bank account). The go-to-flag block will then direct the flow of execution back to the flag marker and close the loop.

If the condition is not met (the number of years is up), then the value of the investments are calculated and then stored in the result storage block called "Total."

### Simulation

Estimate your investment income over the next 20 years if you invest 5% of your yearly income with 50% going to savings.

First, make sure that the initial value of the InvestmentPercent variable is 5 and the initial value of the StockPercent variable is 50.

On the General Settings page of the RENO Simulation window, specify 100 simulations and a seed of 1 for repeatability, as shown next.

+ On the Sensitivity Analysis page, specify to vary the number of years from 1 to 20, and use an increment of 1.

+ When the simulation completes, close the RENO Simulation window and then click the Plot icon on the diagram’s control panel. The results are displayed in the following plot with the plot scaling adjusted to Y = 0 to 120,000 and X = 0 to 25.

+ Compare your investment income after 20 years, varying the investment portion from 0% to 20% of your yearly income.

To vary the investment portion, configure the Sensitivity Analysis page as follows and repeat the simulation.

+ The results are displayed in the following plot.

+ Compare your investment income after 20 years, varying the investment portion from 0% to 20% of your yearly income and varying the amount invested in savings from 0% to 100%.

To vary both the investment portion and the savings portion, configure the Sensitivity Analysis page as follows and repeat the simulation.

+ To view the results in a three-dimensional plot, click the 3D Plot icon on the control panel. The following plot shows the results.

+ 