Example F-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, let’s assume that you are choosing to invest some of your money in the bank and some in the stock market, let’s say NASDAQ and 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 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 linked figures.
You will choose to 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, that your income will increase yearly by a percentage that is normally distributed with mean = 4 and standard deviation = 1.5.
You will decide to 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.
You can use RENO to model this investment strategy and determine a variety of different results. For example, you may wish to:
- 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%.
RENO Solution:
Define two Random Variables to describe the returns from the BANK and NASDAQ investment vehicles.
Define a third Random Variable to describe the yearly increase in your income.
Define three Constants to set the number of years that will be analyzed, the percentage of your yearly income that will be invested and the percentage of the investment that will go to NASDAQ each year. The values of these Constants can be varied during the simulation to determine specific results of interest.
Define two Equation Variables to calculate the amount of money that will be invested in the bank each year. This is determined by calculating the investment amount for the year and then subtracting the amount that will be invested in NASDAQ.
Define a third Equation Variable to calculate the 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).
Note that these Equation Variables refer to defined Storage Variables (i.e. CurrentSalary, StocksPortion and CurrentYear), which hold values obtained from the flowchart during simulation.
Construct the flowchart as follows:
To estimate your investment income over the next 20 years if you invest 5% of your yearly income with 50% going to savings, perform 1,000 simulations (with a seed of 1 for repeatability) for each of the years. The results are displayed in the following plot:
To compare your investment income after 20 years, varying the investment portion from 1% to 20% of your yearly income, configure the Sensitivity Analysis page of the Simulation Console as follows and repeat the simulation.
The results are displayed in the following plot.
To compare your investment income after 20 years, varying the investment portion and the amount invested in savings, configure the Sensitivity Analysis page as follows and repeat the simulation.
The results are displayed in the following three-dimensional plot.
A RENO project with the solution for this example (called "Retirement Strategy.rnp") is shipped with the software and stored in the Examples\Reliability folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Financial Analysis\Retirement Strategy.rnp).
