How are Monte Carlo simulations run and where do the assumptions come from?
How Monte Carlo Works: Monte Carlo analysis works by generating multiple simulations on total returns for every investment in the retirement plan. The steps inside the program work as follows:
a) Generate 1,000 random numbers (there are 1,000 simulations) for each asset class for every year in the plan based on that asset class’s standard deviation and correlation with every other asset class. For our random number generation we use a well-tested third party program, Extreme Optimization. Total returns through time are assumed to be normally distributed, but this can be changed by the user to the Laplace Distribution, which assumes extreme events are more likely than an normal distribution does.
b) Each investment has its own Annual Return assumption, which is taken to be the mean return in Monte Carlo. Each investment is also assigned an asset class classification. For linked accounts, the asset classes are set automatically since the financial institution gives us this information. In each simulation we scale each investment’s mean return (the return inputted by the user) up and down every year based on the random number generated and that investment’s inputted return. Each asset class also has its own volatility (standard deviation) and correlation with other asset classes set by the program using 50 years of historical data.
You can read more about Monte Carlo in WealthTrace in our Monte Carlo retirement simulations blog post.
c) For each simulation we can calculate whether or not the clients run out of money. After 1,000 simulations the program takes the number of simulations where the clients do not run out of money before the end of their plan divided by 1,000. This is the probability that they will not run out of funds before the end of their plan