Monte Carlo Simulation

A Monte Carlo Simulation (MCS) is a statistical model that simulates a range of possible outcomes, making a probabilistic determination of their likelihood of occurrence. The method is used extensively in science, business and finance. In Finance it is most commonly encountered in retirement planning exercises as a tool to answer commons questions like “Am I likely reach my future retirement goal based on my savings and investments so far?”, and “what is the probability of my having X to spend each month at age X based on an assumed lifespan of X years?”. 

A MCS takes into consideration hundreds, or potentially thousands of different outcomes for each set of variables being observed. It is important to note that a MCS will not provide an exact retirement portfolio value at any given time, as its primary function is to illustrate the potential range of outcomes and their likelihood. Observation of the log normal distribution of outcomes will provide the investor with categories of outcome:

very unlikely
unlikely
likely
very likely

This range of outcomes will be grouped into confidence intervals and assigned a % based probability of occurrence. The output of any MCS will be entirely contingent upon the data being sampled, and the inputs of the user; e.g tax assumptions, investment growth assumptions, performance variance assumptions, life expectancy assumptions, inflation assumptions etc.

Aside from its reliance on numerous discretionary assumptions, the MCS has other limitations that preclude its use as a definitive predictor of the future. Used with the awareness of its limitations, a monte carlo simulation is still a robust tool to facilitate a conversation about what is and isn’t likely to happen to a client’s retirement based on mutually agreed assumptions.

Mr. Client goes through a planning exercise with his retirement planning advisor. Using data for Mr. Client’s prior contributions to his retirement account; including the amount and frequency of contribution, asset allocations and historic performance, Mr. Client and his adviser agree on some assumptions. They come to an agreement on potential future tax rates, future growth rates, a target start date to start drawing down (decumulation) and spending of his plan assets. They input these variables into the model, along with his life expectancy.

Mr Client is ultimately keen to understand if the total of his current monthly contributions into his taxable and non-taxable accounts produce sufficient growth to produce a post-tax monthly spend of 18,000 USD per month, adjusted for inflation, starting on his 65th birthday- and whether or not there will be sufficient money available in the plan to make those withdrawals for a period of 20 years.

Based on their assumptions, Mr. Client is pleased to see that he has a 95% likelihood of being able to spend an inflation adjusted 18,000 USD each month for a period of 20 years commencing his 65th birthday. Experimenting with the inputs into the model shows Mr. Client that increasing his monthly retirement savings by just  3% increases his probability of success by 2%- bringing the probability of goal success up to a total of 97%. Mr. Client increases his savings rate by 2% based on the MCS results, and is able to direct his excess disposable income to leisure activities, completely guilt-free.