Sunday, February 16, 2014

Monte Carlo is not Just for the Rich

One of the main tasks of a financial planner is to develop a plan so you can retire the way you want.  Part of doing the plan involves periodic evaluation of your progress and one of the neat tools to do this is Monte Carlo simulation.

What is this and why do it?

You could just look at your savings, your projected average return on your savings (say 6%), estimate inflation (3%), use your retirement age (62) estimate how much you need per year in retirement ($100K), use your projected lifespan and you would get an answer to the question "Will I be able to retire at X and live lifestyle Y for the rest of my life?".  The growth of a portfolio nest egg with this kind of assumption is shown in Figure 1, looks really good, right?  However, this estimate would not reflect what really happens with your savings.
Figure 1: Portfolio growth using average return

You could use the 4% rule and just spend 4% of your nest egg every year.  Better than no plan but still inaccurate.

The issue is that return on investments in stocks, bonds, and even savings certificates varies over time.  Some years the return on stocks is higher than average, some years it is lower, same for bonds.  If, during the first few years of retirement, the stock market and bond market are down, such as in 2008 and 2009, your nest egg loses money, and future higher returns may not make up for this loss and you run out of money before your death.  Figure 2 shows a nest egg depleted by low early returns.  The opposite is also true, if you get great returns early, you may be able to spend more in retirement, or leave more to your deserving (we hope) children.  See Figure 3, much better results.
Figure 2: Poor returns in early years drain the nest egg
Figure 3: Early higher returns maintain nest egg

So what is likely to happen?  The solution is to run a "Monte Carlo Simulation" where a number of scenarios are run with random choices of rate of return per year, based on historical data.  If you run enough simulations, you can come up with a probability that you will have enough money for retirement.  This kind of simulation could be done using Excel or another tool, but luckily the Internet gives us a number of FREE tools that do the same thing.  I like the Vanguard tool, which allows you to input your portfolio composition, years in retirement, and lifespan, and then gives you the estimate.  Figure 4 below shows the result from the Vanguard Tool, an 80% probability you will NOT run out of money..

Figure 4: Monte Carlo simulation of a retirement nest egg
I recommend you or your financial planner consider this analysis and run it regularly to evaluate your progress towards a happy retirement.


  1. Jim Otar has done some really interesting work on this topic as well using an approach called "aftcasting." Has some definite advantages over Monte Carlo simulations (namely it uses actual historical returns in assessing the adequacy of a retirement portfolio instead of making guesses about expected rates of return).

    1. Yes, this is a better approach than truly random returns. The Vanguard tool randomly picks a start year between 1926 and 2005 then uses the historical sequence of stock and bond returns after that date to run a scenario using the sequence of returns. This means the sequence of returns is not completely random, it is based on this historical sequence but the starting date is chosen randomly. They repeat this process of picking a random start year 5000 times to get the analysis. This may be similar to what you are recommending. Picking a truly random sequence of returns using the historical mean and distribution would give a worst worst analysis, too pessimistic. Thanks for the insightful comment.


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