## Tuesday, April 6, 2021

### The Value of Monte Carlo Retirement Analysis

You may have heard of using Monte Carlo simulators to test your retirement plan.  It sounds impressively scientific to hear that your retirement plan has a 95% chance of success.  However, these simulators necessarily make assumptions about future returns, and the simulator outputs are very sensitive to these assumptions.

The term “Monte Carlo” refers to any algorithm that uses random samples to solve some problem.  Such methods are used widely in engineering, science, finance, and other areas.  In finance, Monte Carlo simulators are used to create many random sets of possible future investment returns, and we can test a retirement plan against these possible futures.  In particular, we can define success in some way, such as not running out of money or not having to cut back too far on spending, and see how often a retirement plan succeeds.

Monte Carlo simulators can work in many different ways.  They can just assume some expected return and volatility for stocks and bonds and generate random returns from what is called a “lognormal distribution.”  Alternatively, they could just start with a collection of past monthly or annual returns and select randomly from this collection.  Some simulators leave out the Monte Carlo part and just use actual return histories starting from various dates.

Unfortunately, the outputs of these simulators are very sensitive to the assumptions built into them.  If you use lognormal returns, you get to choose the expected returns and volatilities of stocks and bonds.  These are just 4 numbers, but they can make the difference between a retirement plan failing 5% of the time or 50% of the time.

For simulators that use a collection of past returns, we can get very different outcomes depending on what range of historical returns we use.  For example, bond returns from the past 40 years can’t possibly be repeated in the coming 40 years unless interest rates can drop somehow to negative double-digit levels.  A Monte Carlo simulator can easily hide an assumption that we’re headed to interest rates of minus 10%.  Most experts don’t believe future stock returns can match average 20th century returns in the U.S., but a simulator can assume they will.

Another problem most Monte Carlo simulators have is that they assume future returns aren’t correlated to past returns.  We know that when the stock market is high, expected future returns are low and vice-versa.  In a past article I illustrated this effect in pictures.

Yet another problem is that most simulators assume inflation is some low fixed value.  This problem shows itself most with annuities and bonds.  Inflation only has to bump up a little to cut deeply into the value of annuities and long-term bonds.  If a simulator doesn’t allow for the possibility that inflation could tick up a percentage point or two, how can we take its output seriously when it declares a retirement plan successful 95% of the time?

It’s certainly possible for a conscientious and talented financial advisor to take all these facts into account and choose sensible assumptions to build into a Monte Carlo simulator.  However, it’s tempting to tinker with assumptions so that clients can appear to be able to safely spend more during retirement.  Few advisors would admit to doing this, but because experts disagree over what simulator assumptions are sensible, it’s fairly easy to come up with a plausible justification for a wide range of assumptions to build into Monte Carlo simulators.

In the end, simulators can be less of a scientific tool and more of a marketing tool to impress clients and give them comforting answers.  This may sound damning, but comforting clients matters.  It’s not good to misuse a simulator to comfort a client about a bad retirement plan, but it is good to make a client feel safe committing to a good retirement plan.