*Do I have enough money?*

Almost every client has asked some version of this question and addressing it is an important part of what we do as financial advisors.

To do that, we need a model, which we call your Baseline Financial Plan. Like any model, it’s only as reliable as the inputs. “Garbage in, garbage out” as the saying goes. Our model (your baseline plan) consists of three key components:

- A
**cash flow,**which reflects future inflows and outflows based on agreed upon assumptions between us and our clients for items like Social Security, Inflation, health care etc., and which incorporate all known future financial objectives; - A
**balance sheet**, which should include all the resources that are in place to support that cash flow; and finally - An
**output**, which analyzes the likelihood of that balance sheet being able to support that cash flow over time.

We think that Monte Carlo simulations provide the best way to generate this output because we don’t know for certain what the future will look like. We need to make assumptions about what to model and importantly, model (and plan for) a range of future outcomes. But obviously, comfort in the tool we use to create the output is going to heavily determine how confident clients are in their answer to the “Do I have enough money?” question.

There are a couple of questions that come up often as it relates to the analysis. They are: 1) can I trust the analysis given the wide range of potential future results? And, 2) does it account for fat tails—or in layman terms, low returns?

The purpose of this post to answer these questions related to our Monte Carlo simulations. But first, let’s take a quick look at why we use Monte Carlo in the first place.

## Why Monte Carlo?

We are not (and our clients certainly are not) concerned with how well a financial plan will work in average (or better) markets. Modeling a straight-line return based on the historical averages does little to provide confidence. Further, using a straight-line return based on the historical lows for a given period of time may provide a bit more confidence, but as we’ve written on this blog Timing Really, Really Matters, and modeling even well-below-average straight-line returns wouldn’t properly incorporate the out-sized effect a down market would have if it occurred, for example, the year after retirement. This is why we turn to Monte Carlo analysis. As Wade Pfau. PhD., CFA, has written:

*Simply put, Monte Carlo simulations provide a well where you can develop sequences of random market returns fitting predetermined characteristics, in order to test how financial plans will perform in a wider variety of good and bad market environments.*

Monte Carlo allows us to choose parameters based on historical averages and volatility, and then randomize the order in which those returns occur. In our simulations, we run 1000 scenarios using risk/return based on historical data so that we can understand what percentage of those scenarios end in a workable plan. In other words, we use it to provide the answer to the question above--how likely it is that you have enough.

## But what about fat tails?

Because we work with many engineers and other professionals who are familiar how a Monte Carlo simulation works, we often get questions about whether it accurately reflects the way in which historical returns have actually occurred. A Monte Carlo output is based on a mean and standard deviation (volatility). The randomness is generated according to a normal distribution curve. For example, suppose the S&P has an annualized return of 10% since 1926 with a standard deviation of 20%. According to a normal distribution:

- 68% percent of the returns would have fallen between -10 and 30% .
- 95% percent of returns between -30% and 50%
- 7% percent of returns between -50% and 70%

As many of our clients know, however, in reality, the tails are “fat”—and the shorter the time period (e.g., daily vs. yearly returns) the fatter the tails. That is, actual returns have occurred outside of two standard deviations more often than the normal distribution would suggest. Specifically, if we continue to use the S&P as an example, three times in 90 years we have seen returns below -30% and twice above 50%: returns outside of two standard deviations more often than 5% of the time as the normal distribution would suggest.

Therefor the question arises, if the Monte Carlo doesn’t account for fat tails…

## Is Monte Carlo conservative enough? Does it account for low returns?

Most clients are concerned with how well their Financial Plan works in the bad scenarios—the down markets and the low return environments. And, the answer is, yes. In fact, the Monte Carlo is **more** conservative in down markets when compared with how historical returns have actually played out. Derek Tharp, a research associate for industry expert Michael Kitces, recently posted the following research to address the fat tails question.

Based on his analysis, the worst year to retire since 1871 would have been 1966 with a 15-year real (after inflation) return on a 60% stock and 40% bond portfolio of around 0%. However, the worst case in scenario in a Monte Carlo analysis results in 15-year real returns that show nearly a 60% loss in wealth!

But what about adjusting returns down given current high stock market valuations here in the U.S. and low bond yields? Tharp notes:

*As the results show, when long-term real returns are reduced to just 2% [from 5.9%], then 50 percent of all Monte Carlo trials end up being worse than anything that has ever actually happened in history. In other words, assuming 2% real returns in Monte Carlo analysis may imply there is a 50% probability of a long-term path worse than the Great Depression or the stagflationary 1970s!*

So clearly the Monte Carlo analysis does model very conservative scenarios—worse than any 15-year period throughout history.

But, as most of our smart clients like to point out, a Monte Carlo output also models some very favorable upside scenarios as well. The question is usually something along the lines of “with this wide a range of outcomes, can I trust the analysis at all?”

And this is true, Monte Carlo does produce a very wide range of outcomes in most cases.

The chart below compares the Monte Carlo output by percentile of a 60/40 (total stock market/total bond market) portfolio, with the returns the same portfolio would have if you apply actual 30-year historical returns by the same percentiles. It assumes the portfolio starts with $1 million, and assumes a 4.08% annual spend rate:

**Source: Kitces.com, Does Monte Carlo Analysis Actually Overstate Tail Risk in Retirement Projections?**

As you can see, the Monte Carlo output produces a wider range of outcomes. The worst-case scenario ran out of money in 15 years, while the portfolio *never *runs out money when applying even the worst 30-year actual returns going back to 1871. The Monte Carlo is worse at the 10^{th} percentile as well. However, if we focus on the upside the Monte Carlo results in significantly more money at the higher percentiles.

So…Is the upside result from the Monte Carlo too good to be true? And…

## …Can we trust a model with a wide range of outcomes?

To answer this question, we need to understand why is it worse in the worst case and better in the best case? The answer is mean reversion. Historically, and as the chart below illustrates, bear markets are typically followed by bull markets and vice versa. **Source: CRSP 1-10 Index (i.e., U.S. Total Market)**

But with Monte Carlo analysis, the probability of another bear market is the same regardless of the previous year’s return. In other words, there is the same probability of 2008-type markets in the red circles as there is in the green circles above.

In his research, Tharp notes that Monte Carlo does a good job modeling year to year returns that match the magnitude of historical returns however, the difference comes in that a Monte Carlo simulation (over thousands of scenarios) strings together the bad (and good) years without building in any form of mean reversion. In his worst-case Monte Carlo vs. worst case historical comparison that we looked at above he notes that:

*In the historical scenario, the 2-year decline in years 8 and 9 (which represents the 1973-74 bear market) was followed by an 18.1% rebound. In the Monte Carlo scenario, though, the portfolio started out with a substantial market decline of 14.7%, had “just” a 6.9% rebound, then experienced a 1973-74 style decline in years 3 and 4… after which there was a less-than-3% rebound, followed by another 2-year bear market. And then, after mostly flat returns for 5 years, there was another bear market. And thus, by the end, the Monte Carlo scenario eroded a whopping 57% of its real purchasing power, even though the worst actual historical scenario merely broke even on purchasing power after 15 years (which admittedly is still a horrible sequence compared to a long-term real return that averages closer to 5%/year!).*

The same is true (if opposite) of a bull market. The result is the wider range of outcomes. However, because we are using the analysis to plan for the worst but then adjusting when needed as we go (for example, if we get average returns, it may mean additional spending over time) the Monte Carlo analysis, even with its wide range of outcomes, should give us confidence in our financial plan.

## Monte Carlo: The best tool to answer the question

Ultimately, because our clients are most concerned with the potential downside, and because Monte Carlo incorporates not only downside risk, but sequence of returns risk as well, we use it as the best-available tool in our Financial Plans to answer the question, “do I have enough?” But these inconsistencies at the extremes are important to acknowledge. As with any model, understanding it’s sensitivities and limitations is essential so that we don’t use it to answer a question it isn’t fit to reliably answer.