# Withdrawal Rates in Retirement: Monte Carlo vs. Historical Rolling Returns

Near the very top of everyone’s financial planning list of questions is, “when can I afford to retire?” What may seem like a very straightforward question does not have such a straightforward answer. The value an independent fiduciary wealth advisor brings to their clients is a point of reference when attempting to answer this question. There are a few different ways financial planners can help their investors in addressing retirement readiness.

### Monte Carlo

Many investors are familiar with a “Monte Carlo Analysis” in which the investor provides inputs such as savings, withdrawals, time horizon, and returns assumptions into a big calculator that runs 10,000 simulations to illustrate the many possible scenarios that can happen given the assumptions it has been provided.

### Historical Rolling Returns

Another possible way is to look at actual historical rolling returns data. This assumes that what has happened in the past provides a good indication of what we can expect to happen in the future and, therefore, takes financial planning out of the realm of the “theoretical” into the world of “empirical.” IFA, for example, provides rolling monthly returns of many indexes going all the way back to 1928. As of June 30, 2017, this equates to 1,074, 1,063, 1,015, 955, 835, and 475 1-month, 1-year, 5-year, 10-year, 20-year, and 50-year rolling returns, respectively. Based on this data we can look at best, worst, and median outcomes over various time periods that investors actually experienced to see how things would pan out.

Which is superior? It is a trick question. Both can provide great insight and, if properly used, can assist investors in determining whether or not their personal finances are on the right track.

### Illustration with a Monte Carlo

In a Monte Carlo analysis, a normal distribution is generated based off of the return and standard deviation of return assumptions the investor provides. It then takes the investor’s timeline, beginning portfolio value, net cash flows, and applies a random return based on the normal distribution it generated and a final ending value for that year. For example, if we provide a Monte Carlo with return and standard deviation assumptions of 8% and 11%, respectively, then we would expect the calculator to draw a return between -3% and 19%, 66.7% of the time (one standard deviation). We would also expect it to draw a return between less than -14%, 2.5% of the time (left tail) and greater than 30%, 2.5% of the time (right tail).

It goes through this process for each year of the investor’s timeline and illustrates if and when an investor would run out of money. It then simulates this process 10,000 times to ensure that the randomness built into its calculations is limited in terms of its influence on the overall conclusions the investor draws from the analysis. In the end, it provides a range of outcomes as well as a percent of simulations where the investor essentially ran out of money. For example, if 500 of the 10,000 simulations showed the investor running out of money, then we can say that the investor has 95% confidence that their overall financial plan will be successful.

The benefits of a Monte Carlo analysis is its potential to show you the many possible outcomes that are expected to happen based on the inputs we have provided it even if some simulations are something that we have actually never experienced.

This can also be seen as negative. Respected financial planner, Michael Kitces, recently wrote about how Monte Carlo analysis essentially overstates tail risk when it comes to financial outcomes for investors. Using our own data and tools as an example, let’s take a look at a 65 year old investor who has recently retired. She has \$1,000,000 in total assets, is currently in IFA Index Portfolio 55 on a Glide Path, and is looking to withdraw \$55,000 per year adjusted for inflation from her portfolio, gross of income taxes, and not including Social Security benefits. In other words, she is following a 5.5% “withdrawal rule.” Let’s also assume that her timeline is 20 years and she is not looking to bequeath any of her assets to beneficiaries, just to keep it simple.

Based on IFA’s Retirement Analyzer, 89.74% of the Monte Carlo simulations show that our investor will not run out of money. In other words, just over 10% (1,000) of the 10,000 simulations showed that she would run out of money at the age of 85.

These results show a very strong indication that the investor can afford to withdraw 5.5% of her portfolio adjusted for inflation overtime. But she still may feel in the back of her mind that there is a chance of utter financial ruin and wants to see a more positive outcome.

There are a couple ways of addressing this. We can:

• Lower the annual withdrawal to something more reasonable like 4.5% (\$45,000 adjusted for inflation), or
• Defer retiring for a few more years and still withdraw the 5.5%

If we follow the first strategy, lowering the annual withdrawal to 4.5% (\$45,000 per year adjusted for inflation), the overall probability of success increases from 89.74% to 97.57%. This may provide our investor with greater comfort.

If we follow the second strategy in which we defer retirement for let’s say another 5 years, but keep the withdrawal rate fixed at 5.5%, how does this affect the outcomes? This will assume a \$70,000 gross income, which grows at 3% per year, and our investor contributes 15% of her paycheck towards retirement. Our new time horizon is now 15 years. Our Monte Carlo results come back with a 98.40% success rate compared to the original 89.74%.

So our solution for our investor who may not feel confident about a 90% success rate is to either:

• Withdraw less per year in retirement
• Defer retirement and continue working for another 5 years

### Illustration with Historical Rolling Periods

What if we decided to approach helping the investor a different way? Instead of utilizing a Monte Carlo analysis, we are going to look at historical monthly rolling returns to see how confident our investor’s financial plan would be assuming the worst rolling period returns we have experienced over the last 89.5 years.

Assuming she is currently in IFA Index Portfolio 55 on a Glide Path with a time horizon of 20 years, the worst 20-year monthly rolling return we have ever experienced with IFA Index Portfolio 55 on a Glide Path was from September 1, 1929 to August 31, 1949. Shouldn’t come as a huge surprise as investors experienced the Great Depression as well as World War II. It was a tumultuous time to say the least. See chart below.

During this time period, IFA Index Portfolio 55 on a Glide Path experienced a 3.09% annualized return. Now if we assume that our investor entered retirement on September 1, 1929 and wanted to follow the same 5.5% withdrawal rule for 20 years, how would have things turned out? Starting with \$1,000,000 at retirement, our investor would have \$33,281 (in 1949 dollars) after that 20-year period. Stated another way, utilizing historical rolling period returns, our investor’s financial plan has a 100% success rate.

It is important to mention that this specific time period is unique in the sense that we went through almost a decade of deflation. While the average costs of goods and services went down, it doesn't necessarily mean that investors would alter their withdrawal habits. In our example, if our investor did infact keep her consumption the same over this time period, she would have ended up with some savings from each annual distribution. That savings could be rolled over into the next or reinvested back into her portfolio.

Given the unique circumstances surrounding this time period, let's also look at the worst 20-year rolling return over the last 50.5 years for the same portfolio. In this time period, the worst rolling 20-year period was from June 1, 1997 to May 31, 2017 in which IFA Index Portfolio 50 on Glide Path delivered a 5.86% annualized return. A \$1,000,000 portfolio on the 5.5% withdrawal rule over this time period would have ended up with \$776,526. Still, a 100% success rate.

If our investor happened, by chance, to start retirement during the worst market environment we have ever experienced over the last 89.5 years or 50.5 years, she would have turned out “ok.”

### Practical Ramifications

As you can see, the Monte Carlo overstates the tail risk of the potential outcomes an investor can experience. Although 10% of the simulations failed, they failed under market conditions that we have never experienced before. Without a professional providing some context, this could lead to investors withdrawing less than necessary and therefore leaving a larger bequest to beneficiaries or unnecessarily deferring retirement.

Nonetheless, a Monte Carlo is an important tool since it can simulate market environments that have yet to happen. Although we have never experienced market conditions like those that were simulated, it doesn’t mean that we won’t experience them in the future. Just to give an example, the most recent financial crisis of 2008 and 2009 was one of the worst periods in terms of returns since the Great Depression. Depending on the types of assumptions that were used in financial planning models, 2008-2009 presented a new realm into what was possible in terms of the acceleration of a market drawdown as well as the subsequent recovery.  This is why a Monte Carlo still has practical relevance.