The Problems with Monte Carlo are in Your Mind

Monte Carlo simulations incorporate uncertainty. While only asset class return assumptions are commonly varied, other variables could be adjusted (e.g., spending, age of retirement, age of death, etc)., I define any tool that employs uncertainty, even if there’s only two trials, to be a variation of a Monte Carlo forecast.

The assumptions and underlying methodologies for Monte Carlo are limitless. I’ve heard advisors claim that Monte Carlo must use historical returns, or that it can’t incorporate non-normal return distributions or spending rules. This is categorically false. You can build Monte Carlo tools to do almost anything.

The issue with Monte Carlo in our profession is a problem with the tools available to advisors, not Monte Carlo itself. While this sounds like a nuance, relaying uncertainty of investing and financial outcomes to households is essential. We need to focus on improving tools, not banning.

Life is dynamic, not static

Most Monte Carlo tools used by financial advisors rely on simplistic assumptions that don’t track reality. One common example is static withdrawals (or spending) in retirement. This concept dates back to William Bengen’s original research on safe initial withdrawal rates (and likely before that), where the retirement income goal changes only by inflation during retirement. There is no notion of updating or adjusting the withdrawal rate over time based on the performance of the portfolio (or any other life events).

While assumptions around static withdrawals are at least partially an artifact of computing convenience, since introducing dynamic withdrawal strategies complicates things, there are ways it can work. Static assumptions around spending result in outcomes that diverge notably over longer time periods and produce unrealistic outcomes for clients.

I demonstrate this effect in the exhibit below, which shows how the balance evolves for 50 different runs in a Monte Carlo projection, based on either a static assumed spending rule (a 4% initial withdrawal rate where the amount is subsequently increased by inflation – the 4% rule!), versus a dynamic spending rule (initial withdrawal rate is 5% and it increases by 5% each year cumulatively in the projection).

50 Runs in a Monte Carlo Retirement Income Projection

For illustrative purposes only

In the static projection. there are large differences in the balances, which increase over the 30-year period. The range in balances for the dynamic spending model are much tighter and reflect the adjustments one could make during retirement based on the performance of a portfolio.

While spending in retirement is a combination of static and dynamic withdrawals (i.e., essential and discretionary spending), a Monte Carlo projection using static assumptions will result in widely different outcomes based on the assumed returns. This is not an issue with Monte Carlo; it is an artifact of the assumptions used in the projection. Incorporating a dynamic rule in the model will tighten the distributions and make the outcomes more realistic.

Successfully unsuccessful

Certain outcomes metrics, particularly the probability of success, result in suboptimal advice and guidance. People don’t experience binary outcomes (pass or fail). Capturing the magnitude of failure and incorporating this into an outcome metric leads to a very different perspective about the efficacy of a given strategy. I demonstrate this using the exhibit below, where I assume an individual has a $100 spending goal that lasts for 10 years.

Targeting $100 in Income Per Year

For illustrative purposes only

The goal is not achieved in five of the 10 runs, implying a 50% probability of success. But the individual completed 96% of the goal, based on the withdrawals. This perspective of goal completion versus success rate becomes more compelling given increased life expectancies, where retirement periods stretch well beyond 30 years and most retirees have income that is guaranteed for life (e.g., Social Security benefits).

Success rates can be problematic at both ends of the spectrum. For example, you could have a client with a 0% success rate who is on track to cover 95% of a given goal if they have a significant level of guaranteed income. In contrast, someone with a 90% success rate (which most planners consider acceptable) may still have significant spending shortfalls (this is where annuitization can come in handy!).

Moving away from precise success levels (e.g., 82.45%) to general guidance on the likelihood of accomplishing a financial goal (“Way Off Track”, “Off Track”, “Almost on Track”, etc.) is better given the uncertainty in these projections and life.

Now what?

It’s unrealistic to expect advisors to abandon their tools that employ static withdrawals (and adapt those that use dynamic withdrawals) or abandon success rates overnight. Therefore, while I hope that’s the direction our profession moves towards, here are three things to do in the interim:

1. Focus on outcome percentiles versus success rates. For example, tell a client the expected income that will be generated in the worst one in five trials (the bottom quintile) at age 95 and ask them how that makes them feel.

2. Reduce your target success rate. While higher success rates will be associated with higher levels of certainty (i.e., not going broke) there is a trade-off whereby targeting higher success rates (95%+) results in lower levels of spending earlier in retirement. Retirees who are especially risk averse with respect to an income shortfall should consider strategies like annuities that provide protected income for life, since they are going to be a more effective hedge against longevity risk than a portfolio (e.g., if you’re planning on funding retirement past age 95). The right target success rate for most situations is approximately 80%. Think about how the target success rate interacts with longevity assumption. If both are relatively conservative, the implied probability of failing is materially lower than the resulting success rate.

3. Factor a spending cut into retirement. I’ve previously done research demonstrating that spending tends to decline in real terms during retirement, an effect I dubbed the “retirement spending smile.” Adding this into retirement planning, or assuming a cut at some point, not only better tracks reality, but provides context on how the success rate in a static projection would change if spending eventually is to be adjusted. There are different ways to do this, albeit limited by the tool you use, but it is a robustness check to see how sensitive the resulting success rate (or outcome of the projection) is to a spending cut.

Conclusions

Arguing against Monte Carlo is akin to suggesting people stop using calculators because the one you’re using (or that you’ve seen others use) can’t do time value of money calculations. But this is an issue with the calculator you’re using, not calculators themselves (i.e., it’s not a Monte Carlo problem… it’s a “you” problem!).

While this is nuanced, demonstrating uncertainty, whether it’s two runs/trials/outcomes or 100,000, is important because life is fundamentally uncertain. The alternative to a Monte Carlo projection is a deterministic model, like a time value of money calculation, and going back to that will not move our profession in the right direction.

We need better tools to reflect the dynamic decisions individuals make over their lifetimes that incorporate more realistic metrics to quantify (and compare) different potential outcomes (and move away from the probability of success).

The next time you hear someone say, “Monte Carlo can’t do that,” correct them and say “It’s not Monte Carlo… It’s you!”

David Blanchett, PhD, CFA, CFP®, is managing director and head of retirement research at PGIM. PGIM is the global investment management business of Prudential Financial, Inc. He is also an adjunct professor of wealth management at The American College of Financial Services and a research fellow for the Retirement Income Institute.

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