How Monte Carlo Can Understate Retirement Income Risk Compared To Historical Simulation

How Monte Carlo Can Understate Retirement Income Risk Compared To Historical Simulation

Financial advisors often rely on software that uses Monte Carlo simulations to incorporate uncertainty into their retirement income analysis for clients. While Monte Carlo analysis can be a useful tool to examine multiple iterations of potential market returns to forecast how often a given plan may be expected to provide sufficient income for the client throughout their life, there is a lot about Monte Carlo simulation that we are still learning. For instance, advisors may wonder if there is any benefit to increasing the number of Monte Carlo scenarios in their analyses to provide a more accurate picture of the range of potential sequences of returns a client might face.

While financial planning software typically uses 1,000 scenarios, advances in computing make it possible to run 100,000 or even more scenarios within reasonable amounts of time. To examine the potential impact of various numbers of simulated scenarios that could be chosen, we tested how consistent Monte Carlo plan results are when run at different scenario counts and iterated these simulations 100 different times. We find that the variation of sustainable real annual retirement income suggested by simulations running 250 versus 100,000 scenarios varies only by about 1.5% for given levels of spending risk. However, the variation is wider at the extreme tails (0% and 100% risk), which provides some particular considerations for those who might be aiming for as close to 100% probability of success as possible. Ultimately, the results of our first analysis suggest that the common scenario count levels built into Monte Carlo tools today are likely to be adequate to analyze the risk of different spending levels.

Another common concern is how Monte Carlo results might differ from historical simulations. Monte Carlo results are often considered to be more conservative than historical simulations – particularly in the US, where our limited market history contains the rise of the US as a global economic power. In our analyses, we find that the two methods provide differing results in a few notable areas. First, Monte Carlo estimates of sustainable income were significantly lower than income based on historical returns for the worst sequences of returns in the simulations (which give us risk spending levels of 0–4/96–100% probability of success). In other words, Monte Carlo results projected outcomes in extreme negative scenarios that are far worse than any series of returns that have occurred in the past. Similarly, for the best sequences of returns in the simulations, Monte Carlo suggested sustainable income amounts significantly higher than historically experienced (corresponding to spending risk levels of 88–100/probability of success 0–12%). Both results are possibly due to the treatment of returns in consecutive years by Monte Carlo as independent from each other, whereas historical returns have not been independent and do tend to revert to the mean.

Interestingly, Monte Carlo simulations and historical data also diverged at more moderate levels of risk (spending risk levels of 10–60/90–40% probability of success), with Monte Carlo estimating 5–10% more income at each risk level than was historically the case. Which means that, rather than Monte Carlo being more conservative than historical simulation as commonly believed, at common levels used for Monte Carlo simulation (e.g., 70% to 90% probability of success), Monte Carlo simulations might tend to be less conservative compared to historical returns! One way advisors can address this issue is to examine a combination of traditional Monte Carlo, regime-based Monte Carlo (where assumed return rates differ in the short run and the long run but average out to historical norms), and historical simulation to explore a broader range of potential outcomes and triangulate on a recommendation accordingly.

Ultimately, the key point is that while future returns are unknowable, analytic methods such as Monte Carlo and the use of historical returns can both provide advisors more confidence that their clients’ retirement spending will be sustainable. Contrary to popular belief, Monte Carlo simulation can actually be less conservative than historical simulation at levels commonly used in practice. And while current financial planning software generally provides an adequate number of Monte Carlo scenarios, the deviation from historical returns at particular spending risk levels provides some additional insight into why multiple perspectives may be useful for informing retirement income decisions. Which suggests that incorporating tools that use a range of simulation types and data could provide more realistic spending recommendations for clients!

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