I’ve been writing about Monte Carlo simulation a lot recently. For example, see:
- Why A 50% Probability Of Success Result Can Actually A Viable Monte Carlo Retirement Projection
- Using Probability-Of-Success-Driven Guardrails In Retirement
- Making Monte Carlo Results More Relevant By Finding The Right Level Of Abstraction
In response to these posts, I’ve received a number of questions from financial advisors about the use of “closed-form” solutions (i.e., simple equations) as a computationally efficient approximation of Monte Carlo results (e.g., see Trainor, 2005; Vincent Vizacher’s reply to my recent post).
From an academic perspective, I have no objection to these use of these closed-form solutions. There may certainly be research applications where the computational efficiency matters.
However, from a practical perspective, I see little value in these solutions for advisors for at least three reasons: (1) such solutions are going to use retirement spending pattern assumptions that fail to capture the ‘messiness’ of assumed retiree planned spending (a key advantage of Monte Carlo simulation), (2) computational efficiency is not a significant barrier in most practical applications of Monte Carlo simulation with retirees, and (3) closed-form solutions do not address the much bigger issue inherent to Monte Carlo simulation.
Modeling ‘Messy’ Retiree Spending
While academic research tends to make simple assumptions about retiree spending (e.g., commonly either constant inflation-adjusted spending or an application a decreasing spending over time similar to Blanchett’s retirement spending smile), a key advantage available within most Monte Carlo simulation tools is the ability to actually model retiree-specific cash flows that are anticipated in the future. For instance, a retiree may know they want to buy a new house in five years, fund a grandchild’s wedding in ten years, or incur any other lump sum cash flow that is not easily funded with a consistent annual spending level.
Glossing over the ‘messiness’ of real-world retiree spending can significantly bias results. It’s for this reason that I recently argued that probability-of-success-driven guardrails are superior to withdrawal-rate-driven guardrails for determining if and when to make adjustments to spending in retirement.
Advisors could use closed-form solutions rather than running a Monte Carlo simulation for a client. Trainor (2005) and others have noted that such solutions can approximate Monte Carlo simulation results sufficiently well, but the payoff (computational and data-entry efficiency) is quite small relative to the potential value in accounting for unique retiree-specific cash flows.
Computational Efficiency Is Not A Significant Barrier
In most real-world applications, it is also worth noting that computational efficiency is not a significant barrier for financial advisors. Most programs return results nearly instantaneously. If advisors were waiting minutes, hours, or days to receive the result of an analysis, then worrying about computational efficiency would be a more practical consideration.
But, in practice, that just isn’t the case. Generally, updates are available within a few seconds and many tools even have functionality for adjusting a plan in real-time in front of a client. The better user interface of these tools compared to, say, an advisor maintaining their own spreadsheet, arguably provides an even more efficient means to updating a plan inputs than trying to use an advisor-developed spreadsheet.
Notably, software providers may use some shortcuts of their own to increase computational efficiency. For instance, MoneyGuidePro’s old Beyond Monte Carlo™ methodology (no longer in use) was previously described in plan output as:
…a statistical analysis technique that provides results that are as accurate as traditional Monte Carlo simulations with
Source: 2012 sample client brochure retrieved from http://www.clearviewwealthadvisors.com/wp-content/uploads/2013/09/MGP-Client-Brochure_Retirement.pdf
10,000 trials, but with fewer iterations and greater consistency. Beyond Monte Carlo™ is based on Sensitivity Simulations, which re-runs the Plan only 50 to 100 times using small changes in the return. This allows a sensitivity of the results to be calculated, which, when analyzed with the mean return and standard deviation of the portfolio, allows the Probability of Success for your Plan to be directly calculated.
The sort of optimization above (or similar methodologies) is similar in spirit to what is being attempted with closed-form solutions generally proposed in academic journals—and certainly, some software providers could even adopt truly closed-form solutions in lieu of Monte Carlo simulation—but as I’m describing the different approaches here, I do see a meaningful distinction between product-specific performance engineering and advisors ditching Monte Carlo simulation tools altogether in order to use a closed-form solution when working with clients. (The latter is also more consistent with the types of questions I was receiving that prompted this post.)
Ultimately, although software providers are continuously looking for ways to optimize their products, the type of Monte Carlo simulation done when simulating retiree spending today is just not so computationally demanding that computational efficiency is a major barrier to the planning process.
Closed-Form Solutions Do Not Address The Primary Limitation Of Monte Carlo Simulation
The biggest limitation with Monte Carlo simulation, at least as it is implemented in dominant software platforms today, is that the result is really just not that insightful. Sure, we now know that given a certain spending assumption a retiree has an X% chance of not running out of money in retirement, but we also know that real retirees are going to make spending adjustments based on the market conditions they actually experience, so this static simulation is not that insightful.
Furthermore, there are a number of other related issues with Monte Carlo simulation that do not need to be covered in-depth here (e.g., probability of success levels actually matter far less than most people think when doing ongoing vs. one-time planning; Monte Carlo simulation ignores the magnitude of ‘failure‘; misinterpretation of Monte Carlo results; etc.).
Ultimately, the solution to the problems mentioned above is not a closed-form solution—or at least not a closed-form solution that is currently used in academic journals. The solution to the problems above is to rethink how Monte Carlo simulation is conducted and reported to provide more insightful information to retirees.
Better Communication Of Plan Results
I’ve noted elsewhere that providing results that communicate both short-term and long-term retirement spending expectations is far more useful than reporting a probability of success or failure.
Short-term expectations are communicated better using something akin to a guardrails-type framework that tells a retiree (a) what they can spend now, (b) how much their portfolio would need to increase/decrease to trigger a spending increase/decrease, and (c) what that spending increase/decrease would be upon the portfolio reaching that pre-determined threshold.
Long-term expectations are communicated by providing summary information about how spending patterns would actually change through simulated retirement scenarios.
My recent post on probability-of-success-driven guardrails covers how both the short-term and long-term expectations could be set in practice, but in the context of thinking about closed-form solutions, it’s worth noting that closed-form solutions do nothing to inherently address either of these issues. Furthermore, simulations are actually incredibly helpful for generating the type of information that’s needed to better communicate results that help set long-term expectations.
Unfortunately, few planning software programs on the market today make it easy for advisors to manage either short-term or long-term expectations when presenting results to clients. In my work with Income Lab, we have developed a framework for reporting results to clients that I believe helps address these issues, but getting there required the team at Income Lab to develop a far more sophisticated (and computationally demanding) solution than what is common within currently dominant Monte Carlo software for advisors.
Disclosure: Derek Tharp is a Senior Advisor with Income Lab.
References:
Trainor, W. J., Jr. (2005). Long-range confidence interval projections and probability estimates. Financial Services Review, 14(1), 73-84.
