### Executive Summary

In recent years, Monte Carlo simulation has become a popular tool for financial advisors to motivate their clients to follow recommendations. By presenting a single probability-of-success percentage, Monte Carlo analyses give clients a simple, instantaneous metric on the state of their financial plan. And because many clients naturally like to challenge themselves to do better and score higher, they are incentivized to take action that will increase their plan’s probability of success. The idea of using the same fun and appealing motivating elements found in games that people like to play (e.g., accomplishment, empowerment, and unpredictability) to encourage them to take action on other aspects of their lives is a concept known as “gamification”.

Yet, as many advisors know, the end goal of financial planning is not necessarily to achieve the highest possible Monte Carlo probability-of-success result, as a 100% Monte Carlo success rate effectively guarantees that the client will have excess money left over at the end of their lives (likely more than they would need to have at the end of their plan, and otherwise could have spent and enjoyed earlier in their life). Which means that, while Monte Carlo incentivizes clients to achieve higher and higher probabilities of success, actually working to achieve the ‘best’ success probability of 100% may push clients toward outcomes that are out of line with their goals for spending, giving, and leaving behind assets during their lifetimes.

Fortunately, several ways exist for advisors to use the gamification power of Monte Carlo simulation to motivate clients to follow their recommendations. First, advisors can reframe how outcomes are measured by shifting the focus from an acceptable probability of success to a more dynamic concept of probability of *adjustment*, to emphasize the fact that ever-higher probabilities of success do not necessarily equate to desirable outcomes for the client and that lower probabilities of success can actually be more sustainable than they may sound, when factoring in a client’s ability and willingness to make spending adjustments along the way.

Alternatively, advisors and their clients could pre-define a range of acceptable probabilities (in other words, implement a risk-based guardrail strategy) which allows the probability of success to float up or down with market movements over time, and specifies the point at which the client would need to cut spending if the probability drops too low (or conversely, increase spending if the probability increases above the target range), which serves to help the client understand the long-term ongoing nature of their plan, and that the plan shouldn’t be considered as a one-time blueprint for all future spending up to (and beyond) retirement. Going further, advisors using a guardrails-based approach could even consider shifting the focus away from probability of success entirely, and toward more concrete metrics such as actual dollar figures (e.g., to reflect spending, portfolio balances, etc.) since, to the client, what ultimately matters is not their plan’s probability of success itself, but instead, the *actions* (e.g., the level of spending) that allow them to achieve that probability of success!

Ultimately, what makes Monte Carlo simulation so powerful for clients is the ability to visualize how they can impact their plan’s long-term outcome through the actions they take. However, without first defining the range of probabilities – and whether they serve as metrics for success or adjustment – that will best achieve the client’s goals, the instinct will be to pursue ever-higher probabilities of success (and correspondingly more conservative plans). Advisors can help harness the gamification power of Monte Carlo in a way that is better aligned with the client’s goals by framing the range of desirable outcomes and reorienting the conversation away from probability of success and toward the client’s concrete actions.

‘Gamification’ is a topic that has received increased attention in recent years. Behavioral design consultant Yu-Kai Chou is one of the pioneers in the field of gamification and has defined it as “the craft of deriving all the fun and addicting elements found in games and applying them to real-world or productive activities.”

Video games provide an interesting lens for viewing human motivation and behavior. The key to a good (or at least successful) game is that it keeps players coming back and wanting to play more. This requires the delicate balancing of many factors – intrigue, challenge, etc. – that keep players engaged.

For instance, the game itself can’t be too easy, or people will easily master it and become bored. On the other hand, a game can’t be too difficult, or people will quickly lose their motivation to put time into playing the game.

In his book, Actionable Gamification*, *Chou gives an example of comparing chess versus tic-tac-toe. For most adults, tic-tac-toe is easily mastered, and ‘winning’ against another competent opponent is essentially a game of attrition in which each party is waiting for their opponent to make a silly mistake. By contrast, chess has a simple enough set of rules to be played by most, but is complex enough to keep it stimulating, fresh, and widely loved by millions of people worldwide. As a result, chess is passionately followed by people all around the world, whereas tic-tac-toe is familiar but not a game commonly played by many.

While chess and tic-tac-toe have been around for a long time (tic-tac-toe variants have been observed in Ancient Egypt dating back to at least 1300 BC; and while the true origin of chess is debated, it likely has Asiatic origins dating back to about 600 AD), in the case of video games, we’ve seen games developed that have benefitted from extremely fast and rich feedback loops that allow for fine-tuning of game development to drive engagement and behavior.

Whereas the rules of a game like chess evolved slowly (and the lack of centralization of any rule-making body may have even been a barrier to certain types of evolution), modern video games receive nearly instantaneous feedback and can also be updated very frequently. For instance, video game developers have detailed information about how long users spend playing their games, what barriers lead to disengaging from a game, what prompts lead to re-engaging with a game, etc.

Moreover, this information can be experimented with in real-time. For instance, a developer may choose to A/B test a new game feature, presenting one group of players with the old feature and one group of players with the new feature, and then reviewing real-time feedback to understand whether the new feature seems to be increasing engagement.

This real-world laboratory of sorts has allowed us to learn a lot about human behavior, and companies and researchers both have been interested in drawing lessons from the field of game development and applying them to other behavioral domains in our lives.

## Gamification And Monte Carlo Simulation

While gamification hasn’t been given a lot of explicit coverage within financial planning media, certainly companies like Betterment (see Betterment CEO Sarah Levy’s comments on gamification of stock trading), as well as software vendors more generally, are giving the topic some thought. Moreover, some advisors likely think about gamification-related topics on a nearly daily basis as they consider how to motivate their clients, even if they may not think of what they’re doing as ‘gamifying’ behavior.

One particular consideration for financial advisors is how Monte Carlo simulation can gamify client behavior in different ways. This particular topic was covered in a recent article at Barron’s, ultimately arguing that presenting a probability-of-success metric pushes individuals toward desiring ‘perfection’ (i.e., 100% probability of success), and that this may incentivize behavior that could be detrimental to a retiree’s wellbeing in retirement. While this conclusion may hold some merit, the topic warrants some further discussion.

First, it is worth noting that the presentation of a single metric, like probability of success – where higher numbers may commonly be interpreted as 'better’ than lower numbers – is very likely to lead to at least some desire to take actions that would increase the probability of success result. In other words, since the only feedback (or at least the *primary* feedback) a retiree receives when playing around with a Monte Carlo simulation is generally the probability of success metric, people will naturally be driven to try and explore scenarios that lead to the ‘better’ outcome (i.e., increase the probability of success). People are nudged toward wanting to make changes to improve their results.

Of course, that’s not the worst thing one could do, as we all would likely prefer to have a higher probability-of-success number in retirement if we lived in a world with no limitations. However, we *do* live in a world with limitations, and therefore we must accept trade-offs – and that is something that is difficult to capture with a traditional Monte Carlo simulation.

One easy way to guarantee (mathematically) that one would never run out of money is simply to never retire. Of course, that doesn’t provide an outcome that most people would find preferable (nor is the health and vitality needed to maintain a lifelong career a guarantee we can rely on) so, in the real world, we have to make trade-offs. We accept some risk of running out of money so that we don’t have to work our entire lives.

Similarly, we make all sorts of other trade-offs throughout our financial lives that can be modeled in a Monte Carlo simulation (e.g., how much to save while working, how much to spend in retirement, etc.). There are certainly worse courses of action than those that will move the Monte Carlo probability of success in a positive direction (i.e., save more, retire later, spend less) but, at some point, the continued desire for ever-higher levels of probability of success can certainly be at odds with the course of action that may be best for one’s holistic wellbeing in retirement.

## Applying The Research On Gamification To Monte Carlo Simulation

Yu-kai Chou has developed a framework called “Octalysis” for gaining a better understanding of the core gamification principles that drive human behavior. (Note: While a deep overview of Chou’s framework is beyond the scope of this post, you can read more about his methodology in his book, *Actionable Gamification*.)

Chou’s framework captures what he considers to be the 8 core drivers of behavior:

- Epic meaning
- Accomplishment
- Empowerment
- Ownership
- Social influence
- Scarcity
- Unpredictability
- Avoidance

In the context of Monte Carlo analysis, it is probably Accomplishment, Empowerment, and Unpredictability that have the most relevance to how an individual potentially engages with Monte Carlo simulation.

Specifically, Accomplishment (increasing the probability of success), Empowerment (dynamic feedback from playing with inputs in real-time), and Unpredictability (what happens if I change X?) are the factors most relevant to gamification in a typical Monte Carlo simulation presentation.

There’s a natural curiosity (“How will my plan change?”) combined with some nearly instantaneous feedback (“If I retire at age 67 versus age 62, my probability of success rises from 70% to 95%.”) that can guide a user down a path of trying out various scenarios to find the optimal outcome in terms of a set of factors that provide a ‘reasonable’ probability of success.

In a way, this is very good gamification design, since the feedback is nearly instantaneous and the levers being pulled (e.g., spending more, delaying retirement) are so relevant to one’s own life. There are few things in financial planning that we can get such instantaneous feedback on once a plan itself has been built out.

However, when the outcome that is considered most desirable (increasing probability of success) starts to push someone to become too conservative simply for the sake of reaching a higher and higher probability of success, then there is a cause for concern. Users may be tempted to try and achieve a 100% probability of success, even if this means that they push themselves toward an outcome that does not properly balance goals related to lifetime income, giving, one’s estate balance, and any other use of funds.

Moreover, Monte Carlo analysis is actually *least* reliable at the extremes that individuals may be incentivized to seek. In other words, even beyond the risk of pushing someone toward a plan that is too conservative, the typical gamification of Monte Carlo results also pushes one toward solving for solutions within the areas where Monte Carlo itself is *least* reliable.

As you can see in the graphic above, when comparing Monte Carlo simulation to historical simulation, the two are not far off from one another in the middle probability of success ranges, but the divergence is quite large once you try to push a plan toward a spending risk level of 0, equivalent to 100% probability of success. And yet, this is exactly what a retirement planning process that focuses so much on this single metric does.

While most advisors probably are aware that it is possible to be too conservative when running a plan, this dynamic of how Monte Carlo simulation can use gamifying behavior to push clients into scenarios where Monte Carlo simulation is least reliable seems to be particularly underappreciated.

## How To Manage Gamification Issues Related To Monte Carlo Simulations

To be fair, there have already been some actions taken with respect to how Monte Carlo results are displayed to clients, likely with the intent of pushing back against the tendency for ever (and unnecessarily) higher probability of success outcomes. For instance, MoneyGuidePro has long had a blue zone at the highest levels of their probability of success dial (e.g.., 90% to 100%) that is meant to indicate a level at which perhaps individuals ought to consider spending more. This is in contrast to the green zone (e.g., 75% to 90%) which may indicate a more ideal balancing of risk and reward related to retirement income spending levels.

However, just because that’s the intent doesn’t mean that retirees are going to assess results in that same way. It may be the case that, for instance, despite an advisor feeling like 90% is a ‘good’ Monte Carlo simulation outcome, their client interprets the result as meaning that they have a 10% chance of financial ruin in retirement.

Despite the fact that small adjustments can often keep a plan on track (versus the typical Monte Carlo assumption of charging forward blindly no matter what happens), the reality is that Monte Carlo simulation results generally don’t address magnitude of failure at all. This leaves retirees naturally uncertain about exactly what ‘failure’ may mean in a Monte Carlo simulation.

While shifting the terminology used from “probability of success/failure” to “probability of non-adjustment/adjustment” may be helpful in providing greater clarity regarding the implications of a plan, it’s still the case that presenting a percentage-based result creates an incentive to increase the probability-of-success number. Similarly, retirees might still be nudged in the direction of trying to get their probability of a future adjustment as low as possible, when the reality may be that, given the nature of how a prospective downward adjustment for a particular retiree would actually impact their quality of living (or not!), they would have been willing to accept that downside if it was framed differently.

### Changes In Probability Of Success Over Time

Another issue around gamification within the context of Monte Carlo simulation – and one that is perhaps even less well appreciated – is the impact that the volatility of plan results over time can have on the client’s sense of potential achievement and how that can influence client behavior.

For instance, actual spending levels in retirement are surprisingly consistent regardless of whether one targets a constant 95% probability of success or a constant 50% probability of success in retirement. This may sound odd, but the reality is that whatever happens in the market has far more impact on what spending level is sustainable in retirement – at least so long as one is willing to make adjustments along the way.

What this also means is that it doesn’t take a tremendous amount of market movement to shift a 95% probability-of-success plan result to a 50% probability-of-success plan result. Furthermore, although the statistics behind why it is the case may trip us up a bit, we shouldn’t necessarily even find this surprising, as there is a very big difference between understanding what probability of success means within a *one-time* Monte Carlo simulation with no intention of making any future updates to the plan versus what it means within a plan that is going to receive *ongoing* updates.

If we are running a one-time plan in which a retiree will pick a spending level and then blindly charge forward throughout retirement without adjusting their spending no matter what happens in the market, then a 95% probability of success should imply that about 19 out of 20 times the retiree does not deplete all of their assets in retirement. However, this also means that some of these ‘success’ scenarios will inevitably fall dangerously close to 0%.

For instance, suppose a plan iteration starts at a 95% probability of success level and then, over time, falls significantly to what would only be a 5% probability of success. If that iteration ultimately recovers and manages to *not* run out of money (as we would now expect to happen 1 out of 20 times at the updated probability of success level), then it still was a ‘successful’ scenario under the initial simulation.

Notably, if that iteration were to manifest itself in real life, a retiree would probably not feel very good about continuing to blindly charge forward without making any spending adjustments. It almost certainly would introduce stress around the retiree’s perception of their wellbeing in retirement, but we know in advance that many of the modeled iterations would fall *significantly* in terms probability of success during retirement.

But let’s step away from the more extreme (5% probability of success) scenario and instead consider a scenario where the probability of success level fell from 95% down to only 50% due to a correction in the market. Even then, how would we predict that would make a client feel?

50% probability of success might sound scary, but we’re still essentially saying that there’s a 50/50 chance that someone could continue down their current spending path and not run out of money in retirement.

Nonetheless, this change will almost certainly gamify behavior in several different ways.

First, the lure of empowerment (receiving instant feedback on how changing inputs will impact the plan) and desire to accomplish (increasing a scenario’s probability of success by changing inputs) may lead someone to feel inclined to make adjustments. However, one of the challenges of just simply using Monte Carlo simulation is that it’s not clear *how* a client should necessarily make adjustments. By contrast, using guardrails-based frameworks – where adjustment thresholds and requisite adjustments themselves are defined in advance – makes it very clear how one should make adjustments when the time comes.

Monte Carlo without guardrails is, in a sense, like playing a game without rules. If the probability of success falls from 95% to 50%, what should a retiree do? Cut spending so that the change brings the probability of success back to 95%? 70%? Stick with the plan with the hopes that the market will recover and that this will not be one of the 5% of scenarios that ‘fail’?

We don’t really know how to respond if it’s not defined in advance. Most likely, a retiree might end up thinking something along the lines of, “Well, we targeted 95% before, so maybe we should tweak the plan to try and get back to that probability of success?”

While this certainly is a way a retiree could respond, that strategy – essentially targeting a static 95% probability of success throughout retirement – is far different (and far more conservative) than targeting an *initial *95% probability of success without the flexibility to accommodate future adjustments to the plan.

The contrast here with retirement income guardrails is that guardrails define these rules in advance. Moreover, risk-based guardrails (or probability-of-success-driven guardrails) can still take advantage of all of the analytical benefits of Monte Carlo simulation, while also capturing the communication benefits of guardrails.

Essentially, guardrails provide a more tangible set of rules for an otherwise highly abstract game of deciding when and how to make adjustments in retirement. From this perspective, guardrails can help to manage gamification-motivated behavior for retirees far better than simple Monte Carlo simulation, and this is true even if the guardrails themselves are based on Monte Carlo simulation.

### Shifting The Focus Away From Probability Of Success

Another consideration related to better gamification of behavior is that even when probability of success is an important metric underlying a plan, it does not need to be the focal point of the plan. In the case of risk-based guardrails, everything can still be communicated to retirees in terms of dollars (e.g., monthly income, portfolio balances, etc.), which tend to make more sense than other abstract metrics to most non-advisors.

By reorienting the discussion away from probability of success –a metric which we know will vary substantially over time and perhaps in ways that are not so helpful in terms of understanding next steps – and instead framing plan results around dollars and more meaningful metrics, advisors can help retirees understand the actions that would actually make sense.

This, again, guides us in the direction of using guardrails. As argued elsewhere, most advisors who primarily use Monte Carlo simulation are effectively using a type of guardrails strategy – even if they don’t frame it or think of it that way.

For instance, an advisor might be operating from a simple framework like:

- Recommend an initial spending level at a 95% probability of success
- Recommend increasing spending if the probability-of-success level rises to 99%
- Recommend a spending decrease if the probability-of-success level drops to 70%

Setting aside questions regarding whether these would be the ideal thresholds to use, the framework above is actually, in effect, a guardrail system – with the caveat that it is expressed in terms of probability of success and missing some of the key communication advantages of a true guardrails strategy.

From a gamification perspective, even if the advisor often thinks about these rules in their head, those same rules aren’t being communicated to the client. By simply formalizing those guardrails, we move one step in a positive direction in terms of helping a client actually understand the ‘rules’ of the game they are playing.

At the same time, however, the advisor could go one step further in terms of better communication and shift some of the focus off of the hard-to-understand concept of probability of success. The reality is that if we have calculated an initial 95% probability of success, we could easily calculate the same portfolio values that would generate a 99% probability of success and a 70% probability of success at that same moment in time.

Furthermore, when re-running the Monte Carlo simulation at these higher and lower portfolio values, we could simply take the final step of also computing the dollar value spending adjustments that would get the plan back ‘on track’ (however we decide to define that adjustment) once the guardrail is hit. The end result could look something like:

- We recommend spending $6,200/mo. (after taxes) based on your current portfolio balance of $1.6M
- If your portfolio grows to $1.8M, increase spending $700/mo.
- If your portfolio declines to $1.1M, decrease spending $300/mo.

The point above isn’t the specific numbers chosen, but rather to see how the exact same probability-of-success-driven guardrails strategy could be expressed in terms of either (a) abstract probabilities that don’t mean much to retirees, *or*, (b) with a few extra calculations, as portfolio and spending levels that communicate the same information in a much more practical manner.

And, from a gamification perspective, the ‘rules of the game’ can become more clear and easier for clients to follow when we make this shift.

Ultimately, the main point here is that how we communicate results to clients *does* matter. One underappreciated aspect of our communication is how it could ‘gamify’ certain types of behavior. While there are some very positive aspects of the typical presentation of Monte Carlo simulations – particularly related to how the ability to adjust results and get instant feedback could tap into some of Chou’s 8 core gamification drivers of behavior, such as Accomplishment, Empowerment, and Unpredictability – those positive aspects could be achieved just as effectively (or perhaps even more effectively), through some alternative framing.

For instance, rather than seeing a probability-of-success dial change as plan updates are made, it might be better to see something such as a full set of retirement income guardrails and instantly understand how those guardrails change based on plan changes (e.g., retiring at age 62 versus age 67). This would shift the potentially negative impact of Monte Carlo simulation gamification elements in a more productive direction when framed in terms of guardrails. Of course, this is more demanding from an analysis perspective and would take some more time to generate using planning software, but these are also computations that technology should be able to quickly handle for advisors.

Leo O'Connor says

Great article! Very interesting!