Monday, October 17, 2011

"Monte Carlo Mania"

Today’s classic withdrawal rate study is “Monte Carlo Mania” by Robert D. Curtis, which can be found in Harold Evensky and Deena B. Katz’s 2006 book, Retirement Income Redesigned: Master Plans for Distribution. [Note break: In the future, I’d like to feature more articles from this book.  It is a really good collection.] Though Robert Curtis developed MoneyGuidePro, a financial-planning software package that uses Monte Carlo simulations, in this article he casts a critical eye at Monte Carlo and suggests a more basic deterministic approach which includes stress-testing.  This article has so many good insights that it is really hard to know where to start or what to emphasize. It’s going to be hard to keep a central theme, because there will be so many callbacks to things I’ve discussed before. Please be tolerant of the random and unfocused nature here.

What I find really intriguing about the article is how he sets up a client’s goals and hopes for this stress testing, which I think provides a very practical real-world version of the idea of “diminishing marginal returns from utility.” [Note break: the article never mentions utility, this is my own interpretation] I think this is important, because a lot of people hold a really strong aversion towards utility analysis, thinking that its practitioners are ivory tower lightweights suffering from “physics envy.” I don’t think this has to be the case, and I think that thinking in terms of theoretical models can provide useful insights. This all relates, in particular, to the two articles I discussed here a few days ago which I think have provided some really critical insights about retirement planning.

First, just to be clear, Monte Carlo simulations can provide a real improvement over a simple analysis assuming a fixed portfolio return over time.  This is because of sequence-of-returns risk, as a few bad portfolio returns early in retirement can really derail a retirement plan.  Monte Carlo simulations pick this up, because some of the random simulation sequences will include poor returns at the start of retirement.  What Monte Carlo simulations do is to provide a probability distribution for remaining wealth at the end of some post-retirement point in time.  If in 26% of the simulations, wealth had been exhausted prior to the end date, then we could say that the retirement spending / asset allocation strategy has a 74% success rate.

An important problem about this which he highlights is that one way to improve the success rate is to just reduce the planned spending amounts. Let me share a quotation from the article, because this is the key, I think, for retirement planning researchers to have a legitimate basis for using a theoretical utility maximization framework when exploring the general concepts about what may be most satisfying strategy in the face of the extreme uncertainties facing a prospective retiree:

Another related problem is how this approach devalues the goal-setting process. The heart of financial planning is your ability to help clients identify, quantify, and prioritize goals. You want to give your client the freedom to share all their goals, including wants and wishes, not just needs. But if they do so and add more goals, their probability of success can quickly fall into the bad category. This is nonsense. A 60 percent chance of attaining all of her goals, including dreams and wishes, may be fine. You don’t want your clients to limit their goals to only the most important ones just to get a higher score. That’s why it’s so important to prioritize goals and to be able to demonstrate not just that there may be some risk to attaining them, but which goals are most at risk. A Monte Carlo probability doesn’t illustrate this well because its result is all-or-nothing. Your client succeeds at all goals or fails at all goals.

What “diminishing marginal utility” means is that one’s utility (just think of it as overall happiness or life satisfaction – it is a theoretical concept meant to help us gain insights about the real world) is positively related to her expenditure amounts, but at a decreasing rate.  Just having enough for basic food and shelter provides a dramatic increase in utility.  But as expenditures increase more and more, we are just talking about adding more luxuries which may only provide a very small boost to utility compared to the less luxurious model. I’ve touched on this a lot before, that unfortunately there is an awful lot of retirement planning research that completely ignores this issue, particularly in the accumulation phase, as success or failure is defined only in terms of meeting a wealth accumulation target, and no consideration is made for the magnitudes of failure.  That approach suggests keeping 100% stocks (or even adding leverage) at all times. During retirement as well, the failure rate doesn’t pick up how big the failure was… i.e. how many years passed before wealth was depleted.

What Mr. Curtis is adding here is to say that it is hard to even consider success or failure, because success or failure for what?  It isn’t necessarily so bad if every single dream is not satisfied, but whether all those dreams are included in the analysis has a big impact on what Monte Carlo suggests the failure rate will be.  

Another important problem about Monte Carlo which he highlights is that Monte Carlo has a tough time accounting for particular risks that retirees face. These risks include the chance of experiencing very expensive health problems, the chance of spending time in a nursing home, and the chance of living much longer than expected.  All three of these possibilities can be included into Monte Carlo.  In fact, for the life expectancy issue, I wrote a number of recent posts about looking a failure rates based on random life spans calibrated to mortality data, rather than fixed 30 (or however many) year retirement periods.  Mr. Curtis makes a convincing argument, though, that these are not “probability problems” but rather “possibility problems.”  Though I had convinced myself that adding random lifespans represented an improvement, I need to think about this some more.  Mr. Curtis provides a rather convincing counterargument: “What possible sense does it make to tell your client that she can spend more money now because you’re assuming in some of the Monte Carlo iterations that she’ll die early? How does a person die ‘some of the time?’”

As such, in moving towards his scenario analysis, it isn’t so much that we need to randomly simulate these problems into the Monte Carlo simulations, but rather that we should specifically analyze how experiencing these problems could impact the sustainability of our retirement plans.  In other words, go ahead and plan for a relatively long retirement period, but then investigate what happens if greater health expenses are added at some point, or if one lives another 5 or 10 years longer.

This leads to his alternative approach, which is to assume average portfolio returns, but then do a “stress test” which considers how the results are impacted by risks such as bad returns early in retirement, unexpected and large health expenses, or an extra long life.

What I really like about this is the way he sets up the client goals. Each goal is prioritized on a list from most important to least important.


For example, I’ll make up my own version of what is clearly his idea from Figure 8.4 of his article.

My financial goals – everything in real inflation-adjusted terms:


1. Minimum living expenses: $50,000 per year for 25 years and then $40,000 per year for the 5 years after that


2. Family car: $30,000 this year, and this expense re-occurs every 5th year for a new car


3. Travel: $10,000 per year for the next 10 years, and then $5,000 per year for years after that


4. Gifts: $5,000 per year for 30 years


5. Extra living expenses: $10,000 per year for 30 years


What is unique is that these goals are then funded in order of priority, not time sequence. That means, we do not immediately think to fund goals 1-5 in year 1. Goal 5 will only be funded if we first check and find that goals 1-4 can be funded during the whole period, and so on. Given the average portfolio returns, the software first checks which percentage of goal 1 can be funded over the whole time period.  If 100%, then move on and see how much of goal 2 can be funded. Keep going until savings are exhausted.  If all the goals are fully funded, then the remaining wealth at the end of the planning period is called the “safety margin,” and it provides further provides further protection.

Then, do stress testing... investigate how the results change with the different scenarios for increased expenses mentioned before. In the example provided in the book, the baseline scenario funds all 5 goals with a safety margin of $288,000. But for the test of the impact of sequence of returns risk, the safety margin disappears and only 34% of goal 5 is achieved.  Goals 1-4 are safe.  A Monte Carlo simulation would have classified this as a “failure,” but we can see (related to diminishing marginal utility) that this failure is not so bad as it only cut into the relatively less important “extra living expenses” category.  Retirees may be more accepting of this, whereas “failure” could cause unnecessary fear.

All of these different concepts can be integrated together.  Not only do I think this article ties in to utility analysis very well, but it also provides some explanation and heart to the “income floor / upside potential” approach I discussed yesterday. In this case, the retiree needs to decide which of the goals should be included in the guaranteed income floor, and which to leave for the remaining volatile portfolio. Another interpretation of mine is that this ties in as well to lower overall stock allocations, because a higher stock allocation will probably provide the highest chance for success for all the goals, but will most likely lead to more failures for some of the higher prioritized goals. This is not necessarily what retirees would want to see happen. Mr. Curtis’s article is providing an important piece of the puzzle about how to develop sustainable spending plans for retirement.