Monday, May 14, 2018

Spending Rules and Simulation

My recent post on Monte Carlo(MC) simulation, The Retirement Café: The “Future” of Retirement Planning, seems to have spawned a strange debate about whether a deterministic "spreadsheet" method of calculating safe current spending from a retirement portfolio is better or worse than using Monte Carlo simulation to estimate the probability of outcomes.

This debate is not unlike arguing whether a screwdriver is superior to a hammer: they do entirely different things, a good toolbox includes both, and even when you use both effectively, you're still probably going to need a saw. (I'll write more about the saw in my next post.)

I'm going to refer to the "method of calculating safe current spending from a retirement portfolio" as a spending rule because that is its purpose. The result is typically a single dollar amount as in, "applying the 4% Rule to a $1M portfolio when expecting a 30-year retirement estimates the retiree can spend $44,000 each year" or "the required minimum distribution(RMD) from your IRA this year is $38,517."

An interesting observation about these spending amounts is that if you recalculate this amount in subsequent years (as you should do with any spending rule but must do by law for IRA and other tax-deferred plans after age 70½), it is possible but extremely unlikely that you will ever calculate the same result again. That's because remaining life expectancy, current portfolio value, and other factors will change over time.

On the other hand, the purpose of Monte Carlo simulation is to estimate the probability of outcomes assuming a retiree were to retire many, many times. The probabilities can be used to identify potential problems and allow a planner to attempt to mitigate them.

The result of simulation is not a single number for a single year as calculated by spending rules but one or more probability distributions showing the odds of various outcomes, as in "there is a 5% chance that you will need to spend less than $20,000 under certain conditions."

While spending rules estimate safe current-year spending, MC simulation can provide additional insight into many questions, such as:
  • The 4% Rule says I can spend $40,000. What are the probabilities that I can safely spend $45,000 or $50,000?
  • How much could I spend if I wanted a 1% or 10% probability of ruin instead of 5%?
  • Which equity allocations most often appear in failed scenarios? (I often find that 40% to 60% equity allocations show up in fewer failures.)
  • What is the value of my safe "floor" over time? Are there gaps? Would annuities help?
  • How often does delaying Social Security benefits improve my outcomes?
The list can go on and on (this is the reason MC is used for academic retirement finance research) but it does not include "how much can I safely spend this year" beyond what the simulation's chosen spending rule can tell you before you even begin simulation.

Monte Carlo simulation and spending rules are different tools for different jobs.
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Wade Pfau's book, How Much Can I Spend in Retirement?[2], provides an extensive inventory of spending rules, including:
  • 4% Rule (constant-dollar)
  • Constant percentage
  • Steiner ABB
  • RMD
  • Kitces’s Ratcheting, and others.
At present, I tend to favor Steiner's ABB[3] for determining current safe spending, an approach which Pfau generally refers to as "actuarial" or "PMT" methods. He notes that Moshe Milevsky also believes this is a great place to start[4].

MC isn't tied to any particular spending rule, although most free online programs model constant-dollar withdrawals, aka the 4% Rule. That's unfortunate in my opinion because I consider it a very poor spending strategy.

There is no "Monte Carlo spending rule."

MC models can implement any of the rules in Wade's book or any other. MC takes the spending rule of the modeler's choice and predicts what would happen if that rule were applied every year throughout many lifetimes.

It doesn't make sense, then, to ask how MC spending compares to these rules. MC uses these rules to calculate annual spending.

If I build a simulation model using the 4% Rule, spending for the first year of my model will look essentially the same as the 4% Rule. If I build it using ABB or a constant-percent spending rule, instead, the first year spending in my simulation model will look like those. Results only begin to differ in year two of the simulation as other modeled factors, like expected market returns, change.

Sometimes when I write an MC model I make up my own rule. MC is a good way to compare spending rules.

Not all spreadsheet or "deterministic" models are the same. Ken Steiner's ABB model, for example, is quite different than spreadsheet models that simply subtract fixed spending each year and then grow the portfolio by the same expected market return growth factor. Unfortunately, there seem to be a lot more of the latter out there.

Not all MC models are the same, either, but like spreadsheet models, most of the free ones are pretty much the same. They often assume a fixed-length retirement, 4% Rule spending and probability-of-success as the evaluation criteria. More concerning, they usually predict outcomes for a portfolio, which is only a small piece of a retirement plan (see The Retirement Café: Three Degrees of Bad). A simulation for retirement planning should simulate retirement finances, not just a retirement savings portfolio.

The practical implications are somewhat complicated. Using a spending rule is relatively straightforward and accessible; good simulators not so much. Steiner offers a free spreadsheet for ABB at his website. Free RMD calculators are widely available. If you are unfamiliar with MC simulation, though, learning enough to use the tool effectively is a daunting task and probably not worth the effort.

Your best bets, in that case, are to find a knowledgeable planner who has access to good software or to pay for Laurence Kotlikoff's E$PlannerPLUS[1].

Screwdrivers are great for removing a screw but terrible at hammering a nail. Spending rules are intended to estimate a safe amount to spend from a savings portfolio in the current year but tell you nothing about the probabilities of lifetime outcomes from applying that rule repeatedly.

The smooth path of a spreadsheet projection (red in the chart below) is not a rational expectation for a real retirement, nor is the terminal portfolio value it estimates. The future projections are not a median or "expected" outcome. They're simply an assumption for estimating current spending.

I'm not even sure how to describe that TPV. We could say that it is the terminal portfolio value we would expect if the stock market returned the identical expected return every year with no sequence risk for a fixed lifetime but since none of those assumptions is realistic it is not a meaningful value.

MC simulations only estimate current safe spending by incorporating a spending rule but they're great for understanding the probabilities that determine the outcomes of the retirement finance "game."

When I suggested in a previous post that if you are planning retirement with a spreadsheet model you should test it with simulation, I wasn't suggesting that MC provides a better estimate of current safe spending — it doesn't do that, at all — but that you understand the probabilities of future outcomes. If you don't, then you probably don't have a good understanding of the risk in your plan.

I read a post complaining that these simulations are useless because the retiree can't know which of those tens of thousands of potential outcomes will be hers. That's like a poker player arguing that knowing the probabilities of the card deck is useless because a player can't predict which card will be drawn next.

If you recalculate a good spending rule every year (variable spending) you are unlikely to deplete your portfolio, although spending could become awfully tight should your portfolio fall on hard times.

(For example, there's an excellent post at[5] showing how Draconian spending cuts could become using the Guyton-Klinger Guardrails spending strategy. "Sustainable withdrawals" means you aren't likely to deplete your portfolio. It doesn't imply that the variable amount you will be able to safely spend will be enough to sustain you.)

On the other hand, simply recalculating spending annually means you're planning one year at a time. I prefer a plan with a longer horizon that is updated every year. Keep your eyes on the prize and make the necessary annual adjustments to get you there.

Spending rules estimate a safe amount to spend in the current year. Monte Carlo simulations estimate the probabilities of future outcomes one should expect when recalculating a chosen safe spending estimate every year over many lifetimes. But, MC only thoroughly covers reasonably-probable outcomes. A good retirement plan still needs a "saw" to cover the improbable.

More on that next time in Some Risks Can't be Modeled.


[1] ESPlannerPLUS | ESPlanner Inc.

[2] How Much Can I Spend in Retirement?: A Guide to Investment-Based Retirement Income Strategies eBook: Wade Pfau: Kindle Store

[3] Actuarial Approach – Using Basic Actuarial Principles to Accomplish Your Financial Goals.pdf, Ken Steiner.

[4] It’s Time to Retire Ruin (Probabilities), Milevsky, 2016.

[5] The Ultimate Guide to Safe Withdrawal Rates – Part 10: Debunking Guyton-Klinger Some More – Early Retirement Now


  1. Gallup just published an interesting study that indicates people tend to under-predict their retirement comfort before retirement:

    Possibly, one reason is that the spending rules, like Bengen's 4% SWR, tend to be close to the lower-bound with more likely mean and median values significantly higher.

    Gallup uses $75k/yr as a cut-off point where almost all retirees feel comfortable with their financial situation while $30k is a cutoff below which a substantial percentage of retirees are uncomfortable.

    One thought is that we are getting close enough now to the date when the Social Security Trust Fund is scheduled to run out that Monte Carlo analyses, especially for people expecting less than $75 annual income, may need to start assigning some probability to various levels of reduction of Social Security. Similarly, we are starting to see more pension funds struggling and requiring reductions in benefits, which may also need to be modeled (% funding levels should provide a basis for assigning probability distributions of projected pension distributions).

    Unfortunately, we are starting to see floor incomes threatened by political and corporate governance failures. In general, I don't see these bedrock floor income components going away, but 10% to 30% haircuts appear to be more and more possible as we get closer to key dates.

  2. Great post Dirk ... it helps unravel the differences between rules and models.

    Anonymous' points about pensions brings to mind a great presentation about those just last week (for continuing ed) and a resource that helps those affected see their risk exposure

    As to Social Security, if you Google proposals on fixing the shortfall, you'll notice that they tend to grandfather those aged 55 to 60 (depending on the proposal). So those younger than those ages have time to adjust their plans. Those grandfathered wouldn't be affected by program changes.

    The key point to either or both - is understanding who is affected and how the "fix" may affect them should those occur. Social Security proposals protect retirees. Pension reforms may require current retirees to make changes in order for the whole system to be sustainable for all in those.

    1. The "file and suspend" changes that went into effect in 2016 indicate that Congress is willing to change rules that impact people until they are 62. To my mind, this was a significant change as historically they had grandfathered back to about age 55 at the time a law is enacted. In this case people over 55 only got a few months notice that they would be subject to this change.

      The longer they put off making Social Security funding changes, the more likely it is that changes will impact people up to age 62 or older at the time a law is passed as the budget math starts to take over the decision-making.

      I am in that 55-60 year old window and am already factoring in a significant probability of about a 20% SS reduction in my early 70s which is the current schedule based on the Trust Fund running dry - that is the default condition under current law and will take Congressional action to be something else.

    2. Sounds reasonable but, frankly, I'd rather try to predict market returns than Congressional action. Last year's tax changes showed the folly of long-term tax planning in retirement.

      Probably best to assume, as you do, something less than certainty.


  3. Dirk, you mention ESPlanner Plus, which I’ve used for years. Have you been able to figure out what spending rule is implemented underneath the covers for either the Monte Carlo simulation or the “suggested spending” report? (I would assume it would be the same rule, but not sure). I’ve always been curious about this.


    1. E$Planner is built on the economic principle of consumption smoothing that assumes people prefer stable and predictable consumption over their lifetime to enduring periods of low spending and high spending. Consumption smoothing seeks to transfer consumption from those high-consumption states to increase spending in low-consumption states. This is a very different strategy than the other spending rules I discussed.

      That's an oversimplification and Kotlikoff explains it better at his website, such as here.

      The spending rule, then, would be to spend the amount each year that is on an optimal smooth consumption path. Insurance also fits into this regime (it transfers consumption by paying premiums in good times to increase consumption through insurance claims in bad times) and the MC simulation would simply provide a varying wealth path to be smoothed so, yes, same rule.

  4. I would be keen to better understand your comment "At present, I tend to favor Steiner's ABB for determining current safe spending ..." I actually -- or is it actuarially :) --- find this approach appealing but expect you would have additional insights in terms of pros and cons that I have overlooked.

    I always look forward to posts.

    Much thx


    1. Good timing, Bill. I was just discussing this with Ken over the weekend.

      Ken is an actuary and his objective is to answer the question using actuarial methods. I believe he and I agree that no spending rule can actually determine a safe amount to spend this year that will both meet spending needs and protect a portfolio from premature depletion. I believe we also agree that spending rules, including his, are merely a budgeting estimate.

      Consequently, we can't know if any spending rule will provide better results than any other for an individual household.

      If you keep in mind that the calculation is only a budgetary estimate based on an unknowable future and that the budgetary estimate will likely change, perhaps significantly, in a year or less, and use it that way, then you will be fine. If you think any spending rule ensures that you will be able to meet your expenses and not outlive your savings, then you are overconfident.

      I like Ken's approach simply because it considers more of the important factors but neither Ken or I know if the estimate is better or worse than others.