Thursday, April 18, 2019

Black Holes, the Higgs Boson and Retirement Planning

The first image of a black hole. Credit: Event Horizon Telescope collaboration et al.

What do relativity theory, quantum mechanics and retirement planning have in common? Not a lot and that's actually an important point.

Black holes were implied by Einstein's work on general relativity in 1915 but the first one wasn't discovered until 1971[1]. Physics was able to predict the existence of one of the largest elements of the universe 56 years before one was discovered.

At the other extreme, on the quantum scale, Peter Higgs and five other scientists proposed the existence of the Higgs boson in 1964. Its existence was confirmed in 2012 based on collisions in the Large Hadron Collider at CERN. The existence of the Higgs boson was predicted 48 years before it could be confirmed.

In retirement planning, we do well to predict finances somewhat accurately more than a year or two in advance. Retirement planning is clearly not rocket science.

Physical sciences and their predictions are based on physical laws of the universe. Acceleration due to gravity on Earth is about 9.8 meters/second2, or about 32 feet per second per second as we Boomers learned in high school physics back when a meter in the U.S. was something one paid a quarter to park. On Mars, it's about 3.7 m/s2. Light travels at about 300,000 kilometers/second.

Drop an object from a height of 10 meters on earth and we can predict that it will reach the ground in 1.43 seconds traveling at 14 meters/second at impact. We can build models that predict such things with great accuracy.

Economics, however, is a social science, not a physical science. Finances can be modeled mathematically but actual outcomes are highly dependent upon the behavior of the humans involved. That makes the models far less predictive.

Unlike the universal laws of physics, the inputs for financial models are often unknown, so we make our best guesses. The most important factor of retirement finance, how long you and your spouse will live, is largely unknowable. Half of a group of people like you may live another 18 years but you might live twice that long or get hit by a bus tomorrow.

We know that stock markets have returned about 9% a year over the past 150 years but you won't be retired for 150 years. The geometric rate of market return you would have historically experienced over any single 30-year retirement during those 150 years could have been less than 3% per year or more than 10%, depending on the year you retired. The range of returns is broader for shorter periods.

Black Holes, the Higgs Boson and Retirement Planning.
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Retirement models, whether mathematical, spreadsheet, or Monte Carlo simulation, can't predict the future the way models do in the physical sciences. Monte Carlo simulation was developed for the Manhattan project and was accurate enough to help develop the atomic bomb when the world had minuscule computing power. MC could predict how atoms would behave but it can't predict your retirement finances.

In 2001, William Bernstein published a blog post entitled, "Of Math and History" noting that "it’s the engineers who most often give me the willies."[2]
"The trouble is, markets are not circuits, airfoils, or bridges—they do not react the same way each time to a given input. (To say nothing of the fact that inputs are never even nearly the same.) The market, though, does have a memory, albeit a highly defective kind, as we’ll see shortly. Its response to given circumstances tends to be modified by its most recent behavior. An investment strategy based solely on historical data is a prescription for disaster."
(It's a great read, by the way, as is just about everything at

There is huge risk in believing that we can accurately predict our financial future, market risk or returns, a safe amount to spend annually from our savings portfolio, our optimal asset allocation, our probability of successfully funding retirement, or any such metric with any degree of accuracy for any period beyond perhaps a couple of years, let alone for a retirement that could last 30 to 40 years.

I recently told an audience at a retirement finance conference that the greatest risk of retirement is overconfidence. Believing you can accurately predict the things in the previous paragraph is a prime example.

You might rightly ask, given my perspective of uncertainty, why I spend much of my retirement days building simulation models. The answer is that I don't use the models to predict probability of ruin or to predict anything, for that matter. I use them to study many possible outcomes for hints for improving my retirement plan. I readily admit that I have no idea which simulated scenario, if any, ultimately will be similar to mine. I just want to find the bad outcomes and say, "Whoa! How can I avoid those?"

I was once asked what I think is wrong with spreadsheet models of retirement. My answer is that they only consider a single possible scenario and not a realistic one, at that. It is highly unlikely that you will live precisely 30 years in retirement, for example, and there is an infinitesimal probability that your market returns or expenses will be the same each of those years.

(You could run a spreadsheet model several times with different assumptions, of course, but you can generate tens of thousands of different scenarios in a few seconds with MC.)

The tools we use in the physical sciences can be useful in social sciences like economics but they cannot be as predictive because people, unlike atoms, are unpredictable. Computerized retirement models can look impressive when a computer spits out thirty pages of Monte Carlo simulated data but less so when one considers the huge assumptions that have been input into the program. Computers and simulation cannot remove risk from your retirement but they can help identify and understand it.

In an earlier post, I suggested that the most important retirement decision you will make is how much of your wealth to allocate to safer income assets and how much to risk in the market. Don't be overconfident in your ability to predict the risk and returns of the latter. Have a backup plan (a floor of safe income) in case of portfolio failure. Retirement models are simply the best estimates we can make of a largely unknowable future.

And, if someone tells you that you will die with $5.3M in your investment portfolio or that you can spend 4.27% of your portfolio balance annually with a 95% probability of not outliving your savings for at least 30 years, consider that with a large dollop of skepticism.

Remember when you're considering your retirement plan that all models are wrong but some are useful.

Zvi Bodie explains "America's best-kept secret", I bonds for inflation protection.

The American College of Financial Services has created a wonderful collection of brief video interviews with Rick Miller on topics of personal financial planning.


[1] Who Really Discovered Black Holes?, BBC Science Focus Magazine.

[2] Of Math and History, William Bernstein.


  1. An interesting calculator is Firecalc. It runs about 50 simulations and then draws a line graph of your future earnings. Actually it draws 50 lines on the graph so what you get is kind of a general idea of where you will be.

    1. How does it provide a "kind of a general idea of where you will be"?

      It shows a huge range of possible outcomes that you might experience if you retired 50 times. You will retire once, so where do you believe you will generally be within that range?

    2. With any calculator how do you know the result is accurate. I was just looking for confidence that I was on the right track.

    3. Looking for confidence (or the lack thereof) is a valid use of models even if they can't predict where you will end up. That's generally why I use them.

      What do you mean by "accurate"?

    4. By errors I'm thinking of inflation rates and average returns, as two examples of where we can guess wrong. When I did a retirement budget I didn't figure I'd retire to a house with expensive propane instead of electric and wood heat. I underestimated my Medicare costs. In my favor I made some good real estate investments later on while buying retirement property. These are the kinds of errors I'm talking about. In the end I must have used a dozen retirement calculators, plus a couple of humans associated with my accounts. All to give me some confidence that I was going to be okay.

    5. As I said, building confidence in your plan is a good reason to use models.

      As for "accuracy" and "errors", I can guarantee that the models will be wrong. All models are wrong; some are useful. Or, to quote Robert Merton, "All models are an abstraction of complex reality. As an abstraction, the model is incomplete."

      I was questioning your statement that the models give you an idea of where you will be. I don't think they do. I think they create many scenarios, some that might be something like where you will be, but you only get one retirement so at best you will end up in one of them. It could be the best, the worst, somewhere in between, or in one that wasn't simulated. It's good to know the range of possibilities.

      I think that using lots of models and studying the output of each is a good strategy. I only worry that many people think they provide "the answer."

      Best. . .

    6. I like FireCalc also, but for the opposite reason of user 96Trees: it opened my eyes to how UNPREDICTABLE the outcome is. Simply leave the 3 default numbers in there, click submit, and you have an outcome range of anywhere from running out of money in 25 years, to almost 6 times the original portfolio value in 30 years. I was shocked at how wide a range it was. Since then I've read everything I can get my hands on about retirement planning, and have learned how complex it is (and there are a lot of moving parts). My wife & I decided to use a human planner, and we like the plan he has come up with.

    7. I don't know FireCalc. I looked at it briefly. I seem to recall that showing unpredictability is claimed as a strong point.

      I don't know if FireCalc estimates probability of ruin but I would caution the use of any model that does. Probability of ruin is not a robust metric and can change significantly just by running the model again and changing nothing but the random number draw. In other words, you can run the model 100 times and get significantly different results each time.

      I suspect that models that generate only one probability of ruin do so because they were only run with one draw. That's not Monte Carlo.

      A retirement model is not a retirement plan; it's just one tool. I suspect most retirees would be better off with a good retirement advisor. A good one is hard to find, IMHO, but worth the effort.

      Thanks for writing!

  2. Dirk, or anyone else for that matter. I'm looking for a calculator. The spreadsheet model you disparage. You have to start somewhere before starting to consider the enormous variables that undermine our planning. A tool of this nature may have been discussed in a prior post. If so, let me know.

    I'm having trouble trying to describe what I'm looking for, but here it goes.

    I'm trying to calculate the money needed from savings to fund what Social Security doesn't provide.
    Assumption 1- Social Security doesn't change (not likely)
    Assumption 2- Inflation remains the same (not likely)
    Assumption 3- You don't want to read the legion of assumptions that must be made for a spreadsheet model.

    I know the theoretical amount for year 1, but that amount has to increase annually to compensate for the annual inflation rate. In addition, that greater amount is taxed and one must increase the withdrawal of savings to compensate for the loss to state and federal income tax. It would also be helpful if it could include the number of years I expect to be alive.

    Then I'll need to try to guess my RMD on an amount that may not be right that I may or may not has as part of my retirement.

    While not the same a shotgun fitting, there are similarities. When you adjust one variable, another variable changes.

  3. All models are wrong. I think MC models provide more information than spreadsheet models but so long as you understand a model and what it does well and poorly, and what you are trying to learn, you'll be OK. You especially need to understand that no model is predictive but that might not be your goal.

    Ken Steiner uses a spreadsheet model to estimate the "safe" amount to spend in the current year. For that purpose, I'm not sure any other model is better, though I particularly like Ken's for that purpose.

    Steve Vernon argues that RMD is a good method for determining current safe spending. I believe part of his argument is that if you can't determine which model is better, you might as well select the easiest to use.

    There is a more extensive spreadsheet at Bogleheads that I would recommend.

    It is not my intent to disparage any particular type of model. I vastly prefer MC models for exploring possible future outcomes, though I understand that I can't predict which outcome, if any, will describe my future. I don't like MC models that try to minimize probability of ruin because that is a flawed metric. Unfortunately, most do. I also prefer MC because it allows me to model the interplay of several variables simultaneously.

    I particularly like because it uses MC but not probability of ruin (it maximizes standard of living) but it isn't free. BTW, I believe it would fit your needs quite nicely, including solving the tax problem you describe. It has the benefit of being developed by a top economist, Laurence Kotlikoff, and has been around a long time, both of which should increase your confidence in the model.

    You mention that retirement planning must consider "enormous variables." True, and we fit most of those variables with WAGs. I sense that many believe that because the answer comes from Monte Carlo simulation and a computer that it must be "right."

    Rather than say that I disparage spreadsheet models, I prefer to say that I am highly skeptical of all models and would recommend that they not be your sole source for a retirement plan because, as I said, they're all wrong but some are useful.

    Thanks for writing!

    1. Apologies, that response got published before I intended. I wanted to add that none of the computer models I have used replace a good human retirement planner.


    2. Retirement planning is an unsolvable problem with unlimited variables!!

    3. That is technically correct but I don't find it useful. If you define a "solvable problem" as one in which there is one optimal solution that can be known in advance, then I would agree the retirement problem is unsolvable. We can't predict the future.

      However, we can use probabilities to help us make the best bets and give us a best chance of winning.

      Take backgammon or blackjack, for example. Both are games of luck and skill. The best players make the best bets for each move realizing that, while they can't be guaranteed a victory, they will win more games in the long run this way.

      If the dice (or the deal) are unfortunate, we will likely lose both games no matter how skilled we may be. On the other hand, we can lose with good rolls if we make poor bets, like splitting a pair of tens or leaving an open stone that can be hit by rolling a seven. Lastly, we can win sometimes, though rarely, by doing something unwise. I watched a friend who didn't know better once split a pair of tens and win both hands. Similarly, retirement is a game of skill and luck.

      Make good bets and you are more likely (though not guaranteed) to achieve better results.

      So, if you're looking for the optimal way to plan your individual retirement in advance, you're wasting your time. Your time will be better spent learning the best bets and understanding that you can't win them all. But if you combine your bets wisely, you can win enough of them.

      You could similarly state that backgammon is an "unsolvable" game in the sense that there is no guaranteed optimal strategy. But good players will beat your pants off over the course of many games. That's because they're skilled.

      Thanks for the comment.