Friday, December 5, 2014

Think Like a Bayesian Pig

OK, one more barnyard animal theme and I promise to move on.

I spoke at the RIIA Fall Conference of retirement planners a few weeks back on the topic, "Think Like a Pig". I suggested that they view retirement from the perspective of a retiree who would actually feel pain if their retirement plan failed as opposed to the perspective of a somewhat-interested third-party. I suggest you do the same with your own retirement planning because being retired isn't quite the same as thinking about retiring one day.

It's for real.

Now, I would like to recommend a further adjustment to your view of retirement planning.

Academics often treat retirement as if it is one integrated whole that begins around age 65 and could last thirty years (spherical cow alert!). This often makes sense in an academic environment when we are trying to understand the financial process involved.

Systematic withdrawals of constant dollar amounts are a good example. We can use the strategy to study the probability of failure over 30-year periods and learn about sequence of returns risk, but implementing that strategy doesn't make sense in real life. Calculating that you can spend 4% of a million dollar nest egg, or $40,000 a year for the next 30 years with little chance of outliving your savings and then actually doing that requires that you ignore any new information along the way.

When was ignoring new data ever a good idea?

At the beginning of World War I, horse-mounted cavalry ignored new data and charged machine guns.

That $40,000 spending estimate is based on what statisticians call "prior probabilities," meaning it's the best guess from the starting gate. After retirement begins, things happen that change your probability of success. The updated probability is called the "conditional probability."

Here's an example I used in a post some time ago. Let's say that you leave Los Angeles on a flight to Honolulu and you learn from the airlines that they have attempted this flight 1,000 times and only 10 of those flights didn't reach Honolulu because mechanical problems, weather or something else forced them to return. Your prior probability of reaching Honolulu would be 99%. That looks pretty darned good.

During the flight, your crew will constantly update their forecasts based on new information, running into headwinds, perhaps, or needing to fly around storms (a good model for your retirement plan). They will continuously create a conditional probability of reaching Honolulu and if that probability drops below a certain threshold, they will return to Los Angeles.

At least, you hope they will.

Should you find yourself halfway to Honolulu and discover that a wing has fallen off your plane, the conditional probability of reaching your planned destination has just declined considerably. (That's why I hate when flight attendants announce, "We'll be on the ground shortly." I need more details than that.) Once the wing is gone, you should take little comfort from the fact that your prior probability of reaching Honolulu was actually quite high.

Retirement works the same way. You might start retirement with a million bucks and a safe spending amount of $40,000, but if your portfolio declines 50% in a bear market you need to start spending less. That original $40,000 safe spending amount flew out the window with your bear market losses. To continue spending the same $40,000 after a large decline in your savings balance is simply ignoring new information, to wit, that you have less money.

In the 1700's, Thomas Bayes thought about how new information should be used to adjust our previous expectations. Bayes Theorem essentially says that we should begin with a prior probability, like a sustainable withdrawal rate or the percent of successful flights to Honolulu in the past, and modify that original expectation in light of any relevant new data that comes along.

Relevant new data for an airplane would be like, remaining fuel, unexpected headwinds and structural integrity of the wings.

This Bayesian approach is the way we retirees should view a retirement plan. Rather than view it as one integrated whole, we should think of it as planning for a 30-year retirement based on some set of prior assumptions. After a year, we should take stock of our new life expectancy, new portfolio balance, and any changes in expected spending along with several other variables and use that new information to plan a 29-year retirement.

Rinse and repeat.

That isn't what we do when we plan on a constant-dollar spending SWR strategy. Instead, it is what Larry Frank refers to when he describes Dynamic Updating and what Ken Steiner is getting at when he explains how to re-budget your spending every year with actuarial techniques.

And, it's what Moshe Milevski's equation for the probability of ruin (also an actuarial approach, by the way) tells us: it is a function of current retirement savings balance, expected spending, expected market returns and volatility (asset allocation) and remaining life expectancy. It doesn't matter what those were back on the day you retired.

What matters is what they are today.


  1. Dirk,
    Outstanding post in your trademark style and in particular because it advances the discussion in a direction that is – yet – seldom discussed by too many of us.
    Retirement management is indeed about risk management.

    Retirement Allocations (in all their forms, RIIA®’s, yours and others) are fundamentally risk management techniques allocations.

    Conditional probabilities are the reason why Gerd Gigerenzer is on the RMA® designation’s Essential Readings List (ERL).

    The ERL is publicly available. See link below to download the pdf:

    1. Thanks, Francois! I highly recommend Gigerenzer. I keep Calculated Risks on the bookshelf closet to my desk, next to The Black Swan and Against the Gods.

  2. Hi Dirk. I like the point of this blog. A couple questions though. In a practical sense how does one update their withdrawal rate yearly for new information. I know that you have commented before that using a constant withdrawal percentage means one will never run out of money (though the withdrawals could be greatly reduced), and this would seem to be one way to adjust for new information. I also believe you have stated that one could also re-run ESPlanner with the updated new circumstances. But are there more ways that one could easily update one's acceptable withdrawal rate yearly based on new information. Thanks, Brad.

  3. Good question.

    Personally, I would update it with Milevsky's formula, but that's pretty complicated unless you're comfortable with cumulative gamma distributions.

    You can estimate the same information using sustainable withdrawal rates data. Bengen, for example, estimated the 30-yr sustainable withdrawal rate at 4.4% of remaining portfolio balance. (His book says the figure should be regularly updated. It was the financial press that believed you could spend the same amount forever.) With 20 years remaining, Bengen estimated 4.7% at 25 years, 5.2% at 20, 6.3% at 15, and 8.9% with ten years remaining.

    So, you can spend a larger percentage of remaining balance as you age. Whether or not that translates to spending more money depends on the success of your portfolio.

    This all depends on your market expectations, which were historical for Bengen, but updatable with Milevsky. Wade Pfau would suggest you reduce all of these, given the current interest rate environment. I agree.

  4. I should add that withdrawal rate and portfolio balance aren't the only things you need to review. Expected spending will change over time, as well, for example. You need to update all relevant information when it comes available.

  5. Brad, try this link. I hope it will let you open a spreadsheet that uses Milevsky's formula to calculate probability of ruin. Let me know. spreadsheet .

  6. Dirk - I agree with your view about the importance of not just “setting & forgetting” with something like a static 4% rule. That would be crazy and, as you say, in reality no one is likely to do so. However, I would like to point out what I see as some danger with the alternative dynamic approaches where one adjusts spending in light of investment returns. The danger is that careful monitoring of one’s portfolio might morph into obsessive attending to the inevitable noise of market volatility, and that this in turn might lead to unnecessary worry and underspending.

    Of course, dying too rich is a less dangerous proposition than dying too poor, but it’s still a kind of risk that might unnecessarily burden a retiree. And I think it is a fairly common risk because many if not most retirees are by constitution and habit cautious under-spenders. After all, if they’ve got enough savings to worry about, it means they’ve probably lived their life spending less than they could have. These are the kind of people less in need of having their spending reigned in. What they most need is a way to understand what they can maximally spend within a secure framework and with minimal concern over the comings and goings of the stock market.

    So what to do? In my view this psychological risk is just another reason in favor of the liability matching, create-a-secure-income-floor approach that you and others champion. This has been a very helpful way for me to make sense of my investment portfolio as I begin retirement. Because now when I go through the mental fire drill of imagining a 50-60% drop in stocks, or even a Depression-like 90%, I realize that what is being lost on paper is mostly my children's inheritance and not my basic retirement income. And because my children should have a longer investment horizon than I do, such a paper loss will carry, I hope, a reduced emotional sting as there’s plenty of time for the market to recover. I understand that by devoting so much to securing a floor I am giving up the risk of growing even richer, but that’s worth it for the peace of mind.( I say the “risk” of growing richer so that I remember that the riskiness of stocks runs in both directions).

    This secure floor combined with a mentally separate risk portfolio is far more appealing to me than trying to determine the best overall stock/bond allocation for my savings as a whole and what safe withdrawal rate this might support year by year. In prolonged bad markets, that safe withdrawal rate approach runs the risk of feeling like one is monitoring a slow growing cancer.

    I know that not every investor is in a position to fund a secure 100% floor. But I think think this approach to analyzing one’s retirement situation is still the most intuitive and easily understood by people of varying investment sophistication. It might lead them to decide that extending their working years in some physically and emotionally doable way is their best route to a worry-free retirement. People can be, I think, surprisingly adaptable and roll with the punches if they understand what they are adapting to and rolling with.

    1. Thanks, Barry. It is true that most people can't build a 100% floor, especially in today's low interest rate environment. But the more you can build, the more security you have. Remember that Social Security benefits are part of the floor, as well.

      Statistically, you can safely increase spending a little when your portfolio gets fatter and vice versa. When the portfolio grows, you have the choice of not spending more. When it declines in value, you must either cut spending or realize that you are taking more risk.

      The change in spending, however, is less than many people expect. Even if your portfolio increases by 10% one year early in retirement, you can only spend 4% of that 10% increase annually. For example, if you were spending $40K per year from a million dollar portfolio and it grew to $1,100,000, you could still only spend $44,000 safely. The reverse is true if the portfolio shrinks 10%.

      Thanks for writing.

  7. So cool Dirk. Thanks so much. I actually searched on Moshe Milevsky and probability of ruin, but the formula was outside my skill set. I figured someone must have converted to layman's terms. Sure enough I found something, but while it was in Excel it was in a paper in Adobe so drat I could not use. Can't wait to try this. You anticipated my need, and satisfied it. Thank you so much. I am going to incorporate this spreadsheet into a master workbook I have with all my retirement spreadsheets. I hope others read this as well. Thanks so much. Ann and I hope you and your wife have a great Christmas if we don't correspond before then. Brad

  8. Hi again Dirk. When I tried saving spreadsheet to my drive, and then input data the first item changed the probability of ruin and probability of survival fields to #NAME. I think the link to a table in the formula below was broken when I saved the file.


    I tried inputting data before I saved the spreadsheet, but I could not. Not sure how to get around either issue, but I am going to see whether I can work something out. Thanks so much for giving me the spreadsheet. Brad

    1. Brad, the Excel function is simply Gamma.Dist. Try deleting _xlfn. in that cell. If you still have problems, email me. It should say =GAMMA.DIST(B6,I4,I3,TRUE

    2. Missed the closing paren somehow. It should say =GAMMA.DIST(B6,I4,I3,TRUE)

    3. The GAMM.DIST function isn't available prior to Excel 2010. However, Gammadist is, and does the same thing. If you remove the dot, it should work fine.

  9. Thank you Dirk for the shout out in your post. I see from a couple of the comments that Dynamic Updating may have been interpreted as making an adjustment every time something changes. Not so.

    Making updates is part and parcel to the annual review. One computes their floor (necessary) expenditures and a ceiling (difference from floor is discretionary expenditures). A blog post may be found here .

    The spending doesn’t need to be changed during the year unless markets misbehave. Not all the portfolio is at risk of loss (unless it’s not properly diversified like 100% concentration in Enron for example) – so recognizing how much fluctuation in value one has is key to recognizing how much spending one may have during the year.

    Now, most recognize that markets don’t behave all the time. This blog post discusses how to use Monte Carlo simulators to pre-determine spending ranges as well
    based on using the percentage of simulations that fail as the adjustment signal. The first link above is similar but uses standard deviation as the signal. Both are related – could be translated into the other. I’ve discussed both depending on what kind of data a person has access to about their portfolio (the sum of all the parts).
    This blog post discusses the research that forms the foundation for the above, with links to the published papers and working papers as well.

    The main data point to update, and is best using period life tables, is how long your life expectancy is at your present age EACH year. It changes slowly over time (you can never reach your life expectancy for your PRESENT age – it is always older than you are. The simple updating of this data point helps ensure you don’t outlive your money. There is an exponential nature to all distributions for shorter and shorter periods (even the RMD method has this nature) … so our research recognized this as well to adjust for this effect (multiply your present withdrawal rate by 1 minus 1/n; where n is the number of years left in this year’s computation).

    This sounds complicated. Yet, it simply is looking at the situation each year. What you spent in prior years is no longer relevant. And what you thought you could spend is also no longer relevant. What is relevant is what is prudent to spend over the course of the coming year. Establish a floor and a ceiling, the difference between the two is discretionary. If markets misbehave and your spending at the floor level may not be supportable, then adjust a little spending downward again – if done properly this reduction is both small, not unexpected, and TEMPORARY, until markets recover on the upside of the valley (again, properly diversified portfolios … here's a great book on how portfolio design done properly adjusts sequence risk exposure ...)

    You and I have talked about this Dirk. I share for your readership. A great post – and as one with a degree in physics, I love the spherical cow reference!

  10. Thanks, Larry. Good point – dynamic updating doesn't mean constant updating. An annual review should be just fine unless something dramatic happens (a big loss or a winning lottery ticket, for example) and the review may show that you don't have much need to change. I try to avoid "tweaking."

    1. Me too! Life is so much easier not worrying about all that - and living life with friends and family instead!

  11. Dirk

    Excellent. I agree with all you are saying. What is needed is a continual reassessment of one's financial situation. As I see it, a complete understanding of the financial situation must include estimates of the inflation-adjusted after-tax amounts that are available for the retiree to spend each year for the rest of his life. Such estimates can be made considering any relevant market decline or inflation, or combinations of reasonable worst-case scenarios. Barry's suggestion of a regularly updated "mental fire drill" is spot on. I believe that the key is considering all of this in the context of computing an updated annual available spend as explained in the AP article cited below. By understanding how bad it can be in the context of annual available spend, it is then possible to decide if and to what extent a "create-a-secure-income-floor" is necessary.

    I hope you and others will read or reread the linked article and share your thoughts.

  12. Fellow blogger Ken Steiner has noted that this approach is "actuarial" only if it is used to reassess spending as conditions (such as age) change. He is correct, of course.

    In my post, I was actually referring to this quote from Milevsky's paper: "The SPV concept is borrowed from actuaries in the insurance industry, who use a similar idea to compute the distribution of the present value of mortality-contingent liabilities, such as pension annuities and life insurance policies."

    I believe Ken's point is that if you used the formula to calculate a single spending rate for all of retirement that would not be an actuarial approach.

    I agree and would note that doing so would also not qualify as thinking like a Bayesian pig.

  13. Thank you, Dirk Cotton, for your helpful insights. With regard to the Milevsky calculator, it is important that the expected rate of return should be the arithmetic real rate, as I understand his article. For example, T Rowe Price is using a 60/40 portfolio rate in their Future Path retirement program of 4.5% as I calculate it, compared with 9% shown on the spreadsheet link. Dr. Milevsky also recommends a "slightly higher" volatility rate than actual, and he uses 18%.

    1. That is my understanding, as well. You should use the real arithmetic expected mean. You may or may not choose to use the historical mean as your expected mean. For instance, you might expect lower than historical returns in the future.

      If you are referring to the link to my spreadsheet, those inputs were just randomly selected.

      Thanks for writing!