Fuzzy Retirement Math

When I started this blog I planned to occasionally point out good articles and posts as well as criticize the bad ones.  So far, I’ve done it so infrequently it can’t even be called occasional.  There’s just so much bad stuff out there.

But last week SmartMoney had a pretty good item on the fuzzy math of retirement.  The math in question is basic stuff: how much you need to save, Blackboard Lecturing Crop how much you can expect to draw from your savings each year in retirement, and so on.  But here I mean basic in the sense of being fundamental, not in the sense of being simple or easy.

Nevertheless, as the SmartMoney piece points out, until recently a person visiting their friendly neighborhood financial planner or broker might have gotten the impression that these were simple questions with simple answers.  Your investments will appreciate X%. You can safely withdraw Y% from your savings each year.  When all was going well and the market was (mostly) going up, from where those numbers came and how useful they were didn’t seem like important questions.

Then the Panic of ‘08 set in, and all of a sudden those scientific seeming percentages didn’t seem so accurate after all.

But now that the steep decline in stocks has blown a hole through many retirement portfolios, even the experts who design these models are acknowledging that they have serious limitations. Indeed, some insiders say the number crunching is just an educated guess.

Of course they are educated guesses. Highly educated and thoughtful, based on the best research, but still merely guesses. Any insider who doesn’t say that those percentages are just educated guesses is either lying or doesn’t really understand it himself. 

Much of retirement planning turns on the single issue of expected investment returns.  Plug a rate of return into a spreadsheet, and presto, you can calculate how much money you will have twenty years from now and how much of it you can spend on an on-going basis.  A lot of people built their financial lives around a return number given to them by a professional who at least sounded as if he knew what he was talking about.  And then it was all derailed when actual returns were far, far less than anticipated.

There’s a lot of reevaluating of retirement planning going on right now, and that can only be a good thing.  But I worry that many people are coming to the wrong conclusion about what went wrong.

The problem was probably not that the return number provided by the earnest financial planner was faulty.  In fact, it was probably pretty good, backed up by sound research and reasoning.  The problem was that the person saving for retirement, and possibly that planner too, didn’t understand the nature of the number.

Let’s imagine that the most scientific estimate for long-term stock market returns was 10%.  Most people understand that that does not mean that next year the market will be up 10%, or even that it will be up in the short run at all.  Yet somehow many people manage to keep in their head the conflicting idea that over a long period, say 20 years, that 10% return is more or less assured.  (And if it does not work out that way, then the 10% estimate was wrong.)

In fact, although stringing together 20 years of returns does give some reduction in risk, the effect is easily exaggerated.  Let’s say that our 10% return estimate is paired with a volatility of 12.5%.  (That’s also a reasonable number.  Both are roughly what the S&P has done since 1960.)  Given those parameters, the chances of the market being up between 8% and 12% in any given year is 12.7%, or slightly better than one in eight.  However, over 20 years, the chances of the average annual return being between 8% and 12% is 52.5%, or better than one in two.

You might not find that a 50/50 shot at actually getting within 2% of the estimate after 20 years is reassuring.  But if you do, keep in mind that over a long period of time such as 20 years a small-sounding difference in average annual returns can result in a big difference in wealth.  Reconsider the above numbers in terms of dollars rather than percentages.  If you start with $100,000, after a year you have a 12.7% chance of having between $108,000 and $112,000.  After 20 years, you have a 52.5% chance of having between $466,096 and $964,629.  That’s a pretty wide range and one that is likely to include some meaningful differences in retirement lifestyle.  And you’ve still got about a one in four chance of doing even worse.

The point is that although these numbers are a necessary part of any retirement plan, they are themselves an estimate, not a plan.  You cannot plan on making a certain return from a risky asset such as stocks over 20 years any more than you can plan a certain number of auto insurance claims over the next 20 years.  The numbers used by planners and given to consumers will always be fuzzy.  That’s not the planner’s fault.  It’s the nature of the beast.  What is the planner’s fault is failing to explain this.

No Comments

  • By IndependentOperator, May 6, 2009 @ 1:34 pm

    Good article. But it’s even worse than you describe, because after that variability in return, you have to deduct inflation and tax costs (and transaction costs, if you want to be picky). The truth is, even if they hit their “target” return after 20 years, they’re without a doubt getting far less than that.

  • By SJ, May 6, 2009 @ 3:04 pm

    I think more people need to take stats or probability.

    Do any of those models include variance or higher order moments?

    Also I thought that was the point of pulling out most your money out of stocks during retirement; more predictable models can be used…

  • By Frank Curmudgeon, May 6, 2009 @ 4:12 pm

    SJ: I think stats should be required in all high schools. It really bugs me that maybe 5% of BMA readers will understand this next sentence: No, those numbers I used assumed only normal distributions, IID annual returns, no skew or kurtosis, etc.

  • By ryan, May 6, 2009 @ 4:49 pm

    Good thing there’s wikipedia for a quick refresher on “kurtosis.”

  • By Rob Bennett, May 6, 2009 @ 5:09 pm

    I think it would be fair for me to describe myself as the world’s greatest authority on bad retirement planning numbers, Frank. My take is that your words above greatly, greatly, greatly underestimate the problem.

    I put a post to a Motley Fool board in May 2002 showing that the studies that we all use to plan our retirements (these are called “Safe Withdrawal Rate” studies) get the numbers wildly wrong (they fail to consider the valuation level that applies on the day the retirement begins — this just happens to be the single most important factor affecting retirement safety). The historical stock-return data shows that we are going to see MILLIONS of busted retirements in days to come because of the analytical errors in these studies.

    I have found it gratifying to hear a good number of big-name experts agree with the points I made. William Bernstein said that anyone giving thought to using one of today’s retirement studies to plan a retirement would be well advised to “FuhGedDaBouDit!” Ed Easterling pointed out that many retirees will be serving as greeters at WalMart because of the inability of most investing “experts” to get the numbers right. Larry Swedroe concluded that today’s retirement studies are “Garbage-In, Garbage-Out” research. Scott Burns reported that the studies were two full percentage points off in their identification of the SWR.

    So prompt action was taken to fix the studies and to get the correct information out to people, right?

    Not right. Not one of the studies has been corrected in seven years. Scott Burns told us why. He said that the media has not reported on the errors in the studies because “it is information that most people don’t want to hear.” There’s a ton of evidence lending support to his claim in the Post Archives of The Great Safe Withdrawal Rate Debate (a series of internet discussions on the SWR matter and related topics).

    A large number of today’s middle-class investors DO NOT WANT to hear accurate retirement planning information. They want to hear more of the fairy tales that were used to sell stocks when they were priced at levels at which they could not provide a good long-term return.

    The research needed to generate better retirement planning advice already exists. Lots of experts would be willing to share it with us if the penalties for doing so were not as great as they are today. But I believe that middle-class investors are going to need to make the first move. We will get realistic guidance when we are willing to tolerate realistic guidance.

    There have been some positive signs since the price crash. But it does not appear to me today that we are yet willing to tolerate hearing too much of the truth about how stock investing works in the real world. My personal belief is that it is going to take one more big stock crash to get us there.


  • By Rick Francis, May 6, 2009 @ 5:17 pm

    >Then the Panic of ‘08 set in, and all of a >sudden those scientific seeming percentages >didn’t seem so accurate after all.

    I think the key phrase here is _seem_- the numbers quoted are 20 year averages. Do we REALLY have enough information to believe these averages have been invalidated?

    Unless you sell and lock in a real loss, the paper losses could disappear in a few years, and the averages may again fall within the historical averages.

    Of course it could also get worse, but I see no reason to believe that there won’t eventually be a market recovery.

    SJ, even if they included a variance, and gave a full statistics course to describe it very well there is still a fundamental problem:

    Is it reasonable to plan for a highly unlikely worst case scenario?

    I would argue that it isn’t- because the advice for such an extreme scenario will also be extreme. The extreme advice is also likely to be very bad advice in most cases.

    For example: Because the stock market could crash and not recover for many years, you should put all of your savings in to FDIC insured CDs and save 50% or more of your salary for at least 40 years. That would work as long as the CDs kept pace with inflation, but is it good advice?


  • By SJ, May 6, 2009 @ 5:26 pm

    I admit I understood the first half and not what skew and kurtosis meant; I never knew the 3rd/4th moments had names and I will argue those are redundant statements =)

    So if walmart will have a lot of cheap labor… I should increase my holdings in walmart… Aweesome.

    It’s great when people refuse to learn =)

  • By ryan, May 6, 2009 @ 5:56 pm

    I’m 29. When I’m, oh, I don’t know 70, and I run the numbers, what’s your best guess of an annual return I’ll have seen?

    6%? I can live with that.

  • By IndependentOperator, May 6, 2009 @ 6:11 pm


    How about -5%?

    I think the whole point here is that everyone assumes guaranteed returns in the stock market over the long term. People don’t even consider the possibility that you could end up losing money. Why is that not even an option that’s on the table? Is that realistic? Do you think people’s (140-age)% allocations in stock would change if it *were* a possibility being considered?

    The attitude even in your comment is that worst case, you’ll get 6% return. I think that’s an interesting and unfortunately common assumption. I’m no stock expert, but if a 6+% return were guaranteed, wouldn’t the price of those assets inflate to the point where it was no longer true?

  • By Frank Curmudgeon, May 6, 2009 @ 6:19 pm

    Ryan: Sorry you had to look it up. That’s two minutes of your life you’ll never get back.

    Rob: I guess it’s good to be world’s greatest authority on something, but I’m not sure you made the best choice. ;)

    I think you and I have some (mildly esoteric) disagreements on how to calculate the expected return for the stock market, but I hope we can agree on the importance of explaining to end users what an expected return is. Replacing a bad number with a better one isn’t enough. And, although I am obviously much less knowledgable than you about safe withdrawal rates, it seems to me that calling it “safe” is misleading. Prudent withdrawal rate?

    Rick Francis: I used the word “seem” thoughtfully. If your expected return for the market is 10%, and over twenty years the actual average you get is 5%, that says nothing about how good your estimate was. It could have been dead on, but you got unlucky with returns in those particular twenty years.

  • By Rob Bennett, May 6, 2009 @ 6:28 pm

    I’m 29. When I’m, oh, I don’t know 70, and I run the numbers, what’s your best guess of an annual return I’ll have seen? 6%? I can live with that.

    That’s a good guess for the return you’ll see in 40 years, ryan.

    And it’s of course fine for all concerned if you are happy with those numbers.

    That doesn’t change the reality that most of those who were planning retirements at the price levels that applied before the crash were using bad numbers to do so. It’s better to use no numbers at all than to use bad numbers. If we are going to use numbers to provide retirement planning guidance, we should use accurate numbers.

    In no other field of human endeavor would the claim that using accurate numbers is a good idea be a “controversial” claim. People should be thinking why it is different in investing and what that means about what we all need to know to invest effectively.


  • By ryan, May 6, 2009 @ 6:45 pm

    I actually do belive that no real returns are a possibility, albeit very, very unlikely. Regarding an average of -5% over 40 years, I’m not quite sure the mechanics of that. Would one keep losing a smaller chunk every year, inverse-compounding?

    No matter, though. In addition to healthy stock investing, our life is structured to have the house paid for soon, and from there I’ll build up significant cash reserves that could provide a modest subsistence off the interest in old age. Maybe that would be $1.5-2M. We’ll see.

    On the other hand, if that were to happen; I’m not sure any cash I had would make much difference. Far more valuable, I think in that scenario, would be a well protected isolated compound somewhere out west with the soil and sun to grow our own food, a well stocked grain cellar, a clean source of drinking water, and lots and lots of high powered ammunition.

  • By Rob Bennett, May 6, 2009 @ 6:48 pm

    I guess it’s good to be world’s greatest authority on something, but I’m not sure you made the best choice.

    I didn’t choose the quick path to fame and fortune, that much would be more than fair to say. The other side of the story is that it has been an amazing learning experience.

    although I am obviously much less knowledgable than you about safe withdrawal rates,

    I don’t posses any special knowledge, Frank. I’m just a stubborn kind of fellow who refuses to give up on what his common sense and the historical data tell him regardless of how many bricks get thrown at his head as his “reward” for doing so.

    it seems to me that calling it “safe” is misleading. Prudent withdrawal rate?

    I don’t think that’s right, Frank. Those would be different calculations. The SAFE withdrawal rate as defined in the literature really is “safe” by any reasonable assessment. The idea is to look at the historical data and identify the Worst-Case Scenario. It is a highly conservative number. If it were calculated properly, it really would be safe to use this number as your take-out number. (It would also be possible to calculate a prudent withdrawal rate — that would be a somewhat higher number.)

    The problem is that most of the existing studies use a methodology that caused a high-risk number to be identified as “safe.” At the top of the bubble, a retirement plan using a 4 percent withdrawal had a 30 percent chance of surviving 30 years, according to the historical data. Millions of retirees relied on studies assuring them that this withdrawal was “safe.” No reasonable person would say that a retirement plan that has a one in three chance of working out is “safe.”

    The reason why this is not esoteric is that it tells us something important about ALL investing advice. This sort of thing doesn’t just happen in retirement planning. The dominant consideration in MOST investing “research” is marketing. The idea is to tell people what they want to hear, not what they need to hear. So the investing advice you hear during a huge bull market is very, very different from what you hear during a huge bear market.

    The “research” is always telling us to do the opposite of what works. The “research” spins things wildly in favor of owning stocks when stocks offer a horrible long-term value proposition. And it spins things wildly against ownership of stocks when stocks offer an amazing long-term value proposition. The result is that most of us over the course of a lifetime earn returns far less than what would be available to us if the research reported the realities minus the bull or bear market spin.

    We all delay our retirements by a good number of years by putting so many pressures on the “researchers” to tailor their “findings” to satisfy our emotional desires to believe that stock investing works differently than how the historical data shows it has always worked in the real world.

    Can we change this? I think so. But we are talking about a big change. It won’t happen overnight. The change happens when investing guidance becomes objective in nature and when marketing considerations are no longer the primary drivers.


  • By JakeBrakeman, May 7, 2009 @ 9:41 am

    RE: Rob Bennett, May 6, 2009 @ 6:48 pm

    Maybe you are also “expert” at maximizing the use of “quotes” as a way to “disparage” the work of “others” whose “ideas” may not exactly “Agree” with those of your “thinking”…

    Here is a “tip” — just using more words does NOT make you easier to “believe”. If you have some “bone” to pick, spit it out, in direct language. Just “whining” about how “everyone” else has it “wrong” since 1972, and how you posted to some defunct board back in 1998 and no one “listened” is a good way to get quickly branded as a “crank”.

  • By Rob Bennett, May 7, 2009 @ 10:17 am

    If you have some “bone” to pick, spit it out, in direct language.

    I believe that we should report retirement planning numbers accurately, Jake. That’s all there is to it.

    The Old School SWR studies do not include an adjustment for the valuations level that applies on the day the retirement begins. The New School SWR studies (I am the founder of the New School) do.

    Do you think that valuations affect long-term returns?

    Or do you not?

    Your answer to that question determines whether you are Old School or New School. Either valuations affect long-term returns or they do not. If they do, all of the investing guidance that ignores this factor (that’s 90 percent of what has been provided to us over the past 30 years) is wrong.

    I believe that we need to have a national debate on whether the idea of ignoring valuations makes sense or not. My take is that it does not make sense to ignore valuations.


  • By Frank Curmudgeon, May 7, 2009 @ 10:18 am

    If Rob’s comments upset you, don’t read them. His name appears in bold at the top.

  • By Jeff, May 7, 2009 @ 10:38 am

    I agree that it’s best to not read the comments from trolls, but this one is awfully persistent so you can plan on not reading him for a very long time.

  • By JWR, May 7, 2009 @ 10:56 am

    Guys, you’re being trolled. Try googling “Rob Bennett” “financial advisor” or go to http://www.s152957355.onlinehome.us/cgi-bin/yabb2/YaBB.pl?board=HOCO

  • By Rob Bennett, May 7, 2009 @ 11:17 am

    The name of the fellow who does the research that serves as the engine for the calculators at my site (and also at his site) is John Walter Russell. His site is http://www.Early-Retirement-Planning-Insights. He posts at numerous discussion boards as “JWR1945″ and is one of the most beloved and respected posters in the history of the Retire Early and Indexing discussion-board communities.

    John happened to see this thread and noted that someone else is posting as “JWR.” This is a tactic that has been used at numerous boards and blogs by a group that is led by the author of one of the Old School SWR studies. I linked to this thread at the “Today’s Passion” feature at my site and John put a post to my blog letting people know that the comment that appears here under the name “JWR” was not put up by him.

    I thought that the best thing to do was to let people here know that that comment was not put forward by the fellow who is one of the most respected and beloved posters in the Retire Early and Indexing communities.

    I also of course take exception to the “troll” comment by Jeff. Thousands of my fellow community members have expressed great interest in learning more about the realities of stock investing. There are several articles at my site that contain numerous snippets of comments by my fellow community members expressing great interest and expressing a desire that people interested in the topic be permitted to engage in civil and reasoned discussions.

    Let’s all say a prayer that things are beginning to turn in a more positive direction. I believe that that’s the case (although it would be fair to say that the change cannot happen soon enough for my tastes.


  • By JWR, May 7, 2009 @ 11:29 am


    You assert that only one person is allowed to use my initials? Why is it the other guy? That’s stupid and arrogant.

    Let me see – you’re saying that the other JWR read this thread, then posted something to YOUR blog about it and you are reporting it here. Strange and contorted.

    Don’t worry, though. I’ve been a lurker at this site for some time, but I’m gone now. I’ve seen your tedious trolling destroy too many other sites. It’s all yours, friend.

  • By Jeff, May 7, 2009 @ 11:43 am

    “John happened to see this thread and noted that someone else is posting as “JWR.” ”

    Don’t you think you should have waited more than 20 minutes before claiming that he “happened” to see this specific thread on this specific site and reported it to you elsewhere? No wonder some people think he’s just one of your sock puppets. Things don’t just “happen” to happen that quickly.

  • By John1945, May 7, 2009 @ 12:56 pm

    Going back to the original post, I think that part of the problem is psychological and an unrealistic expectation of certitude. Financial advisers produce a plan for someone that is based upon statistically likely earnings and risk tolerance, then the person just takes it and assumes something like “I’ll have this much money (adjusted for inflation) to spend every year for the next 30 years or so”. Sort of like an inflation-adjusted pension from an entity that is guaranteed not to fail. (The closest to that might be the federal government.)

    Was it Bernstein who commented that estimating a withdrawal rate in retirement that is supposedly 95% safe for 40 years is equivalent to assuming that our financial and political systems are stable over periods of 800 years (= 40/.05)?

    There are certainly problems with that analogy, but it does make a point. People need to recognize that during retirement they should expect to do what they’ve done for most of their lives. Income and needs vary, so you have to be prudent, keep a reserve,adapt your budget as necessary, and don’t worry about risk minimization to the point that you don’t enjoy the ride.

  • By John Walter Russell, May 7, 2009 @ 2:09 pm

    There is one area in which Rob and I disagree. I favor censorship on discussion boards. Rob is willing to tolerate almost anything. I prefer heavy censorship.

  • By critter, May 7, 2009 @ 2:19 pm

    Rob Bennett explains his economic plans on his blog.


  • By Frank Curmudgeon, May 7, 2009 @ 3:40 pm

    I am begining to think that half the commenters on my blog are actually Rob in one of several fake identities, most of which are designed to build sympathy for him by calling him a troll or crank.

    Rob’s views are controversial, as I think he’d agree, but those that disagree with him are not going to get anywhere by dismissively calling him names. If you disagree, say why. You can do it here, on your own blog, or even on Rob’s.

  • By Jeff, May 7, 2009 @ 3:54 pm

    “I am begining to think that half the commenters on my blog are actually Rob in one of several fake identities”

    No argument there. He’s admitted to using multiple names in the past.

    “or even on Rob’s.”

    Actually you can’t disagree on Rob’s blog. At least not if you want your message to be posted.

  • By John1945, May 7, 2009 @ 5:54 pm

    I haven’t commented on Rob’s views, and that’s not because I agree with him. It’s noise and not worth bothering with.

    And, by the way, Jeff’s right: Rob doesn’t let anyone post comments on his blog that disagree with him. But why bother with the guy?

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