Tuesday, October 9, 2012

Dirk Cotton: Statisticians Make the Worst Clients

This is a special guest blog post from Dirk Cotton, a retired executive of America Online (AOL) who currently runs a personal financial planning practice, JDC Planning, LLC, in Chapel Hill, NC. He blogs about retirement finances at TheRetirementCafe.blogspot.com.

Recognizing that the median savings for a family approaching retirement age is less than $100,000 and that half of those households have no savings at all, his writing and practice focus on retirement finances for the “unwealthy”, which make up the vast majority of the middle class.

Dirk is the author of two books, Retiring When Your 401(k) Fails and Locally Groan, a book about growing up in the South. He holds a bachelor's degree in computer science from the University of Kentucky, an MBA from Marymount University, and a certificate for financial planning from Boston University.

This is only the second guest post in the history of this blog, and I hope it will make you think some more about the 4% rule.

Statisticians Make the Worst Clients

A new client came to my office a few weeks ago, a statistics professor from the local university who had been referred to me by a mutual friend.

After a bit of small talk about our buddy, I asked how I could help.

“I have a million dollars in my 401(k) and I’m about to retire,” he informed me. “How much of that can I spend each year?”

“Well. . .”, I told him, “we financial planners like the Safe Withdrawal Rate Strategy. Invest your savings in a diversified portfolio of stocks and bonds and you can withdraw 4.5%, or $45,000 a year in your case, increased by the rate of inflation every year. Do that and your portfolio has a 95% chance of surviving for thirty years!”

He wrinkled his brow a bit.  “95%? What’s safe about that?”

Taken aback, I responded, “95% sounds pretty safe to me!”

“You are aware that the bankruptcy rate for Americans aged 65 and over is about 4.3 per thousand?”

“Well, yes. . .”, I stammered, “I mean, no. . .”

“That’s an average success rate of 99.6% for all retirement-aged Americans. 95% would be 12 times riskier than the average for my age.”

“Well, let me explain how it works,” I insisted.

I described the Trinity study and several since, about how they used rolling 10-, 20- and 30-year periods of market returns and how they keep subtracting a fixed withdrawal rate every year until they either reached the end of the 30-year cycle or depleted the portfolio.
He wasn’t persuaded.

“So, you’re telling me that these are the probabilities of success for retirees who would just keep spending the same amount every year, even when they were obviously approaching financial ruin? What does that have to do with me? I'd stop spending if I thought I was going broke. Wouldn’t you?”

“Well, of course I would, but how does that matter?” I asked.

“That’s referred to as the unrepresentative sample fallacy,” he explained. “It’s like trying to infer the average height of Americans from the heights of NBA basketball players. You’re trying to infer a portfolio survival rate for the general population of retirees from a sample of people who would do nothing to avoid going bankrupt.”

I was beginning to think I didn't want any more statisticians for clients. Certainly not pedantic ones.

“Besides,” he added, “these study results clearly show that you can withdraw 4.5% of your portfolio value when you retire, then you can increase the withdrawal to about 6% of whatever savings you have left with 20 more years of retirement, and then increase withdrawals slowly to about 10% of whatever savings you have left at ten years. You can’t keep taking percentages of your original portfolio balance — finance doesn’t care how much money you used to have."

"Yes, but. . ." I countered.

 "You seem to think the withdrawal rates are somehow locked in on the day you retire. Why do you think those studies imply that I could withdraw the same amount every year, even if my portfolio drops in a bear market?”

“Because everyone says so!”

Finally, I had him.

“Here! Right here in Money magazine a few years ago. Walter Updegrave said it. He said it often, as have a lot of other people.”

Withdraw no more than 4% of your portfolio the first year of retirement and then increase that amount for inflation each year and there will be roughly a 90% chance that your money will last at least 30 years.”

“So, now it’s 90%? That’s 24 times worse than average. But, regardless, Walter is wrong,” he insisted.

I had to admit that ole’ Walt had softened that statement a great deal since all those retirees lost their shorts in the 2008 market crash. Even Scott Burns, who wrote column after column praising SWR for the Dallas Star now calls that rule of thumb a “rule of dumb”.

I decided to keep that to myself for now.

“You realize the numbers predicted by your SWR studies are a priori probabilities, right?”

The guy was really starting to get on my nerves.

“A priority, B priority. I never paid much attention to that stuff,” I replied.

“No, it’s a priori, not priority. It means those are the probabilities of success before retirement starts. After retirement begins and your portfolio goes up or down because you spend part of it or the stock market goes up or down, those probabilities change.

You have a new conditional probability of success depending on how much longer your retirement will last and how much money you have left. If you want to keep your 95% probability of success throughout retirement, you'll have to spend less when your savings decline and you can spend more when they increase.”

“So?” I asserted with my best Dick Cheney false bravado.

 “So, that means you can’t predict how much money you will be able to spend in the future, because you can’t predict the balance of your portfolio. And isn’t that what you were trying to do all along? Withdraw a steady, predictable amount from a volatile portfolio?”

“Think of it this way,” he said as he pushed back his chair and stood up. “Let’s say 10,000 airplanes have left from San Francisco flying to Hawaii in the last several decades and 99% have successfully reached the islands. Every plane that takes off on that flight, based on historical data, has a 99% chance of success, right?”

“Sure”, I answered.

“So, if you're on that flight and a wing falls off over the Pacific Ocean and you’re barreling into the sea, you should take very little comfort from the fact that your odds of reaching Honolulu were once 99%. You are now pretty firmly locked into the 1%.”

As he said this, he took his coat and headed for the door.

"And if you lost over half your portfolio in the 2008 market crash, you can't just keep spending like you used to have a lot more money — say hello to your new neighbors, the 5%."

“Wait!” I yelled. “We didn’t discuss your retirement plans!”

I’ve tried to reach him several times since to reschedule, but the guy won’t return my calls.

Maybe it was something I said.


  1. Of course he made great points as an outsider that insiders don't think about. But I think Wade should have compared the safe withdrawal rate to annuities or defined benefit plans. As US retirement plans change(d), using a withdrawal rate to compare to the pension benefit allows people to better evaluate and plan for retirement.

    But I'd be curious how many people use the safe withdrawal rate in retirement for yearly withdrawals versus just using it to plan for retirement.

  2. Ha ha ha, good story! Seems like statisticians are good candidates for a risk-free income floor for essential expenses, the kind you can't quit spending!

  3. Dirk Cotton has found a clever way to criticize the SWR. Cheers!

  4. The alternative that I believe Wade advocates is to pay a HUGE additional cost, in terms of reduced effective withdrawals, to shore up the remining 5% - be it through simply lowering SWR, using VERY costly annuities, or dooming us to work until we're 80. Regardless of however you go about it, to go from 95% to approaching 100% will require an exponential order cost, not a linear one. "True" safe withdrawal isn't worth the cost, IMO. As Wade even admits in this article, the typical person hasn't the portfolio to support the admittedly moderately risky standard 4% SWR, let alone something more restrictive.

    So, by all means rethink it. Just realize the alternatives are equally unapealling, just for different reasons.

  5. Also, I would have asked this statistican whether or not he paid social security, and if he is aware that hundreds of thousands of Americans live on social security alone without filing bankruptcy. I would have asked him if he had a pension too. A smart guy like that stands a good chance to have one. That'd be two floors that won't be exhausted.

  6. Anon, I was by no means suggesting that the answer is to choose a lower SWR probability of ruin. On the contrary, I don't believe that trying to make fixed withdrawals from a volatile portfolio of stocks and bonds makes economic sense, or that SWR models reality.

    I personally believe a retiree should establish a floor to cover a basic standard of living from TIPs or annuities. After that, invest in stocks if you so desire.

    Granted, with interest rates so low at present, it is hard to understand how anyone can save enough to fund retirement. In fact, almost no one does. The median 401(k) balance for workers approaching retirement recently was $78,000, leaving the stock investment issue moot for the vast majority of the middle class. This is my bigger concern. Portfolio survivability is a rich man's problem.

    As for Social Security, yes, the statistician was aware that he would receive retirement benefits. (I know this because I made him up!) Social Security does provide a floor (at least as long as conservatives lack the votes to end it), but as this recent article in the NYT explains, it isn't a very pretty floor. http://nyti.ms/RloVb9

    1. Dirk,

      That's an interesting NYT article.


  7. Thanks for the though-provoking article. Maybe I'm missing something, but the 4.3 per 1000 bankruptcy rate is an annual rate, while the 5% portfolio success rate is over 30 years, so saying the second rate is 12 times the first doesn't make sense. If you convert both rates to the same time period, the portfolio failure rate is less than half of the bankruptcy rate, negating the statistician's first point.

    1. Thanks Ken,

      Right. Portfolio failures would tend to occur in clumps as well after a year with bad market returns. Of course, so would bankruptcies, probably.

    2. I apologize for that confusion-- I'm unaccustomed to writing rigorous humor!

      If you follow the link in my story, you will see that the bankruptcy rate is 2.7 per thousand for ages 65-74, 1.6 per thousand for ages 75-84, and negligible at ages 85+, for a cumulative total of 43 per thousand over thirty years.

      And correct, that isn't a factor of 12, it's 2. Depending on which study you look at, the "safe" withdrawal rates are 90% or 95%, which is a failure rate of 50 to 100 per thousand. My point being that a "safe" withdrawal strategy should be safer than the baseline failure rate for all retirement funding strategies (or lack thereof). Wade, check my math-- it's late here.

      But I think this misses the larger point. This model doesn't predict the future. It was valuable to help us understand that portfolio volatility impacts safe withdrawal rates. But it predicts that 5 or 10 of every 100 people who execute this strategy will continue to execute it even in the face of obvious pending financial ruin and go broke.

      None of us believes that. We know that these retirees will abandon the strategy when they believe their portfolio is failing and they will suffer reduced income but likely avoid ruin (or bankruptcy). The model doesn't predict that.

      The interpretation of the studies suggesting that a retiree can maintain the same withdrawal amount for thirty years regardless of market performance is also incorrect.

      Like the SIR model for infections, it is informative but not predictive.

  8. I'm impressed that Dirk spelled "pedantic" correctly.John Galvin

  9. Filing for bankruptcy will ruin your credit listing – A declaration of bankruptcy will remain on your credit score from six to ten years. This will make it difficult for you to get new loan approvals. Hence, it is always better to pay off your debt rather than go for bankruptcy filing.