Thursday, October 11, 2012

Statisticians Make the Worst Clients

(This post originally appeared on Dr.Wade Pfau's Retirement Researcher Blog.)

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?”

“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." I thumped the magazine three times with my index finger for emphasis. "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 went 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 are 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 that 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 — if you do, 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.

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