## 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, 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.