The term comes from a story about a farmer who talks to a physicist about his farm's underproduction of milk and asks if the physicist might be able to offer some advice. The physicist goes away to perform some calculations, but soon returns with an answer.

"I have a solution for your problem," he explains to the farmer, "but it only works for spherical cows in a vacuum."

We encounter a lot of Spherical Cows in retirement finance, huge oversimplifications that make the math easier.

For one, we generally assume that market returns are "normally distributed" even though we have tons of evidence that they are not. If they were normally distributed, we wouldn't see nearly as many market crashes as we do. Often we assume they are log-normally distributed, meaning the logarithms of the returns are normally distributed, but they aren't really that, either.

According to Professors Fama and French, "Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions."

They go on to say that longer periods, like years, conform more to a normal distribution. The 23% drop in the Dow of October 19th, 1987 was something that probably never could have happened in a single day under a normal distribution of returns, but the 37% year-long drop in 2008 was a 2.5 sigma event that might happen once every 80 years.

**Their advice to investors is to expect more extreme good and bad returns than a normal distribution would seem to indicate.**So, assuming

*annual*returns are normally distributed works fairly well, but not so with daily or monthly returns.

One of my favorite Spherical Cows is the one used to calculate sustainable withdrawal rates. SWR models assume that a mythical investor will continue to spend the same amount of money each year from savings, even after it becomes obvious that he or she is about to deplete their retirement savings. The models take a percentage, say 4%, of initial portfolio value and subtract that fixed dollar amount ($4,000 from a $100,000 portfolio in this case) from the portfolio balance every year, counting the number of years before the portfolio is depleted.

This assumption makes it far easier to build a spreadsheet than would modeling how a real investor might behave with their spending as their savings grow or dwindle.

I don't think most retirees would behave that way. Would you keep spending the same amount if you saw your savings vaporizing before your eyes? I would expect them to spend a little more when their portfolio grows and a little less when it shrinks. Spending 4% of remaining savings each year instead of a flat $4,000 a year might accomplish that, for example.

In an extreme case, say retirement savings shrink by 50% in the first decade after retiring (or, conversely,

*grow*50%), I suspect a lot of retirees would not only reduce their spending, but abandon the SWR strategy and look for a new adviser. Of course, by then, the retiree has locked in a lower standard of living for the remainder of her life. The life annuity she took a pass on ten years earlier would start to look pretty sweet in retrospect. Despite what you may have read, a shrunken $50,000 portfolio is not assured of doubling in size because the retiree

*used*to have $100,000.

Every retiree will behave differently, of course, and that would be really hard to implement in a spreadsheet or any other software, so we go with the constant dollar spending models because the oversimplified model makes the math a whole lot easier.

Many financial writers argue that no one really "does it that way", meaning everyone adjusts spending based on their remaining portfolio balance instead of spending a flat amount, but I have two responses to that. If no one does it that way, then everyone in the financial press should stop saying that you

*can*do it that way.

And second, the SWR models predict outcomes for you only if you

*do*"do it that way". (Operations Research guys say that a model is predictive only to the extent that its policies are followed.) The SWR results

*aren't*predictive if you do something else, like adjust spending to portfolio value changes – which apparently is what everyone is actually doing.

(In simpler terms, you can't predict the average height of American men by measuring the height of players in the NBA. That's called the

*unrepresentative sample fallacy*. Likewise, you can't predict portfolio failure rates for people who care about their savings balance from the failure rates of mythical retirees who ignore pending ruin.)

SWR predictions work, but only for spherical cows in a vacuum, or retirees who are oblivious to their current savings balance.

Perhaps the biggest assumption we make to simplify the math is that future stock market returns will look like historical returns.

The argument that they will look similar is an inductive argument that is not strong. Inductive arguments can't prove something is true, they can only argue that something is

*probably*true. They are also defeasible, meaning that future information can prove the conclusion wrong. As Nassem Taleb would say, it was accepted as fact that all swans were white until someone found a black one. Future market returns will mirror past market returns until they don't.

It is interesting that some authors choose various periods of U.S. historical market data upon which to base their studies instead of using it all. They say things like, "We used historical data for the post-World War II era, because market data prior to that period is not representative of the current era." If one past period of history was not representative of this one, how do we know that the author's chosen data is representative of the

*future*era, which is, after all, the one we need to know about?

It does make the math easier, though, when we toss in that little assumption.

On the other hand, there are many strong arguments that the future won't look like the past. Wade Pfau showed that 4% sustainable withdrawals only worked in 4 of 17 developed market nations (Canada, Sweden, Denmark and the U.S., in that order), lending credence to the argument that high equity returns in the 20th Century may be an anomaly of American history not to be repeated. Wade also recently argued effectively that future safe spending rates will be closer to 3% than 4% because the current risk-free rate in the U.S. is so low. That means that both stock and bond returns will be lower in the future than they have been.

Is it safe to assume that the worst thirty-year period of stock returns in our limited history is the worst that will ever happen? Well, no, because a black swan could reset the bottom. The bottom was reset in October 1929, for example.

The 30-year period beginning in 1966 was rough on retirees, but 2007 through 2009 were bad years and their returns are currently showing up only at the end of 30-year periods, like 1979 through 2008. With sequence of returns risk, however, we know that the real damage from these years will show up in studies that begin, not end, around 2008. That will be in 2037 and, again, that's the period recent retirees should wonder about.

But it certainly makes the math easier when we assume that we have already seen the worst.

I'm not saying that the work based on these Spherical Cows is without value, because sometimes having a questionable forecast is better than having none. Sometimes, it's the best we can do, given the shortage of reliable fortune tellers. As a friend of mine is fond of saying, "Bad breath is better than no breath at all."

But I also think it's important to understand the strength of the arguments and the assumptions upon which our plans are based. Assuming you're safe because your portfolio would have survived the worst bear market in the past 50 years is a big assumption.