All Stock Price Drops Help You, All Stock Price Gains Hurt You

Rob Bennett developed the first retirement calculator that contains an adjustment for the valuation level that applies on the day the retirement begins. His bio is here.

You are 35 years old. You know that you need to start saving for retirement if you hope to be in good shape by the time you turn 65. Fortunately, you just received a $10,000 raise. You make a decision to invest this entire amount in a broad index fund every year for the next 30 years.

S&P 500 over the Last 30 Years

A year passes and you take a look at your portfolio statement to see where you stand. Yuck! Bad news! Stock prices have fallen 30 percent. Isn’t it just your luck to begin investing in stocks just before a significant price crash?

Another year passes and you check your results again. This time the news is much more encouraging. Stocks didn’t go down 30 percent this year. They went up 30 percent! That’s more like it. You console yourself with the philosophical reflection that it all evens out in the end. All long-term investors must endure some unluckily years for the pleasure of being able to participate in the lucky ones that also inevitably come along for those who stick at it.

Does all of that sound more or less reasonable?

It shouldn’t.

It’s 100 percent backwards. The mathematical realities are precisely the opposite of what I have described in the scenario set forth above. The first year, the one in which stock prices went down 30 percent, was the lucky one for investors. The second year, the one in which stock prices went up 30 percent, is the one which you should be cursing your bad luck. Price drops are always good news for stock investors. Price increases are always bad news.

I have an Excel spreadsheet that I used to check this (it was set up by my friend Sam, who is a lot more skilled than I am with numerical calculations). The spreadsheet lets me plug in any annualized 30-year return that I please. (I use 6.5 percent real, since that is the long-term return for U.S. stocks for as far back as we have records and I assume dividends of 2 percent.) I can then plug in any return pattern for the individual years that I please; the calculator does the job of seeing that the annualized return for the 30-year time-period will remain at 6.5 percent real. The idea is to test what sort of return patterns are good for investors, given that long-term returns of index funds are determined by the nation’s long-term economic productivity and thus “fixed” in the sense that they are not affected by the emotional mood swings of investors that cause short-term price swings in both directions.

If I presume a perfectly stable return pattern, one in which a 6.5 percent return applies for every one of the 30 years, and I contribute $10,000 to the portfolio each year, I end up with a closing balance of $929,892. Now I can check whether less stable return patterns work to my benefit or detriment, and see whether it is price increases or price drops that help me out in the long run.

If I change the return for the first year to a negative 30 percent, the calculator increases the returns for the remaining 29 year so that the 30-year annualized return is 6.5 percent real, as I stipulated. By itself, this change has no effect on the total portfolio value. A 6.5 percent annualized return produces the same end-point numbers no matter what return pattern is used to obtain it.

But there is another factor that needs to be taken into account. When prices drop in the first year of a 30-year return sequence, that lowers the price that I pay for stocks in the following years. When I make my $10,000 purchase in Year Two, I am able to obtain more stocks for the same amount of money when they are selling at a lower price. So seeing a price drop in Year One helps me! A 30 percent price drop in Year One increases the 30-Year portfolio value from $929,892 to $1,189,555.

It works just the opposite when there is a price increase. A price increase of 30 percent in Year One pulls the 30-Year portfolio value down from $929,892 to $818,350. Price drops are good news. Price gains are bad news.

The numbers of course get much bigger when the price gains or price losses continue for a number of years. The price gains we saw in the late 1990s caused the greatest loss of middle-class wealth ever seen in our nation’s history. We’ve made a bit of a comeback over the past 10 years. But we need to see much deeper losses in the years ahead if we are to have much hope of ever being able to afford decent retirements.

What if everything you thought you knew about stock investing turned out to be wrong?

Yesterday I wrote a post about Rob’s investing methodology. -George