By Rob Isbitts via Iris.xyz

## The Mathematics of Loss Appear Again

At the start of 2019, The S&P 500 could have used a classic line from iconic comedian Rodney Dangerfield: “I’m OK now, but last week I was in rough shape, rough shape I tell ya!” As the chart below shows, the noted U.S. stock market gauge fell about 20% from September 20 through December 24 of last year. Then, like a phoenix rising from the ashes (too dramatic?), it has rallied 20% the last 3 months. Or has it?

Certainly, if you look at the S&P’s closing price on Christmas Eve and compare it to last Friday’s price, the increase is 20%. But one thing that investors sometimes forget is that when your investment account drops in value, you must earn more than what you lost in percentage terms to get back to even. In the case of the most recent move higher, it only took a quarter of a year. Other times, it can take a quarter of a decade, or a decade, or in one case (following the Great Depression) nearly a quarter of a century. This is what we call the mathematics of investment loss, and any investor that has concerns about steep declines in the value of what they have accumulated should make sure they understand this.

Let’s use simple figures to make sure the concept is clear. If you have \$100 and the stock market drops its value to \$80, you have lost 20%. If that \$80 then appreciates by 20%, do you have \$100 again? No, you have \$96. And that is why the chart above shows that through the drop and comeback for the S&P during the past 6 months, the end result was a loss of 4% over the period…or, an ending value of \$96 versus the \$100 you started with.