# How About That 20%… er… 16% Rally In The S&P 500?

### 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 marketdrops 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.This is less of an issue when the entire thing happens in 6 months. It’s when a true bear market hits, and instead of the recovery starting the second the decline ends, there is a period in between where stock prices do not move sustainably in either direction. Frankly, with the S&P 500 still below its peak from 14 months ago, it is a growing possibility that this is what is happening now. But it is too early in the bear cycle to conclude that.Related: Why The Next Recession Will Be DifferentThe other aspect of this is that the mathematics of loss are certainly not confined to the S&P 500. If you own a portfolio of stocks, and a few of them “blew up” on you (as tends to happen more often these days…thanks algorithmic trading!), you have a decision to make about your tolerance for loss and patience waiting for the recovery of each one of those. And naturally, there is also a chance the recovery doesn’t happen at all, as some prominent American businesses have found out over the years.So, the 20% rally in 3 months is certainly a relief for many investors, who were probably frozen in thought as the new year started, unless they have an ongoing risk-management approach (which everyone should!). But whether it’s a quickie like the S&P 500 experienced recently, or a true bear market in the future, understanding how the mathematics of loss work is another important part of the perspective for any serious investor.After all, we have seen two S&P 500 declines of 50% each in the past 19 years. Each of those required a 100% gain (not 50%) just to get back to even.Follow Rob Isbitts on Twitter @RobIsbittsListen to Rob’s latest podcast on TheStreet.com