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The Correct Math to Consider During Corrections

This article was originally published on RealMoney.com at 4:00pm EST on September 2nd, 2015

“If you lose X %, you have to make Y % to get back to even.” (Where X = 20, 25, or 33%; and the corresponding Y = 25, 33, or 50%)

Have you heard someone make this argument? While it’s mathematically correct, it’s also a little misleading and—though the person making the argument may not realize it—nothing more than a scare tactic.

Yes, simply using a crude numerical example, a portfolio that goes from \$100,000 to \$80,000 has “lost 20%” of its value. To go from \$80,000 to \$100,000 requires a gain of 25% (since you divide the dollar change into the original value to find a percentage change).

You mean I have to make more than I lost just to get back to even??

Sort of…

Let’s say your sole holding is an S&P 500 index and it’s worth \$100,000 before a correction. You have 50 shares and each is worth \$2,000. The S&P 500 undergoes a correction, falling by 20%—your 50 shares now trade at \$1,600 each and are worth \$80,000. What needs to happen in order for you to “get back to even?”

The S&P needs to trade back to where it was prior to the correction. Nothing more.

At an S&P index fund value of \$2,000 per share your 50 shares will be worth \$100,000 again—plus any dividends accrued in the meantime.

Harping on the idea that I have to “make more” on the way up than I just lost on the way down doesn’t embrace mathematics, it ignores it. And it also assumes a generally bearish point of view.

Of course, if I think the market will never reach—or will take a very long time to reach—the levels from whence it came, then this may not be a worthwhile exercise. But if I am willing to acknowledge that, over time, the market tends to move higher and not lower, then I am less likely to let a half-baked scare tactic get in my way of making sound investment decisions.

The most notable, quotable, and well respected investors in the world have a generally bullish stance. They are optimists with a medium- to long-term investment horizon. I can’t name a single pessimist who has been proven right over anything more than a very short timeframe.

So if I’m bullish long-term, and we have already endured a 10% correction, am I going to batten down the hatches and reduce the odds of recapturing what I’ve just “lost?” Certainly, that’s what my emotions and the “You’ll never get back to even now!” headlines are telling me—but history and discipline tell me just the opposite.

I’d prefer to side with the optimists. They’re much richer than the pessimists.