The Cruel Math of Investing

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Math is a beautiful, universal language. And it's a critical part of the adventure of investing, too. But math can play havoc with investors.

For instance, with even well-regarded stocks suffering big losses these days, many investors want to know when they're going to get back to even on their initial investments. As an example, check out how far the following stocks -- each of which has a top five-star rating from our Motley Fool CAPS community -- have fallen over the past year:

Company	52-Week Return
MEMC Electronic Materials (NYSE: WFR)	(73%)
Foster Wheeler (Nasdaq: FWLT)	(66%)
Vimpel Communications (NYSE: VIP)	(66%)
Valero Energy (NYSE: VLO)	(56%)
Suncor Energy (NYSE: SU)	(52%)
Fluor (NYSE: FLR)	(50%)
Noble (NYSE: NE)	(52%)

Source: Motley Fool CAPS.

You might assume that after a 50% drop in the price of a stock, you'd need a 50% gain to get back to even. Not true. Imagine that shares of Scruffy's Chicken Shack (ticker: BGAWK) fell from $80 to $40, a 50% drop. To get back to $80, the stock will need to double, gaining 100%. If it drops 80%, say, from $100 to $20, it will need to gain 400% in order to get back to $100. Even a more modest 20% drop in value will require a 25% gain. (Yes -- as the drop gets bigger, the required return for a recovery gets much bigger.)

That's the bad news.

The good math
But consider how an investment can grow. If your stock gains $100 in value, going from $100 to $200, you're sitting on a "two-bagger" and a 100% gain. But later on, if it gains $100 going from $500 to $600, that only requires a 20% gain.

When a stock grows from this price per share ...	to this price …	The gain in dollars is …	But the gain in percent is …	Making the stock a ...
$100	$200	$100	100%	Two-bagger
$200	$300	$100	50%	Three-bagger
$300	$400	$100	33%	Four-bagger
$400	$500	$100	25%	Five-bagger
$500	$600	$100	20%	Six-bagger
$1,000	$1,100	$100	10%	11-bagger
$1,500	$1,600	$100	7%	16-bagger
$3,000	$3,100	$100	3%	31-bagger

What to do
It's good to understand how the math works, but it's more important to understand that we shouldn't get hung up on the past. With investing, what really counts is the future. A stock may have fallen 60% on you, or it may have risen 200%, but either way, you just need to know how likely it is to keep growing at a good clip. If you think it will, hang on. If not, sell and move the money into a more promising investment. Don't look back -- look forward.

For more Foolishness:

• How to Snag Those 50-Baggers
• Oh No! My Stock Has Surged!
• Six Signs of a Winner