This information has been partially covered in other posts, but I think it bears repeating – mostly because your intuition can trick you sometimes with the stock market.

One of the more common rules of trading that seasoned professionals give to beginners is to cut your losses early. We are advised not to let small losses develop into large ones, because large losses can be hard to come back from.

Of course it’s a bit of an art to learn to use this rule effectively, because many stocks – even large caps with lots of shares outstanding – have large price swings in a given week. If you cut your losses too early, you could very well end up quickly selling most stocks that you buy, just due to the day-to-day volatility. And of course the trading fees will eat you alive if you do this.

To understand why “cutting your losses quickly” is such an often-recommended strategy, we have to look at the math behind gain and loss percentages.

In a nutshell, + and – percentage price swings were not created equal. And the larger the swing, the larger the inequality. If you haven’t put many brain cycles on it, you may find that you’re intuitively assuming that there is a certain symmetry to price swings that doesn’t really exist.

Let’s say you buy a stock. Shortly after buying the stock drops 20%. You think of selling but decide instead to hang on. Now at the end of year 1 your stock is down 50%. But you continue to hang on and the following year the stock closes up 50%!

Smart you, right? It went down 50% one year but then up 50% the next year so you broke even, right? Good thing you didn’t sell at that original 20% loss point, right?

Let’s do the math…

Say your original principal was $10,000. If you sold when your investment was at -20%, you would have walked away with:

$10,000 x (1 – 0.2) = **$8,000**.

But what if you held on?

At the end of Year 1 (50% loss), your stock is worth:

$10,000 x (1 – 0.5) = $5,000

At the end of Year 2 (50% gain), your stock is worth:

$5,000 x (1 + 0.5) = **$7,500**

So by hanging on, you would have walked away with an *even smaller* $7,500! 🙁

Whoa! This so-called “symmetry” isn’t so symmetrical after all. Despite the -50% and +50% swing, you’re down 25% when you could have sold early and only been 20% down.

As mentioned earlier, the larger the swing, the larger the inequality. Take a look at the following table. In column 1 is a stock loss. In column 2 is the following gain you would need to make *to break even*.

What’s more, it doesn’t matter whether the loss or gain comes first.

**Asymmetrical Symmetry**

Initial Loss |
Gain to Break Even |
---|---|

-5% | +5.3% |

-10% | +11.1% |

-15% | +17.6% |

-20% | +25.0% |

-25% | +33.3% |

-30% | +42.9% |

-35% | +53.8% |

-40% | +66.7% |

-45% | +81.8% |

-50% | +100% |

Or maybe you prefer it in continuous, graphical form. Don’t have to twist my arm to fire up Matlab…

Where exactly you decide to pull the trigger and cut your losses is up to you. The key takeaway is that for a large loss, you need an even larger gain just to break even.

If you’ve let a stock drop all the way down to -30%, ask yourself how often you make +43% on a stock buy, because that’s how the stock will now have to move in order for you to just get your original money back. 😉