# Playing the Percentages: The Effect of Gains and Losses

Question: When is 50% not equal to 50%?

This is a relatively simple mathematical truism, but I find it interesting just the same… Did you know that if you experience a 50% investment loss you’ll need a 100% gain just to break even? It’s sad, but true… And the order in which these gains and losses occur doesn’t matter. Indeed, consider the following:

If you start with \$100 and lose 50%, you’re down to just \$50. Now, if you gain 50%, you’re only back up to \$75. Similarly, if you start out by gaining 50%, you’d have \$150. But if you then lost 50%, you’d fall back to \$75. See? It’s the same either way.

In fact, this is a generally true phenomenon that holds for larger or smaller percentages, as well. Consider a 10% loss on that initial \$100 investment – you’d be down to \$90. If that was followed by a 10% gain, you’d be back up to \$99. Start with a 10% gain and you’re up to \$110. Follow that with a 10% loss and your back below where you started at \$99.

I’m really not sure what my point is here… I’ve always just found this interesting to think about, and it’s a good thing to keep in mind when roughing out investment returns in your head.

### 11 Responses to “Playing the Percentages: The Effect of Gains and Losses”

1. And don’t forget that you have to take the tax bite out of that too. 🙂

2. Right. That’s the point. It’s essentially the difference between and arithmetic mean and a geometric mean.

3. Kurt said:

Assume you have \$1,000 to invest and two options. 1) that returns +50%, -50%, +50% over the next three years and 2) that is +10%, +20%, +5% over the next three years.

I calculate that the annualised average returns are 4.0% and 11.5% respectively. With percentages you can’t average by adding them up and dividing by three and percentages are multiplied not summed.

4. He’s just kissing butt because he wants to win a flash drive. 😉

5. that was so nice of you to apologize patrick! 🙂

6. Begging your pardon, the “stupid” comment was a little harsh. Forgive me? The applications of what you are saying are indeed meaningful.

7. Unlike the last comment, I think this is a very useful post. Mainly because most investors miss this point when they try to pick a ‘good’ mutual fund.

Assume you have \$1,000 to invest and two options. 1) that returns +50%, -50%, +50% over the next three years and 2) that is +10%, +20%, +5% over the next three years.

If you chose option 1, you would end up with \$1,125 after the three years and if you chose option 2 you would end up with \$1,386. But if you read the average returns for these funds over those years then option 1 has an average return of 16.7% whereas option 2 has an average return of 11.7%.

People think they read average returns and know that they will end up with more money, when this post is a great example of why higher average returns does not mean more money.

8. Sorry nickel, love your site, but this is stupid. Percentages are only meaningful when it is understood what it is a percentage of. If you have a hundred dollars as your original balance, and you lose 50% of your original balance, you then need to gain 50% of your original balance to break even. But it is true that you now have less money to work with and thus less opportunity to make a gain.

If you lost 50% last year in a stock, yes, that stock will need to gain 100% of its current value in the next year for you to be able to sell at break even–but that’s still only 50% of its purchase value that it needs to gain.

Stores exploit this confusion by giving you “additional” percentages off. This new discount is off the “new” price after the regular “sale”. For example, if you have a \$100 list price shirt on a 50% off “sale”, then a “20% additional off clearance”, the shirt will cost \$40 (50% + 20%*50% off), not the \$30 you thought (50% + 20% off).

9. So in other words, I should just aim for 50% gains in anything that I do? Heheh…

10. As basic as this seems, it is amazing that many people don’t really seem to grasp this fact.

IMO, this is a big reason why I feel it is so important to cut your losses early on stock transactions. Trying to hang on and wait for a stock to “come back” often results in a loss that is difficult to recover from.

11. I often wondered this about commission-based broker fees also. If they charge you 1.5% of the balance when your portfolio is up 5% one year but still charge 1.5% when it is down 2% the next year, wouldn’t your effective fee rate be higher than 1.5%?

Or do they charge 1.5% of earnings? Or does it vary?