Question: When is 50% not equal to 50%?
Answer: When you’re talking about investment gains and losses.
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.