If a security drops 50%, it needs to rise 100% to break even. What about if it drops by a percentage different than 50%?
For the mathematically inclined, follow what Pythagoras might say:
When something drops 20%, you have to perform an “indirect” calculation. (This is not an official term, hence the quotation marks.). That is, you start by calculating what 20% is. Then you subtract that 20% from the starting value.
1.) Understand this first:
Here’s an easier approach: Think about the end result. If you lose 20%, that’s the same as keeping 80%.
Say you have $X. If you lose 20%, you’re left with 80%, which is 0.80 * X. Let’s call that value Y.
Y = 0.80 * X
If you start at Y and want to get back to X, you invert that operation.
X = Y / 0.80
Expressing that as multiplication instead of division:
X = Y * (1 / 0.80)
That is, you multiply by the inverse (of what you’re left with, not the drop).
2.) For total understanding:
Above I expressed a percentage drop (in this case, 20%) as the amount remaining (80%). Mathematically, that is:
Y = 0.80 * X
To express that as the percentage drop instead: Y = (1 – 0.20) * X
Then, to get from Y back to X:
X = Y / (1 – 0.20)
X = Y * [1 / (1 – 0.20)]
3.) To conclude:
If the percentage drop is P, to recover, you multiply by [1 / (1 – P)].