Understanding the math of gains and losses is an important investment management skill. The best way to learn it is through running the numbers. Below is a percentage gain calculator to help you see what I mean.
Previously, we discussed the volatility tax and its impact on investment returns. Volatility tax increases as the size of losses increase.
Why? Because the larger the loss, the larger the gain needed to recover the loss.
Unfortunately, the percent gain to recover a loss is not a 1-to-1 relationship. The percent gain needed is greater than the loss.
The math of portfolio losses is “nonlinear.” If it were linear then it would be a 1-to-1 relationship.
For example, if you suffer a 50% loss, what is the gain needed to recover that loss?
If the percentage gain needed to recover a loss was linear the answer would be 50%. However, since the percentage gain needed to recover a loss is non-linear, the answer is 100%!
Here is a chart that quantifies the percent gain needed to recover a loss:
While that chart is nice, I find this image to really show you the “nonlinear” relationship between gains and losses:
I stopped the chart at a 75% loss since it makes the chart look a little crazy.
To really put a bow on this concept, I created a percentage gain calculator:
