The Down 50%, Up 100% Conundrum

Average people think in terms of dollars, not percentages.
When comparing investments, the use of percentages allow one to compare investment returns without having to know the amount of money invested, only the time period needs to be the same. This is the Time Weighted Rate of Return. If one compared dollar increase or decrease, one would need to know the amount invested to compare the investments. This would be quite tedious and futile. All performance returns you see on TV and in the papers are stated in terms of Percentage gain or loss.

The problem is average people have a hard time thinking in Percentages. We tend to ignore the Base Number upon which the percentage is based.

For example, assume you have a $1,000 portfolio that loses 50% of its value or $500. What percentage increase would be needed to return the portfolio to its original $1,000. Consistently, in Adult Ed classes I teach, the asnwer comes back 50%.  NO, the answer is 100%.

People answering 50% forget that the Base Number has changed. Their mind tells them that if I lose 50% of $1,000, then  I have to gain 50% of 1,000 to get back to $1,000. That is actually a true statement, but after losing 50% of  $1,000, you only have $500. This $500 is now how much you have in your portfolio after the loss and becomes the new Base Number. Now to increase your $500 portfolio so that it  becomes $1,000, you would have to earn another $500 or a 100% gain in your $500 portfolio.

In short, if your investment loses 50%, it takes a 100% gain to return to even - the Down 50%, Up 100% scenario.

I should note that the above is a mathematical calculation that would need to be done if you plug in other percentage scenarios.  So, if  your investment loses only 10%, it does not mean that you have to earn 20% to get back to even. If your $1,000 investment lost 10% or $100, you would have to earn 11%  ($100 / $900) to get back to even. The Down 50%, Up 100% example is normally used in explanations since the answer is so dramatically different that what our minds expect the answer to be.