Percentage gain and loss

When an investment changes value, the amount needed to return to its initial (starting) value is the same as the amount of the change - but opposite in sign. This is not the case when working in percentages.  shows that the percentage gain or loss to recover an initial investment is different than the initial change.

Overview
The formula is expressed as a change from the initial value to the final value.



\text{Percent change} = \frac{(\text{Final value} - \text{Initial value})}{\text{Initial value}} * 100% $$

For example: A $125 investment drops by $25, then increases by $25 to recover the initial $125 investment.


 * Drop by $25 :
 * Initial Value: $125
 * Final Value: $100
 * Loss in $: -25 = Final value - Initial value = $100 - $125
 * Percent change: -20% = ($125 - $100)/$125 * 100%


 * Then, increase by $25 :
 * Initial Value: $100
 * Final Value: $125
 * Gain in $: +25 = Final value - Initial value = $125 - $100
 * Percent change: +25% = ($125 - $100)/$100 * 100%

The example showed a sequence containing a $25 loss, then a $25 gain. The same amount of money was lost as was gained.

In percentage, the sequence is described as a 20% loss, then a 25% gain. To say this another way, you will need to gain much more in percentage than you have lost to return to the initial value.

Working in percentage
Percentages are used when reporting gains and losses of the market. For example, the market drops 10%. What is implied, but not stated, is that a gain of 11% is needed to recover the loss.

Figure 1 below plots the equation. To show gains and losses in percentages alone, the actual value of the investment is not needed. This allows comparison of investment performance.

The plot shows some important points. First, the percentage increases with increasing gain or loss. For example, a loss of 50% will require a 100% increase (double its value) to recover the initial investment.

Next, the math works the same for gains but goes in the opposite direction. Investors may think of gains and losses in terms of Risk tolerance, but framing the problem from a different perspective may help. For example, a gain of 100% (investment doubles its value) only needs a 50% drop (cut in half) to get back to the original value.

Effect on an investment
The impact of percentage changes on the value of the above example ($125) is listed in Table 1 below.

You can try this with your own investments (or experiment what will happen with stock market changes) using a spreadsheet available on Google Drive. The spreadsheet covers a broader range than the table shown here, along with figure described in this article.

Download the appropriate version: Microsoft Excel or LibreOffice Calc.