The percentage gain is indeed bigger when a stock goes from 13c...

The percentage gain is indeed bigger when a stock goes from 13c to 14.5c than when it goes from 14.5c to 13c. This phenomenon arises due to the way percentage changes are calculated, specifically because percentages represent proportional changes rather than absolute differences.

Here's why:

Calculating Percentage Change:
The percentage change is calculated by dividing the absolute difference by the initial value and multiplying by 100.

When the stock goes from 13c to 14.5c, the percentage change is [(14.5c - 13c)/13c] * 100 = 11.54%.
When the stock goes from 14.5c to 13c, the percentage change is [(13c - 14.5c)/14.5c] * 100 = -10.34%.
Proportional Impact:
The key point is that the base value used for the calculation matters. A gain of 1.5c on a smaller initial value of 13c represents a proportionally larger increase than a loss of 1.5c on a higher initial value of 14.5c.

Imagine dividing a pie into slices. Gaining a slice from a smaller pie (13 slices) has a bigger relative impact than losing a slice from a larger pie (14.5 slices).

Non-Linearity of Percentages:
Percentages are not linear, meaning that equal changes in absolute values do not translate to equal percentage changes depending on the base value. This is why seemingly small differences in price can lead to significantly different percentage gains or losses.

Therefore, it's crucial to consider the initial value when interpreting percentage changes, especially when comparing gains and losses of the same absolute amount. Remember, a percentage change reflects the proportional impact on the starting value, and this impact can be larger for smaller starting values, even if the absolute change is the same.

I hope this explanation clarifies the reason behind the seemingly counterintuitive observation about stock price changes and their corresponding percentage gains!