Math 101: How can I have a net profit when average trade percent gain is negative

This kind of question surfaces from time to time, usually in the context of "I found a bug". On the surface it seems "logical" that negative average trade percent gain must lead to overall loss. But as always, doing maths yourself is a good idea.

Let us consider a system that takes two trades. Each time we trade 10 shares. The only difference is the stock price.

First trade buying 10 shares for $20 each and selling with -10% loss for $18 each

10 shares * $18 - 10 shares * $20  = $180 - $200 = -$20

First trade net loss is -$20, percent loss is -10%

Second trade buying 10 shares for $50 each and selling with +5% gain for $52.50 each

10 shares * $52.50 - 10 shares * $50 = $525 - $500 = $25

Second trade net gain is $25, percent gain is +5%

Average trade percent profit/loss is negative:
(-10% + 5%) / 2 = -2.5%

Net system gain is positive:
-$20 + $25 = $5

The key to understanding is realizing that trades usually have different entry value. Beginners typically forget that.

Bottom line percents do not sum up the same way as dollars.