# 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.