What is Gross Profit?
Gross profit is the sum of the gain of all winning trades. We can write this as follows:
\[ GP = \sum_{t=1}^{N} P_t \]
where
- \( GP \) is gross profit
- \( t \) represents each successive round-trip winning trade
- \( N \) is the total number of winning trades
- \( P_t \) is the net profit of each winning trade, which will be positive because we're only looking at winners
If you're not familiar with the summation ( \( \sum \) ) symbol it just means sum. Let's expand it:
\[ GP = P_1 + P_2 + P_3 + ... + P_N \]
The gross profit will always be a positive value because it's always a sum of positive gains.
What is Gross Loss?
Gross loss is the sum of the losses of all losing trades. We can write this as follows:
\[ GL = \sum_{t=1}^{N} L_t \]
where in this case
- \( GL \) is gross loss
- \( t \) represents each successive round-trip losing trade
- \( N \) is the total number of losing trades
- \( L_t \) is the loss of each losing trade
Note that the trade loss, \( L_t \), is a positive number meaning that gross loss will also be positive because we're only dealing with losers now.
Since gross profit and gross loss are both positive numbers, profit factor is also a positive number.
Why would we make gross loss a positive number instead of a negative one?
Imagine you're looking at a trade and you ask, "What's the net profit?" If the trade made money you expect a response like, "The net profit is $40." You don't normally say, "Positive $40," but that's what you mean.
But what if the trade lost money, how do you answer the question. "What is the net profit?" You'd say something like, "It lost $40." You say lost to indicate a value in the negative direction. If you could only report it as a single number, you'd say "Minus $40."
Now let's switch it up and ask the question, "What is the loss on this trade?" If it didn't lose, well, you might say, "Actually, it wasn't a loss, it gained $40." But you have to say all those extra words to mean that it performed opposite to the question. A profit is in the opposite direction of a loss, therefore it's a negative loss of minus $40. If a trade gains $40 and you're asking, "What's the loss?" and you can only give one number in reply, the answer is, "-$40."
And that's why we report a loss as positive. Loss means down, negative, unfavorable, etc. So, yes, if the trade lost money, then it's in that same direction as the word loss. It's in agreement with the word loss. So, we say the loss is a positive $40 and if the trade made money then we say the loss is negative $40.
Clear as mud?
You may think I'm belaboring the point, but a minus sign in the wrong place can ruin your whole day.
What is Profit Factor Good For?
Let's understand profit factor by looking at it's extremes.
What happens when all of our trades are losers?
In this case, gross profit is zero and gross loss is some positive value. Our profit factor is therefore zero.
What happens when all of our trades are winners?
Well, that means we have no losers so the gross loss would be zero. Because it's on the bottom of the fraction, the profit factor is infinity ( \( \infty \) ).
We know from this, therefore, that profit factor is always a value between zero and infinity.
Now, what happens if we lose exactly as much as we profit? In this case the ratio is exactly one. This would be a breakeven strategy.
If profit factor is less than 1.0, then the strategy is a loser. If greater than 1.0 the strategy is making at least a little profit.
So, is a profit factor of 10 better still? That would mean our strategy earns ten times more than it loses.
In theory, this would be great, the higher the better. But in practice I'm not so sure you'll see a profit factor of ten. I'd certainly take a second look at my calculations.
Rules of thumb seem to be this:
- Kevin Davey says values over 1.0, meaning they are breakeven or better, may have some merit, but that values less than 1.5 will likely be challenging.
- Others say that by the time you get up to values of 2.2 that you may already be over-optimizing.
Looks like the sweet spot for profit factor is about 1.5 to 2.5.
If you get higher values, that's great, just be sure to double check your numbers.
What Profit Factor Isn't Good For
Profit factor does not compare the number of winning trades to the number of losers.
You could have a backtest with 51 trades in which one was a winner and 50 were losers and you could still have a nice profit factor.
For example, suppose your average loss is $10 and your one win is $1000. That's a profit factor of
\[PF = \frac{1 \times 1000}{50 \times 10} = 2.0 \]
That's a good profit factor, but clearly you wouldn't want to trade this system.