Befuddled by profit factor (kinda maths heavy)

This is kinda confusing me.

The formula for profit factor is pf = sum of wins / sum of losses

However, this can be misleading as our account balance will fluctuate over time, meaning the size of our winners and losers will change as well. Lets say you have $10,000 in your account, you risk 1% at 1:1 R:R and win $100. You then withdraw $10,000, leaving $100 behind. You then risk 1% of $100 and lose, losing $1. Your profit factor will be $100 / $1 = 100, which is absurd.

So in order to get an accurate profit factor, we need to normalise our winners and losers. We can normalise our winners and losers with respect to the size of our stop loss, or risk, in each trade. If you use a fixed stop loss (fixed risk), then the size of your normalised loser is always 1. If you use a fixed 2-to-1 reward-to-risk, then the size of your normalised winner is 2. If you use a variable R:R, then you can find the size of your average winner and normalise that.

We then add our % chance of winning a trade and % chance of losing a trade to get our accurate profit factor.

The formula becomes:

pf = (winrate% * normalised average size of winner) / (loserate% * normalised average size of loser)

I hope my maths is correct so far.

Assuming it is, I’ve been backtesting two versions of a mechanical system.

The first version uses a 2-to-1 reward-to-risk and has a profit factor of 1.33. The second version uses a 0.5 reward-to-risk and has a profit factor of 1.49.

You assume the system with the higher profit factor would have a steeper equity curve. But this is not the case.

Equity curve for 2-to-1 reward-to-risk, profit factor = 1.33, risking 1% equity per trade.

Equity curve for 0.5-to-1 reward-to-risk, profit factor = 1.49, risking 1% equity per trade.

The version with the higher profit factor ends up making less money. I always assumed a higher profit factor = steeper equity curve. But this doesn’t seem to be the case? I’m frakken confused. Either my maths is off or I’ve misinterpreted the meaning of profit factor.

Interesting topic KK…

Let’s wait for [B]Clint[/B] to wake up…


It’s kind of simple really.

The basic definition is this: Profit Factor is a measure of how many times the gross profit (the sum of all the winning trades) exceeds the gross loss (the sum of all the losing trades).

Remember that the steepness of the equity curve is relevant to time, as time is plotted on the X-axis. Therefore do both of your strats have the exact same number of trades per day per X axis unit.

[B]Profit Factor does not take time into account, and therefore can not be linked to how steep an equity curve is going to be [/B]

I would have thought that the higher the profit factor the more [B]net[/B] ROI you are making [B]relative[/B] to the trades placed. You could have two strats that offer a totally different number of trades per week. Providing they are both profitable the strat that has the greater number of trades should have a steeper equity curve, however this will be proportional to the profit factor as you pointed out.

For Example. If you had two identical strats with the same profit factor of 1 to 2, but one strat yields 10 trades a week and the other yields 5 trades per week, then the equity curve gradient will be twice as steep for the 10 yield strat against the 5 yield strat - because its time (x axis of the equity curve) that contributes to the gradient of the curve.

Hope that makes sense

I totally agree. The system with the higher frequency will have a steeper curve over time. Perhaps I should clarify - both versions of the system I’ve tested have the same exact entry point, so the total number of trades for each version is exactly the same. The only difference between the two versions is the R:R I use. When I reduce my reward:risk, my profit factor increases (up to a point), but my final equity falls. It’s confusing.


The basic maths…

When Reward:Risk is 2:1
profit factor = (0.41 * 2 ) / (0.59 * 1) = 1.39 -> approx 1.33 after spread

When Reward:Risk is 0.5:1
profit factor = (0.76 * 0.5) / (0.24 * 1) = 1.58 -> approx 1.49 after spread

Okay, I think I know what is happening. The equity curves of both system versions are based on 1% risk, but one version is alot closer to the optimal risk level (Kelly criterion) than the other, hence it will have a steeper equity curve.


I have 2 versions of the same strategy with a similar equity difference…

The reason the lower profit factor has a steeper equity curve is simply that you give it more oppurtunity to make you money.

The higher pf stategy is cutting off losing trades early with it’s lower risk tolerance, but its exiting eventual winning ones as well. It gets a higher pf, but less money in the end because it misses out on more than it protects.

Any strategy that genuinely has a pf above 1 will make you more money the more trades you do, or more time you let it run…whether that be letting the strategy run for longer, or letting a trade with a statistical probability have the chance to work out…If you exit every trade that ticks a little the wrong way you’ll get nothing.

While we want pf’s of 1.5 (apparently this is the magic number…?) and above the reason for this is not to turn your nose up at a 1.2, but to be sure that there is enough evidence that the strategy is statistically significant, and to make sure us non billionaires can afford it.

If you have the money and the risk appetite then to maximise profits… take ALL trades with probabilities in your favour…


As another poster pointed out, what makes you think that higher profit factor should mean a steeper equity curve?

It seems if you want to maximize equity curve steepness (if this represents for you the most appealing system) then that trait should be your fitness measure. Now you’ll just have to think of how to define equity curve steepness and then maximize it and see if you like what you see.