# Why “profit factor” is used to compare trading strategies?

A lot of books/articles/trading forums mention that "profit factor" is probably the most important measure and should be used to compare different trading strategies. They define profit factor as total gains/total loss. I can understand having a profit factor > 1 means the trading system is making money but I think you can't use this number for comparing trading strategies. Trading system with higher profit factor doesn't necessarily make more money than one with lower profit factor. For example if we have two trading strategies A and B as below,

Trading strategy A: Has a profit factor of 2

Trade 1: Buy XYZ @ 100 on Monday and sell it @ 150 on Tuesday making a profit of $50. Trade 2: Buy ABC @ 100 on Wednesday and sell it @ 75 on Thursday for a loss of$25

Profit factor = $$\frac{\\\50}{\\\25} = 2$$

Rate of return for this strategy = $$25\%$$

Trading strategy B: Has a profit factor of 3

Trade 1: Buy XYZ @ 100 on Monday and sell it @ 109 on Tuesday making a profit of $9. Trade 2: Buy ABC @ 100 on Wednesday and sell it @ 97 on Thursday for a loss of$3

Profit factor = $$\frac{\\\9}{\\\3} = 3$$

Rate of return for this strategy = 6%

Isn't the trading strategy "A" better than "B"? What am I missing here?

• Although I have seen this "profit factor" mentioned in trading blogs and trader discussion groups, it is never mentioned in textbooks or published papers etc. as far as I know. I agree with you that it seems intellectually dubious. Among other things it seems to mix together return and risk considerations. – noob2 Jan 31 '19 at 0:45
• Thanks. I am kind of new to trading and trying to build/test trading strategies as a hobby. I am trying figure out how to compare two different strategies. If you can recommend any book/articles that would be great! – user10697426 Jan 31 '19 at 2:02
• I think the point is that is does mix return and risk, and I also don't think its utility is made clear by considering an example of only two trades. Run a Monte Carlo analysis of a 2 PF strategy vs a 3 PF strategy, and you will see much shallower draw downs in the 3 PF strategy – Ian Ash Jan 31 '19 at 11:05
• The commonly accepted comparison metric in the industry is the Sharpe Ratio, which originated in academia. It has its drawbacks too, however. So I do not want to completely dismiss the Profit Ratio; amateurs make good contributions too in this field. – noob2 Feb 2 '19 at 16:42

When it comes to trading systems, and not investment strategies, profit factor is a great metric to use. Sharpe Ratio is for comparing returns as an excess over a risk free option per unit volatility, but when it comes to trading, the risk free option like bonds or a low risk market index isn't really an option.

To be clear, $$pf = \frac{\%win rate \times avg win} {\%loss rate \times avg loss} = \frac{total wins}{total losses}$$. That division sign makes the metric a ratio, comparing the wins to the losses, or comparing returns to per unit loss. Note that this excludes all issues of position sizing and leveraging.

In your example, strategy A: pf = 2, ror = 25%, strategy B: pf = 3, ror = 6%. Based on the ror, A performs better, based on the pf, B performs better. What's the difference? The pf tells you that for A, it made 2x as much as it lost (+50/-25), but for B, it made 3x as much as it lost (+9/-3), the equity graphs for A and B would be very diferent. In other words, the drawdown in profit/performance/equity for A was 50% (-25/+50), but for B it was 33% (-3/+9). All B has to do do is to increase position size or use leverage to exceed the raw \$ returns of B, and it'll do so with less volatility in it's balance.

TDLR:

• pf compares wins per unit loss
• pf excludes position sizing in describing the profitability of a trading system
• a higher pf may indicate a smoother equity graph with less proportional drawdown
• In the comparison that OP presents, both strategies have the same position size (they are investing the same amount of money). Clearly, strategy A is better since the returns are better, even if pf is smaller. I am not sure how you can make a conclusion on draw-down with knowing when the trades were executed. – nitin Dec 24 '20 at 19:46
• OP had profit first. 'A' has a loss that is 50% it's win, B has a loss that is 33% it's win. 'A' has made more money with a riskier approach. If future win/loss sizes are the same, then A's single win will be wiped out with 2 consecutive losses, whilst it'll take 3 losses to wipe out B's single win. Comparing wins and losses of each, wins A:B (50/9)=5.5, losses A:B (25/3)=8.3. 'A' is chasing 5.5x the gain for 8.3x the risk compared to B. If B leveraged 8:1, it would've gained (8*9)=72lev-points whilst losing (8*3)=24lev-points, ie greater raw return with similar risk/loss. – jeanlouie Dec 24 '20 at 20:23