The Math of Trading
Post By: Renzo Bazargani
As a follow up to the important topics about Trading, this post will be on the importance of knowing the math or statistics of your trading results and whether your strategy is profitable or not. Previously, I talked about the importance of having the right mindset for trading and that without it, you will simply not be successful. I wrote about “The Psychology of Trading” outlining the specific actions that are required to have the right mindset, and if you haven´t read it, then please click here. Then I wrote a post in checklist format on the “Evolution of a Trader”, which is very important to understand what it takes to become a profitable trader, perseverance and many years of practice and sacrifice - please click here to read this post.
In Trading it is very important to measure our performance and know the statistics of the results of our strategy in order to learn how to improve our performance. And, there is always room for improvement. Therefore, it is vital to know the statistics of your strategy on a weekly basis. Essentially, you need to know your Win rate, Loss rate, Average Win and Average Loss. The following are the equations you need to use and I have provided real examples of trading results:
- Expectancy is calculated by the formula:
Expectancy = (Win% x Avg Win) – (Loss% x Avg Loss)
(Trading expectancy is a calculation that shows what the typical profit is for each trade placed)
* A positive value (above zero) indicates that the trading system is profitable
* A negative value (below zero) indicates that the trading system is not profitable
- Profit Factor is calculated by the formula:
Profit Factor = (Win% x Avg Win) / (Loss% x Avg Loss)
* A value above 1 indicates that the trading system is profitable
* A value below 1 indicates that the trading system is not profitable
Example 1. (Emini S&P500)
24 Trades in 5 days (1 contract)
13 Win and 11 Loss
Win Rate: 13 / 24 *100 = 54%
Loss Rate: 46%
Now, 13 Win totaled 47 pts and 11 Loss totaled 22 pts
So, Avg Win: 47 / 13 = 3.6 pts and Avg Loss: 22 / 11 = 2 pts
Expectancy: (0.54 x 3.6) - (0.46 x 2) = 1.02
Profit Factor: (0.54 x 3.6) / (0.46 x 2) = 2.11
Example 2. (Emini S&P500)
76 Trades in 15 days (multiple contracts)
60 Win and 16 Loss
Win Rate: 79%
Loss Rate: 21%
Now, 60 Win totaled $31,240 and 16 Loss totaled $14,462
So, Avg Win = $521 and Avg Loss = $904
Expectancy: (0.79 x 521) - (0.21 x 904) = 221.75
Profit Factor: (0.79 x 521) / (0.21 x 904) = 2.17
(NOTE: In this example the Avg Loss was bigger than the Avg Win, but since the Win Rate was much bigger than the Loss Rate, then the strategy was very profitable)
Example 3. (Stocks)
62 Trades in 1 year
27 Win and 35 Loss
Win Rate: 44%
Loss Rate: 56%
Avg Win = 19.4%
Avg Loss = 5.8%
Expectancy: (44 x 19.4) - (56 x 5.8) = 529
Profit Factor: (44 x 19.4) / (56 x 5.8) = 2.63
(NOTE: In this example, the Win Rate was lower than the Loss Rate, but since the Avg Win was over 3 times bigger than the Avg Loss, then the strategy was very profitable)
In conclusion, it is best to have a system or methodology with the Avg Win at least 1.5 times bigger than the Avg Loss, as well as having a higher Win Rate, let’s say around +/- 60%.