"Position Sizing" (2) Performance Metric: "Profit Factor"
Profit Factor
Let's consider the performance of a certain trading system (Account A). If you have traded several times so far, with a total profit from winning trades of $20,000 and a total loss from losing trades of $10,000, your capital will continue to grow if you keep trading with this system. This is a concept called the Profit Factor, expressed as Profit Factor = Total Profit / Total Loss. A trading system with a high Profit Factor can be said to have high performance. Let's break this down. We will add probability to both the numerator and the denominator.
Numerator: Total Profit / Win Rate x Win Rate
Denominator: Total Loss / Loss Rate x Loss Rate
If we add the total number of trades to both the denominator and the numerator,
Numerator: Total Profit / (Total Number of Trades x Win Rate) x Win Rate
Denominator: Total Loss / (Total Number of Trades x Loss Rate) x Loss Rate
This becomes, and since Total Number of Trades x Win Rate = Number of Winning Trades, and Total Profit / Number of Winning Trades = Average Profit, the Profit Factor can be broken down into
Numerator: Average Profit x Win Rate
Denominator: Average Loss x Loss Rate
In other words, just like the concept of expected value, the Profit Factor involves the average profit and the win rate. To increase the Profit Factor, it is important to "keep average losses down" and "increase the win rate". To keep average losses down, you can see that you should set a stop-loss and make the stop-loss level stricter. To increase the win rate, in addition to selecting the right stocks to trade, you should ensure that the profits you have worked hard to gain are not turned into losses (using trailing stops or backstops), and lower the level of your profit-taking.
To increase the Profit Factor
Let's say you set your trading system to take profit at +20% and stop loss at -10%, and your results are an average profit of +20%, an average loss of -10%, and a win rate of 40%. In this state, the Profit Factor is 1.33. To raise the Profit Factor, first, you want to increase the win rate. To do that, of course, you should wait to trade until the market environment improves, but if you set your profit-taking at +16% and your stop-loss at -8%, lowering your profit-taking range and raising your stop-loss line, your average profit will decrease, but your average loss will decrease and your win rate will likely increase. If your win rate rises to 50%, your Profit Factor will rise to 2.0. Whether your performance has improved due to your own management or because it is a bull market where everything is going well, if your performance metric—your trading results—or Profit Factor has increased, you should increase the number of individual stocks you invest in or increase your position size. You cannot know your current state without trading records to improve your trading results. In other words, the first step to improving your own performance is to grasp your own performance and create a trading performance record.
Pessimistic Return Ratio
The Profit Factor is highly likely to yield the same performance in the future if the number of trades is high, but the Pessimistic Return Ratio is a metric that can also be used when the number of trades is low. The Pessimistic Return Ratio is adjusted to become a good value as the number of trades increases and reliability grows. The Pessimistic Return Ratio is calculated by subtracting or adding the square root of the number of winning or losing trades from the Profit Factor. The calculation formula is as follows.
Numerator: Average Profit x (Number of Winning Trades – Number of Winning Trades ) / Total Number of Trades
Denominator: Average Profit x (Number of Losing Trades + Number of Losing Trades ) / Total Number of Trades
As a guideline for the Pessimistic Return Ratio, a system exceeding 2.00 is considered a very good system, and one exceeding 2.5 is considered an excellent system.
Reference: Ralph Vince, "Portfolio Management Formulas"