Understanding a better substitute for win ratio and profit/loss ratio
Like any other business, successful trading requires an analysis of our performance. While applying strategies in a backtest, in a forward demo test, or during live trading, we look at various metrics such as Net Profit, Win Ratio, Profit/Loss Ratio, Average Profit, Drawdowns, and so on. With so many metrics to look at, on which metric should we optimize our strategy parameters?
Let’s discuss the two commonly used trading performance metrics, win ratio and profit/loss ratio, and a lesser understood metric called expectancy ratio. The latter is one of the best trading metrics any beginner or serious trader should understand.
How often do you win? — This is probably the most common and easily understood metric. This is defined as the ratio of the number of winning trades to the total number of trades for a certain period of time.
Generally, a trade resulting in a positive profit is considered a win while those resulting in a negative profit is considered a loss. We take note that this does not differentiate a big win from a small win, nor a small loss from a big loss.
Furthermore, without proper context, this metric can be deceiving. A high win rate most probably indicates a profitable performance, but this is not always the case.
The reverse is also true: a low win rate does not always mean poor profitability. We must carefully consider other metrics alongside the win ratio.
Here’s a hypothetical example of 10 trades. The figure below shows all the taken trades 1 to 10 and their corresponding profit/loss in USD. The table of trades and trade statistics are also shown.
While the win ratio is an impressive 90%, this is clearly not a profitable performance. The average loss of $500 from that single losing trade was just too great it wipes out all the smaller gains. You will probably expect this kind of loss to happen again sometime in the future if you don’t change something in your strategy.
Win ratio tells us how often a win happens but its weakness is that it doesn’t show us how small or big these wins are. The metric Profit/Loss ratio tries to qualify this, which we shall discuss in the next section, and to be followed by Expectancy and Expectancy Ratio.
This is defined as the ratio of the average profit of winning trades to the average loss of losing trades. The formula takes the absolute value of Average Loss so that the Profit/Loss Ratio always takes a positive value.
Intuitively, a profitable performance should always give us a profit/loss ratio greater than 1.0, such that the average profit is greater than the average loss. The higher this metric, the better the performance.
However, like the win ratio, the profit/loss ratio can be deceiving in the absence of proper context. The following figure presents another hypothetical set of 10 trades that shows a profit ratio of a seemingly acceptable value of 2.1 (profit/loss figures are in USD).
In this scenario, While the average profit is way greater than the average loss by a factor of 2.1, the win ratio is so low that we get a negative net profit.
Taking this understanding of the profit/loss ratio, we can review back on the first scenario of 10 trades. The win ratio was an impressive 90% while the profit/loss ratio was unacceptable at 0.11, an indicator of very poor trading performance. Taking the two metrics into context together creates a better picture of actual performance. Is there a single metric that we can look at rather than checking two?
In the next section, we talk about the metric Expectancy that incorporates the elements of win ratio and profit/loss ratio into one single metric.
Expectancy and Expectancy Ratio
Expectancy is basically the average amount that we expect to earn/lose per trade. For example, an expectancy of $100 indicates that future trades will have average profitability of $100. An expectancy of -$20 indicates a losing strategy because we expect to lose an average of $20 in future trades. Expectancy is defined by this formula:
This metric considers three items: the average size of winners, the average size of losers, and the probability of winning (from which the probability of losing is just the inverse). In the formula, we take the absolute value of Average Loss so that the Expectancy takes a positive value when the strategy is profitable, and a negative value when it is not.
We can normalize this metric by dividing expectancy by the absolute value of the average loss as follows:
Expectancy ratio becomes a more generic, dimensionless metric (like profit ratio) that doesn’t discriminate among variations of position sizes. For example, two traders may have respective expectancies of $350 and $2,000 but may have the same expectancy ratios of 1.25. Both traders are then performing similarly well, though they may have different account capital sizes.
In the following figure, we present a hypothetical and profitable scenario of 10 trades with an expectancy ratio of 2.2. Observe that while the win ratio is relatively low at 40%, the profit ratio is impressive at 7.1. Although the average profit is at $62, the expectancy or average profitability per trade is just $20.
You can also look back to the two previous scenarios and determine the expectancies and expectancy ratios for each. Recall that both scenarios had very poor performance.
How do these metrics relate to each other
The expectancy ratio takes the context of win ratio and profit/loss sizes into one single metric. This clearly makes it a superior metric than the other two each taken by themselves. I optimize my trend-following forex strategies based on this. However, I do not have a good benchmark that makes a good level for this metric, yet.
The following graph presents the actual results from my backtesting efforts and sets an initial reference point for future activities. Each data point represents a backtest of a set of strategy parameters. I backtested the strategies on the daily timeframe with 3 years of historical data for the EURUSD pair and applied these filters:
- The total number of trades is greater than or equal to 25
- The expectancy ratio is greater than or equal to 0.10 (therefore all points here gave profitable results)
By visual inspection, related levels of expectancy ratio seem to follow a linear pattern from the upper left-side towards the lower right-side of the graph. The graph indicates that if we were only looking for a strategy with the best win ratio, we would have missed out on other strategies with similar or better expectancy.
Having various options that have similar levels of profitability is quite important. For one, each option would perform differently in terms of other metrics, including those not discussed in this article. They may differ, for example, in their maximum drawdown and maximum number of consecutive losing trades. Furthermore, some options may be slightly profitable in a different time period and market condition, while some may just fail.
What now …
The expectancy ratio is a measure of average profitability per trade. This indicates how much profit or loss we can expect, on average, in our next trade. This is clearly a very important input for a decision if we should continue using a strategy and take the next trade. It makes sense, therefore, to maximize expectancy ratio, chosen among other metrics, if we want to optimize on just a single metric.
After optimizing the expectancy ratio, the next step is to validate the selected best strategies in different time periods and with other instruments. But that is for another post.