What Is A Good Equity Curve? – Profit & Loss Curves Best Practices and Analysis
If you have come so far in your trading that you rely on backtesting to validate your trading strategies, you definitely are ahead of the masses. Most people haven’t understood that all strategies and patterns they want to trade need to be validated before they may go ahead and risk any real money. However, while validating a strategy by assessing the equity curve might seem easy, there are some things you need to know not to get lured by the results. So, what is a good equity curve?
A good equity curve is one that has an even slope, small and short-lived drawdowns, and a good amount of trades to make the observation statistically significant. It’s also important that the profit and loss aren’t impeccably smooth, since one that appears like a perfectly drawn line indicates that the underlying trading system is curve fit, and unlikely to perform well going forward.
In this guide to equity curves, we’re going to look at how you should assess the profit & loss curves that your systems produce, and what they tell you about the strategy. Although the appearance of the curve on its own doesn’t predict the probability of the strategy working in the future, it tells us a lot of important information about the strategy. It is simply a great tool that shouldn’t be overlooked.
Let’s begin!
(Before we go on, we’d like to mention that we have a backtesting course that covers all aspects of how to backtest.)
What Is An Equity Curve?
The equity curve is a graphical (or visual) plot of your trading equity/account over time. The x-axis shows the time, and the y-axis shows the value of our account or strategy.
For example, if you backtest one trading strategy, you might start with a hypothetical 100,000. You might invest 100% of your equity per signal as you generate buy and sell signals.
Thus, over time, the equity line shows your accumulated or compounded account as it goes up or down. Hopefully, it’s more up than down!
Below is an example of an equity curve for a trading strategy in Amibroker:
The equity curve started at 100,000 in 2002 and ended at 275 355 in 2021. The equity curve slopes upward from left to right, and the strategy is making money, but not a significant amount considering the time of nearly 20 years.
The chart below is a real-life example of the equity curve of Brummer & Partners Multi-Strategy Fund:
The red line is the strategy’s performance, while the grey line is the Swedish Total Return Index (for stocks). Both ended up at the same level, but as you can see, the ride has been much less bumpy for the owners of the Brummer funds.
This is exactly what you look for in a strategy! You want the equity line to be smooth.
The more smoothly the equity chart rises from the left to the right, the better the strategy, as long as it’s not curve-fitted. By looking visually at the equity chart, you get a pretty good estimation if the strategy is worthwhile on its own or needs some additional variable(s).
If the equity line goes like a straight line, the strategy must be pretty good. In these circumstances, you don’t need much of a mathematical confirmation if the strategy is good (or not). However, some traders focus on the maximum drawdown, while others focus only on the outcome (the profits).
But in most cases, it’s not as apparent as it looks: You need some quantitative backtest on the significance of the strategy. That’s why all trading software has built-in trading performance metrics to evaluate strategies. Below is an excerpt from Amibroker, which shows the standard metrics on every strategy backtest:
The Metrics We Use To Assess Equity Curves and Strategies
You could use an endless amount of trading metrics when evaluating equity curves and strategies, and we understand that it might be hard to know which ones to focus on. In addition to the common ones like profit factor, average trade, and other similar metrics, you have advanced mathematical ratios and formulas that, according to us, are given more attention than they deserve.
Here are the most important metrics, according to us:
Profit factor
The profit factor of the trading system is a critical metric. The profit factor is a metric that takes the aggregate profits of a system divided by the aggregate losses. For instance, if the system made $2000 in profits, and lost $1000, you would have a profit factor of 2.
In our strategies, we want a profit factor of at least 1.75, depending on the strategy we’re dealing with. In breakout strategies, 1,5 might be on the lower end, but still fully acceptable, if the other strategy metrics look okay.
However, in mean reversion strategies we demand a higher profit factor of at least 2, depending on the circumstances.
Remember that the more restrictive you are about the trades you take, the higher the profit factor tends to become. Similarly, the more you loosen your criteria, the lower the profit factor.
Average Trade
It’s essential to ensure that the strategy has an average trade that is enough to cover commissions and slippage and leave some of the profits for you. As we’ll cover in a bit, too many people forget this step and subsequently build trading strategies that are losing strategies once transactional costs have been applied.
The evenness of the curve
The more even the PnL curve is, the better. It simply shows that the strategy has managed quite well in all the varying market conditions that arose during the testing period, and makes you more confident that it will work well going forward.
This means that you want flat periods to be as short-lived as possible and the curve slows at roughly the same angle throughout the testing period.
Sometimes you’ll see how the strategy’s performance seems to degrade towards the end of the testing period. In these cases, it could just be that the trading edge is waning due to unknown reasons. However, you’ll often find that it has to do with recent volatility levels that have become much lower, which reduces the size and profit of most market movements.
To see how the volatility of a market has changed over time, and if it correlates with the behavior of your strategy, you may simply look at a monthly chart of the market in question. This is precisely what we’ve done in the image below, where you see how the volatility of the market got substantially lower toward the end.
Drawdown
Obviously, the drawdown is one of the most critical aspects of an equity curve. We want the profit-to-drawdown ratio to be as high as possible since smaller drawdowns mean we can trade more securities and make more money while remaining within our calculated risk level.
Now, an excellent profit-to-drawdown ratio depends a lot on the market you trade. For instance, when trading the major stock indexes, a good trading strategy could realistically have an annual ratio of 2-1. However, if you were trading more challenging markets, like lean hogs, then a ratio of 1-1 or even less may be considered great!
The drawdown aspect of the equity curve might seem fairly straightforward, but there is one aspect you must consider that could have a huge impact on your assessment of the strategy. We will look at this just a bit under the sub-heading marked “Important”. It’s important because empirical research suggests that retail traders and investors tend to sell into a market panic and reenter after a bottom is formed.
The market periods that the curve goes through
If you are testing a trading strategy for the stock market during market crashes, you may be a little more certain that the strategy will cope well with future bearish scenarios. In other words, include various market conditions in the backtest. It’s no feat to construct an P&L curve that goes straight up in times of very bullish market behavior.
Of course, this applies to all other markets as well. Make sure to know your market and compare the equity curve to the market developments during your testing period.
The Most Common Pitfall: This is NOT a Good Equity Curve
As you see in the conditions we outlined above, we prefer the equity curve to be smooth and show a steady 45-degree slope. That might seem quite uncontroversial, given that everybody strives to have their returns coming at as regular intervals as possible.
However, having a too-perfect equity curve isn’t good either, since it often implies that the strategy has been curved fit!
Curve fitting simply means that you have imposed rules that managed to define random patterns in your data set rather than true market behavior. And since the patterns your strategy used were random, the future outcome will also be random. In other words, the chances of it continuing to make new equity highs in the future are quite low, and the most likely outcome is that the strategy will fail miserably in live trading.
The image above shows a chart where the strategy has obviously been curved-fitted. The curve goes up seemingly without any drawdown at all. This simply isn’t realistic!
Another common Pitfall
Always make sure to include proper slippage and commission in your backtest. We often see beginning traders backtest strategies with very small average trade sizes. Therefore, they often have strategies that look great without any transactional costs taken into account but which fall apart once they are applied.
For example, imagine a case where you’re backtesting a strategy with an average profit of $10 on the ES futures market (S&P500). In that case, the strategy will even result in a negative return once slippage and commission have been accounted for.
What Characterizes a Curve Fit Strategy?
If you ever see strategies with equity curves like the one presented above, you could rightfully assume that the strategy is a curve fit and won’t work going forward.
So, here are two signs that a strategy might be curve fit:
- It has a lot of rules: Good strategies usually are made up of no more than a few conditions. If you have a trading strategy consisting of more than 5 individual conditions, you should start asking yourself if that’s not too much. The risk of curve fitting increases the more conditions you include.
- The Parameters are very exact: If your strategy only works with very exact parameter options and falls apart as soon as you change the settings slightly, that’s not a good sign at all. The chances are, again, that those very exact parameters were the result of randomness and nothing else!
Of course, the two points provided above are merely guidelines, and there always will be strategies that work despite contradicting any of the two above rules.
For more information about how to build your own trading strategies and ensure that they’re robust, we recommend that you take a closer look at our system and trading performance metrics article.
Mark to Market vs Closed Trade Equity (Important)
One detail you should know about regarding how trades are presented in the backtest is the difference between mark to market and closed trade equity. Let’s bring them up separately below to make the difference clearer:
- Closed trade Equity: The closed trade equity curve only plots trades once they’re closed. So if you enter a trade that goes against you before reverting and ending at a profit, the initial loss won’t be visible at all.
- Mark to Market (detailed): This type of equity curve also shows the swings that go on as the trade develops. So in the earlier example, where the trade starts off with a loss and then recovers, the initial loss would be visible. This is a much more accurate way of displaying the performance of a strategy.
In some strategies, the difference between these two methods could be huge. For instance, in mean reversion strategies where you try to catch a falling market, it will often continue to fall for some time before it finally reverses. And since you usually use conditions that get out of the trade when the reversion is complete, you could have endured a big drawdown, which doesn’t show in the equity curve, since you got out of the trade once the market had turned around and you were at a profit.
If you had used a detailed equity curve (mark to market), that intra-trade drawdown would have been visible, meaning that you had gotten a more realistic view of the market’s action.
Below you see an example of the EXACT same strategy, with the only difference being that the first image shows closed trades, while the latter shows the mark to market equity curve.
Conclusion
A good equity curve is one that has an even slope, with short and shallow drawdowns, and consistent behavior even in varying market conditions. However, a too-perfect equity curve does raise concerns that we’re dealing with curve-fit strategies that aren’t likely to continue to perform well in the future.
In addition to the appearance of the equity curve itself, it’s also important to remember that the performance metrics, such as the average trade, profit factor, and profit to drawdown ratio should be strong enough to make the strategy worth your time.
FAQ:
– What characterizes a good equity curve?
A good equity curve is characterized with an even slope, small and short-lived drawdowns, and a sufficient number of trades to ensure statistical significance. It should not appear perfectly smooth, as this may indicate a curve-fitted trading system with questionable future performance.
– How can I assess the performance of a trading strategy using equity curves?
Key metrics for assessing equity curves include profit factor, average trade, the evenness of the curve, drawdown, and consideration of different market conditions. These metrics provide insights into the strategy’s robustness and potential for success in live trading.
– Why is the evenness of the equity curve important?
The evenness of the equity curve is important because it indicates that the strategy has performed well in various market conditions, increasing confidence in its future success. A more even PnL curve suggests the strategy has adapted to different market scenarios.