Are you getting a comprehensive assessment of your strategy’s downside? This post will discuss several methods to measure drawdowns, helping you build and select strategies that better suit your risk appetite.
Risk management is a cornerstone of successful trading. Most traders quantify risk by measuring the drawdowns incurred by their strategies or portfolios. Drawdown is the decline in account equity from a prior equity peak. For example, if your peak equity is $5000, and your current equity is $4000, you have a $1000 drawdown.
As trading progresses, your current drawdown will fluctuate in response to your individual trade outcomes. The chart below shows an equity curve and its corresponding drawdown distribution as a function of trades.
Whenever a new equity peak is reached (green dot), the current drawdown is 0. At the right end of the equity curve, the absence of new equity peaks creates a long series of drawdown values.
Open vs. Closed-Trade Drawdown
The chart above displays closed-trade drawdown; it was constructed using only the profit/loss of each closed trade. Account equity was not tracked when the trades were open. If you instead have an equity curve built by taking the sum of closed trade equity and open profits/losses, you can track your open-trade drawdown. Consider the hypothetical scenarios below on how an open trade may play out.
Suppose you just closed your first trade with a profit of $100. If you use a closed-trade equity curve, you will get the green line, which shows zero drawdown. But if you take floating profits/losses into account as well, you will likely get an open-trade equity curve resembling the blue or orange lines above.
For Curve 1 (orange), a $300 open profit was accrued, of which $200 was lost by the time the trade was closed. In this case, the closed-trade equity curve fails to capture the open trade profit retracement. For longer-term trend following strategies, this profit retracement can make a big difference to your bottom line.
For Curve 2 (blue), the trade immediately goes negative, reaching a $200 open trade drawdown before recovering to close in profits. Here the closed-trade curve neglects to show if the winning trade was ever in a losing position. If you trade a small account and barely meet your margin requirements, open-trade drawdown may be needed for risk assessment.
If you use an open-trade equity curve, it pays to find out how frequently the open-trade drawdown is measured. The higher the measurement frequency, the more accurately you can track your drawdown variations over the course of your trades. As shown below, I currently use Myfxbook to track my live trading performance, where both the open-trade and closed-trade equity curves (yellow and red, respectively) are updated daily.
Despite these advantages, closed trade drawdown is easier to compute and is commonly featured in trading software. For the remainder of this post, we will focus on closed trade drawdown.
$ Drawdown vs. % Drawdown
During strategy development, where I backtest with a fixed lot size, I measure drawdowns in absolute dollar terms. Percentage drawdowns would be unsuitable because the effect of each trade on the account equity would vary as the account grows/shrinks.
If you develop with variable position sizing, or wish to measure drawdowns as a fraction of equity, percentage drawdowns will be more appropriate.
Three Ways to Measure Drawdown
The following drawdown measures can be easily computed using the closed trade profits/losses from MT4’s default strategy tester report. You can open the report in Excel and carry out the computations. Two equity curves will henceforth be used to compare the different drawdowns. Both have a profit factor of 1.25 over a 10-year period, but exhibit very different profiles. The first is a 15-minute trend following strategy that is flat for extended periods, but contains a handful of big winers.
The second is an hourly countertrend strategy with a deep drawdown at the start, but is otherwise consistently profitable.
Let’s dive into the metrics!
1. Maximum Drawdown
This is the most common drawdown metric; practically every trading platform uses it. To get your maximum drawdown, simply select the largest value from the series of drawdowns obtained over the course of your backtest/live trading.
Maximum drawdown is certainly a psychologically satisfying measure, since it implies worst case trading conditions. For capital allocation purposes, using maximum drawdown is a prudent approach.
If you wish to compare strategy performance, however, maximum drawdown falls short. By selecting a single maximum value over the course of your backtest, you are overestimating your strategy’s typical drawdowns. A particularly bad sequence of trades may ruin an otherwise excellent backtest. Consider the maximum drawdowns from the two equity curves above.
The countertrend strategy has almost double the maximum drawdown, occurring where a few large losers were clustered together. Is it fair to penalize its overall performance because of a bad string of trades? Personally, I’d prefer trading it over the trend strategy.
Performance comparisons aside, the predictive value of your strategy’s maximum historical drawdown is often overstated. Drawdown is a consequence of the magnitude of your losing trades, as well as the sequence of losing trades. If your backtest contains a large number of trades, you may have a reliable estimate of the size of your average losing trade. Your trade sequences, however, are largely affected by market conditions and are unlikely to be replicated in future. This supposed ‘worst case’ drawdown is a poor estimate of future risks, and may be giving you a false sense of security.
A metric that better reflects a strategy’s typical drawdowns would certainly be handy.
2. Average Drawdown
Over the test period, this is the average of all the drawdown values after each closed trade. Since every drawdown value will affect the overall average, average drawdown gives you a better idea of what your strategy’s ‘normal’ drawdown is.
Average drawdown also takes your strategy’s stagnation into account. Stagnation is the time between consecutive equity highs, and is a measure of the consistency of your strategy. A long period of stagnation will create a series of non-zero drawdowns, which will add to the overall average drawdown. Let’s evaluate the two equity curves using average drawdown.
The countertrend strategy still has a higher drawdown, although it’s a much tighter contest this time. By using the average instead of maximum drawdown, the countertrend strategy’s multiyear profitable run mitigated much of its deep drawdowns at the start.
What if you’re a more conservative trader? Surely the deep drawdowns hurt more than the profitable run-ups. If you want to place more emphasis on the drawdowns, the Ulcer Index may be what you need.
3. Ulcer Index
The Ulcer Index was developed by Peter Martin in 1987 to circumvent some of the limitations of using standard deviation to measure risk. For the mathematically-inclined, this is the root-mean-square of the drawdowns after each closed trade. Like the average drawdown, every drawdown value is involved in the computation. The Ulcer Index can be calculated as follows:
- Using your closed trade history, obtain the drawdown after each trade
- Square each drawdown value
- Calculate the average squared drawdown by summing up all the values and dividing by the number of trades
- Take the square root of the average squared drawdown
The squaring of drawdowns gives higher weighting to the large values. This makes perfect sense, since the large drawdowns tend to cause stress and ulcers (hence its name). The Ulcer Index could be the ‘golden middle’ between the average and maximum drawdown measures; it gives a good estimation of your strategy’s typical drawdowns, and the higher weighting of large drawdowns makes it conservative.
Compared to the average drawdown, how much more conservative is the Ulcer Index?
The countertrend strategy’s average drawdown is 28% higher than that of the trend strategy. Using the Ulcer Index, the difference is 56%.
Measuring Risk-Adjusted Returns
Returns and risk should always be evaluated in tandem. Now that you have decided how to measure your drawdowns; how about returns? I usually use a simple metric for returns — the annual rate of return (AROR). Depending on your trading timeframe, a monthly or even weekly rate of return may be more appropriate.
To adjust for risk, simply take the AROR and divide it by the drawdown. You can use this robust performance metric to rank the performance of different strategies and markets. As described here, I used the AROR/Ulcer Index ratio to select strategies during portfolio composition.
Using Drawdown for Capital Allocation
Since maximum drawdown is the most conservative, many traders use it to compute capital requirements. An alternative is to use a multiple, for example 1.5x, of the average drawdown or Ulcer Index to estimate worst-case drawdowns. I prefer this approach since it remains conservative, yet helps me circumvent the limitations of using maximum drawdown. For most practical trading applications, it probably makes little difference.
Measuring drawdowns is an essential part of risk management, and is especially crucial when you have just started trading a strategy. If you suffer a 50% loss of capital, you will need a 100% return just to break even!
The choice of drawdown metric ultimately boils down to personal perference. I like the Ulcer Index for the reasons mentioned above, although maximum drawdown is far more conveniently obtained. I think the ideal drawdown metric would be a distribution showing the probability of reaching each drawdown level. For example, what is the % probability of reaching a $1000 drawdown? An exponential curve can be plotted to show the drawdown probabilities, like the one below.
Obtaining this distribution requires effort, and is a story for another day. Regardless of which metric you choose, err on the side of caution since your backtest can never fully predict future performance.
It is good to include the equation of average drawdown. You mentioned it also takes into account of stagnation but the content does not discuss much. Thank you!
it is the average of the drawdown values obtained at each sampling