To do this, we calculate the percentage of scenarios in which maximum drawdown is likely exceed our risk threshold. However, we can say with some level of confidence that the maximum drawdown experienced won’t exceed our threshold. We won’t be able to totally constrain our results on expected drawdown, as the value for max drawdown could fall within a wide range. If we want to use drawdown as a risk metric, we need to deal with its inherent uncertainty.
The maximum drawdown varies from less than 30% to over 70%! This is a huge range of possible values. Reordered = np.random.permutation(returns) We’ll demonstrate this below by shuffling the order of S&P returns and examining the resulting equity curves.Ĭurves = pd.DataFrame(index=returns.index) Unlike compounded returns, the value for maximum drawdown depends on the order in which returns are realized. However, there are limitations to using drawdown as a risk metric. It’s a much more visceral experience to watch one’s account balance drop from $100,000 to $50,000 one that can de-rail trading strategies. In practice, few traders base their decisions whether to follow their strategy on the standard deviation of returns or similar measures of volatility. In order to protect from the possibility of a 25% drawdown, we’d need to scale back the leverage from our optimal f value by almost 9 times!Īs noted above, drawdown is a good risk metric for practitioners because this it most directly impacts their emotions. Geometric Holding Period Return: 0.01427% Spy_f_bounded = get_f_bounded(spy_returns, drawdown_limit=25) _ghpr = _twr ** (1 / len(equity_curve)) - 1ĭf = pd.DataFrame(columns=) _drawdown = eq_series / eq_series.cummax() - 1ĭef max_drawdown(equity_curve, percent=True):Ībs_drawdown = np.abs(drawdown(equity_curve))
Code to calculate max drawdown code#
Source code for this value has been provided as well feel free to substitute it in. We use maximum drawdown as a proxy for risk because this is the number that investors “feel”, which tends to drive allocation decisions for emotional reasons.Īn alternative metric is the Ulcer Index, a root-mean-squared calculation based on drawdown that takes into account both drawdown severity and duration. Let’s see how increasing position size increases drawdown by constructing a curve similar to the one for GHPR for maximum drawdown. We left off with an example showing that investing in SPY at optimal f would cause some extreme discomfort along the way. Read here and feel free to follow along with provided notebook. This post will help traders maximize their gains while still getting their beauty rest! Since a 20% retracement from peak equity causes most investors to start tossing in their sleep, this approach doesn’t seem very realistic. This would have yielded the greatest compounded rate of return, but would have induced a 97% (!!!) max drawdown along the way. To realize the greatest return on capital, an investor in SPY since its inception should have used over 3x leverage to buy in.
Code to calculate max drawdown series#
While passing over the series we keep track of two numbers - the peak of the series and the maxDrawdown in price between peak and i.What does “optimal” mean, anyway? In the first part of this series, we discovered that the staked fraction of capital that yields the greatest compounded returns also yields a less-than-optimal level of drawdown. Iterating over each index i of the series in order, the maximum decline ending at point i will start at the highest point of the series so far. Instead of comparing every value with every other value, we can exploit the sequential requirement and make only n - 1 comparisons: var peak = 0 įor ( var i = 1 i dif ? maxDrawdown : dif For series covering a long period of time or with a great deal of granularity, this algorithm might be too slow even for a fast computer. The number of comparisons increases faster than n - if there are 100 values, 4950 comparisons are needed, while 200 values requires 19900 comparisons. If the series has n prices, n*(n - 1)/2 comparisons are needed (the number of comparisons done during the ith pass through the inner loop is n - i - 1 the sum of all those comparisons is 1 + 2 + 3 +.
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