DrawdownBootstrap: Monte Carlo of the maximal drawdown - library for MetaTrader 5

DrawdownBootstrap.mqh estimates how deep the drawdown of an account or a strategy can get over the coming months, from its past daily results. The worst drawdown of a backtest happened once, in one order of events; a Monte Carlo of the same results in other orders shows the range to expect, and how often the worst of the history is exceeded.

Usage

#include <DrawdownBootstrap\DrawdownBootstrap.mqh>

double days[];                      // daily results in money (or in percent)
// ... fill the days ...
double dd[];
CDrawdownBootstrap::Run(days, 252, 10000, 10.0, 12345, dd);   // horizon, paths, mean block, seed
double p95 = CDrawdownBootstrap::Quantile(dd, 0.95);          // 1 period in 20 goes deeper than this
double worst = CDrawdownBootstrap::MaxDrawdown(days);         // the drawdown of the history itself

How it works

• Stationary bootstrap (Politis and Romano, 1994): a simulated path starts on a random day, continues with the following days, and jumps to a new random day with probability 1 / meanBlock. Whole stretches of days are kept together, so losing streaks and days when several positions lost at once stay in the simulation; drawing single days independently would make the drawdowns look smaller than they are.
• For each path the largest fall of the cumulated results from their peak is recorded. Quantile() gives any percentile of these drawdowns, with linear interpolation.
• CSeededRandom is a small mulberry32 generator: the same seed gives the same simulation on every computer, so a result can be checked again.
• Days are taken as they come: results in money assume fixed lots; for lots that grow with the balance, pass daily results in percent of the balance.

Example

The script DrawdownBootstrapExample.mq5 takes the daily closed results of this account (all of them or one magic number), or a CSV file of daily results, simulates 10 000 paths of one year and prints the percentiles of the drawdown in money and as a percent of a capital, and the share of the paths that go deeper than the worst drawdown of the history (picture 1).

Checked

On 1 041 days of results, three runs (2 000 paths of 252 days with blocks of 10 days, 500 paths of 63 days with single days, 300 paths of 500 days with blocks of 25 days, three different seeds) gave the same drawdown for every path as an independent Python version of the same algorithm, within 2e-11.

Files

DrawdownBootstrap.mqh goes to MQL5\Include\DrawdownBootstrap, DrawdownBootstrapExample.mq5 to MQL5\Scripts\DrawdownBootstrap.