Monte Carlo Simulation for Trading Strategies

Why one equity curve is not enough

A backtest produces the trades in the order history happened to deliver them. If the five largest losses had occurred consecutively rather than spread across three years, the drawdown would have been far deeper and you might have stopped trading. That alternative ordering was just as likely.

Backtest result (the historical ordering):
   Total return        +64%
   Maximum drawdown    -18%
   Longest underwater   7 months

Monte Carlo over 10,000 reshuffles of the same trades:
   Median return          +61%
   Median max drawdown    -24%
   75th percentile DD     -29%
   95th percentile DD     -38%
   99th percentile DD     -46%
   Worst simulated DD     -57%
   Probability of DD > 30%   about 22%

The strategy has not changed.  The historical -18% was
a favourable draw, and planning around it would have
underestimated the risk by roughly half.

Resampling methods

Trade shuffling

Reorder the historical trades randomly. Preserves the exact set of outcomes, changes only the sequence. The simplest and most common method.

Bootstrap with replacement

Draw trades randomly with replacement, so some appear multiple times and others not at all. Produces a wider distribution and reflects that your sample is itself a draw.

Block bootstrap

Resample blocks of consecutive trades rather than individual ones. Preserves clustering and serial correlation, which matters for most real strategies.

Daily return resampling

Resample daily strategy returns rather than trades. Useful for strategies with overlapping positions where trades are not cleanly separable.

Parametric simulation

Fit a distribution to trade outcomes and draw from it. Convenient but imposes a distributional assumption that financial returns usually violate.

Randomised entry timing

Shift entry dates by a few bars to test whether results depend on precise timing. A different question, but a valuable robustness check.

Running a simulation correctly

1. 1

   Express trades in R or in percentage terms

   Using currency amounts confuses position sizing changes with strategy performance. R multiples make the analysis clean.

2. 2

   Apply your actual position sizing rule

   Compound the equity path using fixed fractional sizing, so position sizes shrink after losses exactly as they would live. This materially changes the drawdown distribution.

3. 3

   Run at least 10,000 iterations

   Fewer produces unstable tail estimates, which is precisely the part you care about.

4. 4

   Use block resampling if trades cluster

   If your strategy opens several correlated positions at once, or if losses cluster in specific conditions, independent shuffling understates risk substantially.

5. 5

   Record the full distribution

   Median, 75th, 95th, and 99th percentile drawdowns; the probability of exceeding your tolerance; and the distribution of time underwater.

6. 6

   Re-run at different position sizes

   Find the risk per trade at which the 95th percentile drawdown matches your tolerance. That is your sizing answer.

What Monte Carlo cannot tell you

• It assumes the future resembles the sample. If the edge decays or the regime changes, the simulated distribution describes a world that no longer exists.
• Simple shuffling assumes independence. Real trades cluster: losses arrive together in adverse conditions. Block resampling partially addresses this; nothing fully does.
• It cannot fix a biased backtest. If the underlying trades came from an overfitted or look-ahead-contaminated test, the simulation propagates that error faithfully.
• It ignores unseen tail events. If your sample contains no crisis, the simulation will not invent one. Add a stress scenario manually.
• It says nothing about whether the edge is real. It characterises variance given the trades, not whether those trades reflect a genuine effect.
• Results depend on the sample size. With 50 trades, the resampled distribution is extremely wide and only tells you that you do not have enough data.