The math behind the verdict.

The original trade sequence is one of many possible orderings. Monte Carlo shuffles the order (preserving the PnL of each trade) thousands of times and re-computes the equity curve for each shuffle. Read the distribution of outcomes — the worst-case drawdown at the 95th percentile is the relevant number, not the original drawdown.

Limit: Monte Carlo here destroys serial correlation. If the strategy's edge comes from streak-following behavior, MC understates it. Use the bootstrap with block size > 1 (§ 01.03) to preserve serial structure.

Split the data sequentially into in-sample (IS) and out-of-sample (OS) windows. This is a holdout-stability check — no parameters are re-optimised between windows (true walk-forward optimisation would re-fit the strategy on each IS window). Walk-Forward Efficiency compares OOS to IS performance:

WFE = (avg OS return-per-trade / avg IS return-per-trade) × 100

Per-trade returns are used so the larger IS window isn't credited with more return simply for holding more trades — comparing window totals would penalise the strategy for the train/test split rather than for any real edge decay. A WFE above 70% suggests the edge survives unseen data; below 50%, suspect overfitting. Five non-overlapping 70/30 windows by default — adjustable in the dashboard.

Distinct from Monte Carlo: bootstrap samples trades with replacement. A single trade can appear twice in one resample and not at all in another. The result is a confidence interval on every metric — not just a "worst case" number.

Block bootstrap. Setting block size > 1 samples contiguous runs of trades. This preserves serial-correlation structure that simple bootstrap destroys. If serial correlation (§ 04.02) is meaningful, use a block size of 5–20.

CI_95(metric) = [pct(metric_dist, 2.5%), pct(metric_dist, 97.5%)]

What if execution decays? Stress injection applies worst-case modifications to the trade list in a fixed order:

1. Skip best % — remove the top X% of winning trades (those "lucky" home runs you couldn't have anticipated)
2. Add random losses — inject K losses sized at the strategy's average loss
3. Extra loss % — multiply existing losses by (1 + X%) to model deeper drawdowns
4. Slippage pips — subtract a per-trade execution cost

The order matters. Compare the original metrics to the stressed metrics; a strategy that loses its edge after 2 pips of slippage was probably never tradable in size.

Bucket trades two ways: by calendar (year / quarter / month) and by rolling-volatility tercile (low / mid / high stdev of PnL over the trailing N trades). Compute return, win rate, and drawdown per bucket.

The "top contributors" table reveals where PnL is concentrated. If 60% of the strategy's PnL comes from a single quarter, the edge isn't durable — it's a regime artifact.

The maximum expected loss with 95% confidence. If VaR is $1,000 per trade, there is a 5% probability the next trade loses more than $1,000. Computed as the 5th percentile of the per-trade PnL distribution.

When things go wrong (the worst 5% of trades), how bad on average? CVaR is the mean of the per-trade PnL distribution conditioned on being worse than VaR. Captures tail risk that VaR misses.

The probability the account loses all its capital given the strategy's edge. We express the per-trade expectancy as an edge in units of the average loss (the risk staked per trade), and the starting capital as a count of those units:

edge = expectancy / avg_loss;   units = capital / avg_loss
RoR = ((1 − edge) / (1 + edge)) ^ units,   bounded to [0, 1]

A positive edge makes the base < 1, so more capital (more units) drives ruin toward zero; a zero-or-negative edge makes ruin certain (1). This always lies between 0% and 100% — unlike the naïve ((1−W)/W) form, which exceeds 1 (an impossible probability) whenever the win rate is below 50%. Anything above 5% is a flashing warning; above 20% means stop trading.

The optimal fraction of capital to risk per trade for long-run geometric growth.

K = W - (1 - W) / R

Where W is win probability and R is the win/loss ratio. Practical traders use half Kelly (K/2) to reduce volatility — full Kelly is mathematically optimal but emotionally untradable.

Ralph Vince's Optimal F: the fraction of capital that maximises geometric growth over the actual distribution of past trades — not just the average win rate and ratio. We search f ∈ (0, 1] for the value that maximises the Terminal Wealth Relative:

HPR_i = 1 + f × (pnl_i / |worst loss|);   TWR = ∏ HPR_i
Optimal F = argmax_f  TWR

Wald–Wolfowitz runs test on the win/loss sequence — a run is a streak of same-sign results. Fewer runs than chance (negative Z) means results cluster: wins follow wins, losses follow losses (trend persistence). More runs than chance (positive Z) means they alternate (mean reversion).

Z = (runs − E[runs]) / √var
E[runs] = 2·n₁·n₂ / n + 1
var = 2·n₁·n₂·(2·n₁·n₂ − n) / (n²·(n − 1))

where n₁ = winning trades, n₂ = losing trades, n = n₁ + n₂.

Pearson correlation of trade i's PnL with trade i+1's PnL. Near zero means trades are independent; far from zero means past trades predict the next one.

Asymmetry of the PnL distribution. Negative skew (frequent small wins, occasional massive losses) is the "picking up pennies in front of a steamroller" profile — popular and dangerous.

Tailedness. High excess kurtosis means more outlier events than a normal distribution predicts. Strategies with high kurtosis blow up in ways VaR doesn't anticipate.