Apex
Executions

Standard Sharpe ratios inflate with every parameter trial run during research. Our Deflated Sharpe Ratio (DSR) adjusts for the number of trials, return skewness, and kurtosis — producing a conservative, statistically honest performance measure. Paired with the Probability of Backtest Overfit (PBO), we mathematically bound the probability that any result is merely a lucky artifact of the parameter search.

Walk-forward validation splits the historical record into sequential in-sample and out-of-sample windows. Strategy parameters are optimized on the in-sample period, then frozen and tested on the following unseen period — with no look-back allowed. This process repeats across the full price history, producing a realistic out-of-sample equity curve rather than a curve-fitted simulation.

Block bootstrap resampling preserves the autocorrelation structure of financial returns while generating thousands of alternative price paths from the same underlying data. If a strategy is genuinely skilled, it performs across all resampled scenarios — not just the specific historical sequence it was developed on. Strategies that profit only from one particular market path are filtered out.

Combinatorially Purged Cross-Validation (CPCV) is the most rigorous form of strategy evaluation available. The historical record is divided into multiple folds with embargo periods between them to prevent information leakage. Every possible combination of training and test sets is evaluated, producing a distribution of out-of-sample performance paths rather than a single pass/fail number. If the distribution is tight and consistently positive, the strategy passes.

Monte Carlo simulation reorders actual trade sequences thousands of times to build empirical distributions of Sharpe ratio, maximum drawdown, and profit factor. Instead of a single point estimate from one historical path, every key metric is presented with confidence intervals. A strategy that shows excellent statistics in its exact historical sequence but wide confidence intervals is flagged as potentially path-dependent.

The Kelly Criterion derives the theoretically optimal position size for each strategy given its win rate, average win, and average loss. We implement fractional Kelly (typically half-Kelly) to account for estimation error and reduce drawdown volatility. Per-strategy and per-ticker drawdown limits override Kelly sizing when equity curves breach predetermined thresholds — automatically halting or demoting any strategy showing signs of regime change.

Market regimes change. A strategy that only performs in trending bull markets is not robust — it is a bull market passenger. Every strategy's performance is sliced by regime (bull, bear, lateral) and required to show consistent results across all conditions. Strategies that concentrate their edge in a single regime are flagged, demoted, or halted until broader regime coverage can be demonstrated.

A plain shuffle mixes calm and volatile periods together, destroying the way real drawdowns cluster. We simulate thousands of alternate market histories using a regime-persistent model — a Markov chain over trending, choppy, and volatile conditions — so each synthetic path respects how regimes actually transition, not just their long-run average. The result is a percentile cone of plausible outcomes, laid directly over the real regime history the strategy actually traded through. Advisory today, feeding tomorrow's live drift monitoring.

A strategy can clear every statistical gate and still just be a levered bet on the market going up. Gate 7 backtests a plain buy-and-hold of the same ticker over the identical bars and costs, then measures alpha — the return left over after subtracting market exposure (beta). A one-sided block-bootstrap test on the excess-return series confirms that edge is statistically real, not noise dressed up as skill. No alpha, no pass — regardless of how good the raw Sharpe looks.