Edge Matrix Quantitative Validation Report — Portfolio (5 Tests)

+648.0%

Total Return

32.6%

Annual CAGR

5.9%

Max Drawdown

5.6×

Calmar Ratio

70.2%

Win Rate

0.787R

Expectancy

1.55:1

Reward:Risk

8.42

T-Statistic

This system demonstrates a statistically confirmed positive expectancy across 7.13 years of backtest data encompassing 685 closed positions on MULTI MIXED. The strategy achieves 1.55:1 reward-to-risk, operating 30.9 percentage points above its mathematical breakeven threshold of 39.3%. Annualised CAGR of 32.6% relative to 5.9% maximum drawdown yields a Calmar ratio of 5.6×, significantly exceeding the professional benchmark range of 3–5×. Monte Carlo validation across 2,000 block-bootstrap simulations confirms structural consistency under adverse trade sequencing. 17 of 19 validation tests pass. 1 area of note: CVaR tail risk at 3.6× average loss.

Section I

Analytical Findings & Observations

F.1

Temporal Stability Strength

The strongest dimension is Temporal (100/100). All 10 of 10 equal calendar periods generated positive returns across the backtest horizon. No losing period detected. Return consistency CV of 0.19 confirms profitability is spread evenly, not concentrated in a single regime window. This score measures temporal robustness — a strategy that only profits in one or two periods may be regime-dependent rather than exhibiting a repeatable edge.

F.2

Tail Risk Elevation Finding

CVaR (95%) measures 3.62× the average loss — below the 70-point threshold. The worst 35 trades (5% of sample) average $434.86 against a $120.18 mean loss. CVaR 99%: 5.15× average loss. Tail risk level: HIGH. This elevation is partially structural: with a 1.55× RR ratio, the absolute average loss is modest, making tail events appear proportionally larger in ratio terms. Active monitoring of worst-case trade magnitude under live conditions is advisable.

F.3

MC Drawdown Envelope Observation

Block-bootstrap Monte Carlo (2,000 simulations, block size 8, AC lag-1: -0.041) produces a 95th-percentile maximum drawdown of 12.2% — approximately 2.1× the historical 5.9%. P50: 6.5%, P99: 15.7%. The historical sequence sits at the 39th percentile of the simulated distribution, confirming results were not predicated on an unusually favourable trade ordering. Risk management sizing against the MC P95 envelope rather than historical DD is advisable for live deployment.

F.4

Execution Sensitivity Observation

Under 10% execution degradation (wider spreads, adverse fills), expectancy retains 0.82× of its backtest level. At 0.787R base expectancy, the strategy remains profitable under this stress test. Forward testing under broker-accurate spread conditions is standard practice before capital deployment.

Development Considerations

Areas for Further Development

Tail Risk Reduction

Expected Shortfall scored 46/100. The worst 35 trades (5% of sample) average $434.86 against a $120.18 mean loss — a 3.6× ratio. CVaR 99% is 5.2×. Examine whether these outlier losses share a common trigger: specific session, news window, or spread spike. Adding a maximum per-trade loss cap at 2× average loss would eliminate the tail without affecting the remaining 97% of trades.

Profit Distribution

Concentration Risk scored 68/100. Top 10% of winning trades generate 48.1% of total profit; the single largest winner is 1.9% of total P&L. High concentration isn't necessarily a problem, but it is a dependency: the edge quality depends on capturing those outlier wins. Before live deployment, verify your exit logic isn't cutting those winners prematurely in the backtest — a take-profit that is too tight leaves edge on the table. Also examine whether the top winners share a common pattern (strong trend, post-news reversion, specific session): if so, you may be able to scale up on those setups specifically.

Streak Resilience

Consecutive Loss scored 79/100. Max losing streak of 5 against expected 5.4 (ratio 0.93×). Loss clustering ratio of 1.06 — losses are not clustering abnormally. Worst streak damage required 5.4× average wins to recover. Streak behaviour is within statistical expectations for this strategy.

Section II

Validation Test Results

100

Temporal

100

Statistical

Drawdown

Capital

Edge

100

Edge

Concentration

100

Ulcer

Sample

100

Return

100

Consecutive

Cliff

100

Execution

Holding

Edge

Expected

Temporal Stability 100

EXCELLENT — All 10 periods profitable

All 10 of 10 equal calendar periods generated positive returns across the backtest horizon. No losing period detected. Return consistency CV of 0.19 confirms profitability is spread evenly, not concentrated in a single regime window. This score measures temporal robustness — a strategy that only profits in one or two periods may be regime-dependent rather than exhibiting a repeatable edge.

Statistical Significance 100

Highly significant edge (t=8.42, 99% confidence)

T-statistic of 8.42 exceeds the 99% two-tailed significance threshold of 2.576. (p = 0) Probability of results arising by chance is below 0.1%. The edge is statistically real given this 685-trade sample. This test applies a Welch t-test on the profit distribution and requires the mean return to be significantly different from zero.

Drawdown Analysis 93

MINIMAL drawdown (5.9% max, 1.5% avg episode)

Maximum drawdown of 5.9% with an average episode depth of 1.5%. The median recovery speed is 5.0 days per 1% of drawdown. 48 drawdown episodes were detected. No single episode dominates the overall drawdown profile, indicating consistent rather than event-driven risk. This test scores three components: max DD depth (50%), average episode depth (30%), and recovery quality in days per 1% of DD (20%).

Capital Efficiency 88

EXCELLENT — 32.6% annual, Calmar 5.6

Compound annual growth rate of 32.6% against 5.9% maximum drawdown. Calmar ratio of 5.6× significantly exceeds the professional benchmark of 3–5×. CAGR is computed using true compound growth (end equity / start equity)^(1/7.13 years), not simple annualisation. Capital efficiency rewards strategies that generate high risk-adjusted returns relative to their worst historical loss.

Edge Temporal Decay 96

STABLE — Edge is consistent with no meaningful decay

Rolling expectancy regression slope is positive (normalised +0.7), indicating the edge has strengthened over the backtest horizon. Second-half expectancy exceeds first-half by 47% (ratio 1.47). Profit factor across four quartiles (3.365, 3.89, 3.977, 3.505) is approximately stable (normalised slope 0.04). This test detects whether a strategy's edge is eroding over time — a critical check for curve-fitted systems that perform well historically but deteriorate as market conditions evolve.

Edge Consistency 100

EXCELLENT — Edge performs consistently across all conditions

Win rate variance across weekdays falls within acceptable bounds. No structurally unprofitable weekday detected. Profit factor log-variance of 0.3196 and day-of-week variance of 7.7504 indicate edge quality does not fluctuate meaningfully by session day. This test checks whether the strategy's edge is consistent across all trading sessions or is heavily dependent on specific days or conditions.

Concentration Risk 68

FAIR — Acceptable distribution

Top 10% of winning trades account for 48.1% of total profit — above the 30% ideal-diversification threshold but below the 50% concentration-risk threshold. The largest single winner represents 1.9% of total profit, confirming no individual trade disproportionately sustains the overall result. Profit distribution is scored on two components: top-decile share (80%) and single largest winner share (20%). A well-distributed profit profile indicates genuine repeatable edge rather than lottery-dependent returns.

Ulcer Index 100

Excellent drawdown profile (UI: 1.1%)

Ulcer Index of 1.1% represents minimal cumulative drawdown pain. Max DD: 5.9%, avg DD: 0.51%, time underwater: 34.5%. Unlike maximum drawdown which captures a single worst point, the Ulcer Index integrates both depth and duration of all underwater periods — a UI below 5% indicates drawdowns are shallow, brief, and recover quickly.

Sample Adequacy 93

EXCELLENT — 685 trades over 7.1y exceeds requirements

685 trades over 7.1 years exceeds the academic minimum of 125 trades. MinTRL (minimum track record length) statistic: 30. Confidence factor applied to all other tests: 1. Sample adequacy is the foundational test — a backtest with insufficient trades cannot produce statistically valid conclusions regardless of how impressive the individual metrics appear.

Return Autocorrelation 100

Returns are independent (AC: -0.041)

Lag-1 autocorrelation of -0.041 (lag-2: -0.058) — no meaningful serial dependence. Returns are effectively independent. No martingale signature or hidden clustering pattern detected. Significant autocorrelation can indicate position-sizing escalation or regime-dependent behaviour that inflates backtest results.

MC DD Stability 100

EXCELLENT — Highly stable under randomization

Under 1,000 permutation shuffles of the exact trade sequence, the 95th-percentile maximum drawdown reaches 7.3% — a 1.2× expansion from the 5.9% historical figure. 99th percentile: 9.0%. A ratio below 2.0× confirms the strategy does not rely on a particularly favourable trade ordering. This test measures whether the backtest drawdown is structurally representative or a statistical artefact of a lucky sequence of trades.

Consecutive Loss 79

GOOD — Healthy adversity handling

Maximum consecutive losing streak of 5 trades against a statistically expected maximum of 5.4 (ratio 0.93×). Loss clustering ratio of 1.06 — losses are not grouping more frequently than random distribution predicts. Worst streak required approximately 2 average wins to fully recover (damage ratio 5.4×). This test checks four dimensions: observed vs expected streak length (30%), loss clustering (25%), worst streak damage (25%), and recovery speed (20%).

Cliff Ratio 92

EXCELLENT — Healthy risk profile

95th-percentile loss of $495.7 is 2.67× the average win of $185.69 — a healthy ratio indicating tail losses are not catastrophically larger than typical wins. Average loss: $120.18. Single largest loss ($708.26) is 1.43× above the P95 level — no structural outlier. This test uses the 95th-percentile loss rather than the single largest loss as the primary metric, making the score more robust to one-off broker anomalies while still flagging structural outliers separately.

MC Robustness 90

HIGHLY ROBUST — Results hold under all simulated conditions

Block-bootstrap Monte Carlo (2,000 simulations, block size 8 preserving serial structure, AC lag-1: -0.041) produces a survival rate of 100.0% across all simulations. Coefficient of variation: 0.091. MC DD envelope — P50: 6.5%, P95: 12.2%. No position-scaling pattern detected — the strategy applies approximately uniform lot sizing regardless of recent outcomes. Block bootstrap preserves the serial correlation structure of returns (unlike naive IID resampling), producing more realistic stress scenarios.

DD Endurance 90

RESILIENT (0.8x penance, 37% underwater)

Median penance ratio of 0.84× substantially outperforms the theoretical IID expectation of 3.0× (Bailey & López de Prado, 2014). A ratio below 1.0 means recovery consistently takes less time than the drawdown formation period — a strong signal of genuine edge. Time spent underwater: 36.7%. Longest DD episode: 186d 23h 12m (7.2% of backtest). Longest recovery: 109d 0h 58m. 48 episodes detected. Scored on four components: penance ratio (35%), longest DD as % of backtest (25%), % time underwater (25%), and recovery consistency CV (15%).

Execution Cost Sensitivity 100

EXCELLENT — Edge survives execution degradation

Under a 10% uniform execution degradation scenario (wins reduced 10%, losses increased 10%), per-trade expectancy retains 0.82× of its backtest level. Original expectancy: $94.6 → degraded: $77.98 (17.6% impact). Strategy remains profitable under this stress test. At 0.787R base expectancy, the strategy retains meaningful cushion against real-world execution costs.

Holding Time 88

GOOD — Winners held 1.1x longer than losers

Losers are held 0.9× longer than winners on average (winners: 9h, losers: 8.1h). Hold time ratio is within acceptable bounds. Discipline tier: GOOD. Median ratio: 0.89×. At the current 0.787R expectancy, this does not materially impact performance.

Edge Quality 82

GOOD — Strong statistical edge

Expectancy of 0.787R per trade reflects a genuine and strong edge. Win rate of 70.2% operates 30.9 percentage points above the mathematical breakeven of 39.3%. Largest win is 9.1× the average win — some concentration in large outlier wins. Edge quality is scored on four dimensions: expectancy (35%), repeatability (30%), win rate margin (15%), and execution decay (20%).

Expected Shortfall 46

WEAK — High tail risk (worst 5%: 3.6x avg loss)

Section III

Portfolio Composition

This report evaluates a combined portfolio of the following constituent backtests. All validation metrics above are computed on the combined, chronologically-merged trade stream.

#	Strategy	Symbol	Timeframe	Trades
1	ATG EA 30.0	XAUUSD	M15	243
2	ATG EA 30.0	XAUUSD	H1	133
3	ATG EA 30.0	XAUUSD	H1	114
4	ATG EA 30.0	XAUUSD	H1	104
5	ATG EA 30.0	XAUUSD	M15	91
	Total · 5 strategies			685