Momentum Omega Quantitative Backtesting Methodology & Simulation Reference

The Momentum Omega alpha calculation executes across three mathematical stages:

Step 1: Return Horizon Quantification

For each asset $i$ at day $t$, two distinct horizon returns are evaluated using split- and dividend-adjusted closing prices:

$$R_{\text{long}}(t) = \frac{P_t}{P_{t - N_{\text{long}}}} - 1.0 \quad (N_{\text{long}} = 252 \text{ trading days})$$

$$R_{\text{short}}(t) = \frac{P_t}{P_{t - N_{\text{short}}}} - 1.0 \quad (N_{\text{short}} = 21 \text{ trading days})$$

Step 2: Raw Momentum Differential

The raw differential measures intermediate trend persistence relative to short-term price velocity:

$$\Delta_{\text{momentum}}(t) = R_{\text{long}}(t) - R_{\text{short}}(t)$$

Step 3: Volatility Normalization (126-Day Standard Deviation)

To prevent high-beta, highly erratic equities from dominating rankings, the differential is scaled by historical return dispersion over volatility window $W_{\text{vol}} = 126$ trading days:

$$r_{t-k} = \frac{P_{t-k}}{P_{t-k-1}} - 1.0, \quad \bar{r} = \frac{1}{W_{\text{vol}}} \sum_{k=0}^{W_{\text{vol}}-1} r_{t-k}$$

$$\sigma_{126}(t) = \sqrt{\frac{1}{W_{\text{vol}}} \sum_{k=0}^{W_{\text{vol}}-1} (r_{t-k} - \bar{r})^2}$$

$$\text{Score}_{\Omega}(t) = S_{\text{raw}}(t) = \frac{\Delta_{\text{momentum}}(t)}{\sigma_{126}(t)}$$

Candidate equities are partitioned and verified through technical confirmation:

• Long Candidate Pool: Equities exhibiting positive score conviction ($S_{\text{raw}}(t) > 0.0$), ranked in descending order of conviction.
• Short Candidate Pool: Equities exhibiting negative score conviction ($S_{\text{raw}}(t) < 0.0$), ranked in ascending order.
• Intraday 15m EMA Gatekeeping: Long candidates must verify that intraday 15-minute price action is trading above key EMA levels ($EMA_{50} > EMA_{200} > EMA_{800}$), tagging candidates with an AAA regime rating.
• Strict Look-Ahead Defense: Indicators calculated on day $T$ close are strictly barred from execution until day $T+1$ open.

To ensure that reported alpha is robust across liquidity regimes and lookback horizons, Momentum Omega is backtested across an exhaustive 35-scenario parametric matrix:

Dimension 1: Liquidity & Traded Volume Tiers (Groups A through G)

• Group A: USD 10M $\le \text{ADV} <$ USD 25M (Micro/Small-Cap).
• Group B: USD 25M $\le \text{ADV} <$ USD 50M (Small-Cap).
• Group C: USD 50M $\le \text{ADV} <$ USD 100M (Small/Mid-Cap).
• Group D: USD 100M $\le \text{ADV} <$ USD 250M (Mid-Cap).
• Group E: USD 250M $\le \text{ADV} <$ USD 500M (Upper Mid-Cap).
• Group F: USD 500M $\le \text{ADV} <$ USD 1.0B (Large-Cap).
• Group G: $\text{ADV} \ge$ USD 1.0B (Mega-Cap).

Dimension 2: Lookback Horizon & Parameter Variations (Indices 1 through 5)

• Index 1 (12M Secular Trend): $N_{\text{long}} = 252$, $N_{\text{short}} = 21$, $W_{\text{vol}} = 126$.
• Index 2 (9M Intermediate Trend): $N_{\text{long}} = 189$, $N_{\text{short}} = 21$, $W_{\text{vol}} = 94$.
• Index 3 (6M Medium Trend): $N_{\text{long}} = 126$, $N_{\text{short}} = 15$, $W_{\text{vol}} = 63$.
• Index 4 (3M Short-Intermediate): $N_{\text{long}} = 63$, $N_{\text{short}} = 10$, $W_{\text{vol}} = 42$.
• Index 5 (Tactical Horizon): $N_{\text{long}} = 21$, $N_{\text{short}} = 5$, $W_{\text{vol}} = 21$.

Complete 35-Scenario Parametric Matrix Reference Table

Execution Realism Standards

• Trade Timing: Day $T$ close signal triggers Day $T+1$ open fill.
• Commissions: USD 0.0035/share ($1.00 min, 1% cap).
• Slippage: VolumeShareSlippage ($c_{\text{impact}} = 0.05$, 20% bar volume limit).

Diagnostic Tearsheet Interfaces

The simulation produces two complementary diagnostic interfaces:

1. Single-Scenario Tearsheet (report.html)

Focuses on a single tranche (e.g. C3 or F2), providing cumulative equity curves, configuration parameters, final portfolio holdings, monthly returns heatmaps, rolling Sharpe ratios, underwater drawdown curves, and top winner/loser attribution tables.

2. Comparative Multi-Scenario Analysis (analysis.html)

Evaluates all 35 cells simultaneously in a heatmapped grid and ranked summary cards, allowing researchers to verify parameter stability across liquidity tranches and lookback horizons.