Market-Optimized Stock Index (MOSI)
The Smith–Hazel Index is a statistically optimal selection index widely used in quantitative breeding. It maximizes correlation with true aggregate merit by optimally weighting correlated traits.
This logic translates directly into finance as the Market-Optimized Stock Index (MOSI), a mathematically grounded, multi-factor stock score designed for advanced portfolios and PMS-style selection.
Core Formula
MOSIs = Σi=1k bᵢ · xs,i
where b = P−1 · G · a
where b = P−1 · G · a
Meaning of Symbols
- MOSIs – Market-Optimized Stock Index score of stock s
- xs,i – Observed factor value (PE, growth, momentum, volume)
- bᵢ – Statistically optimal weight of factor i
- P – Covariance matrix of observed market factors
- G – Covariance matrix of long-term performance drivers
- a – Investor priority vector (risk, growth, quality preferences)
The matrix expression b = P−1Ga ensures that:
- Redundant factors are down-weighted automatically
- Highly informative factors gain stronger influence
- Investor priorities directly shape the index
Note: In production systems, P and G are estimated using historical data. This calculator demonstrates the logic using simplified diagonal matrices.
Simplified MOSI Calculator (Demonstration)
Each factor is treated independently for clarity. You provide:
- Observed factor value xs,i
- Variance of observed factor (proxy for P)
- Variance of long-term driver (proxy for G)
- Investor priority ai
The system computes:
bᵢ = (Gᵢ / Pᵢ) · aᵢ
| Factor | xs,i (Observed Value) |
Pᵢ (Observed Variance) |
Gᵢ (Long-Term Variance) |
aᵢ (Investor Priority) |
bᵢ (Optimal Weight) |
|---|
Interpretation:
MOSI is a statistically optimal score that balances factor information, correlation structure, and investor intent. Stocks with high MOSI values represent candidates for professional-grade, data-driven portfolios.
MOSI is a statistically optimal score that balances factor information, correlation structure, and investor intent. Stocks with high MOSI values represent candidates for professional-grade, data-driven portfolios.
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