Pillar 10 · Fundamentals

Fundamental-Quality Screen — M · Z · F

Three accounting scores applied in a deliberate order to filter the S&P 500 down to the most fundamentally sound companies: the Beneish M-Score gates for statement integrity, the Altman Z-Score gates for solvency, and the Piotroski F-Score ranks the survivors.

Why this order.
  1. M-Score first (integrity gate) — tests whether the financial statements themselves are trustworthy. Z and F are computed from those same statements, so filtering suspected manipulators first stops garbage from propagating downstream.
  2. Z-Score second (solvency gate) — removes firms in or near distress; a fundamentally improving but insolvent firm is still a high failure risk.
  3. F-Score third (ranking) — ranks the clean, solvent survivors to surface the strongest operators.

# Company Sector M-Score Z-Score F-Score Alpha Beta 52-Wk Range P/E vs Peers
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Source: yfinance annual statements · Beneish (1999), Altman (1968), Piotroski (2000) · scores are point-in-time on the latest reported fiscal year.

From screen to portfolio. The eligible universe is the fundamentally sound survivors with a Piotroski F-Score of 6–9 (they cleared the Beneish integrity gate and the Altman solvency gate). Each name carries a CAPM annualised alpha and beta from the pillar-07 factor model. Four construction methods build a long-only book from that set, and a single risk-aversion setting drives all four at once — more risk aversion always means a broader, lower-risk book.
  1. Screen → equal weight — take the n highest-alpha names and weight them equally.
  2. Screen → cap weight — take the n highest-alpha names and weight by market capitalisation.
  3. Stratified — take the j highest-alpha names within each industry, then equal-weight the selection.
  4. Quadratic program — maximise value added α′w − λ·w′Σw under full-investment, no-short-sales and a 10%-per-name cap, at risk-aversion λ.

Value added — every method at each risk-aversion setting

Each cell is the book's value added α′w − λ·w′Σw for that construction method at that risk-aversion setting — every column uses its own breadth and penalty λ. Value added is comparable down a column (same λ); the highlighted cell is the method that adds the most at that risk setting. Pick a setting below to break any column down into holdings.

Risk aversion

Strategy Param Holdings Exp. Alpha Beta Fcst Risk Value Added

Risk model. Forecast risk and value added use a single-factor (market) covariance model: Σ = σ²ₘ·β β′ off-diagonal, with each name's total variance set to β²·σ²ₘ / R² so its idiosyncratic share follows the CAPM R² (floored at 0.05). Expected alpha is the weighted CAPM annualised alpha; value added is α′w − λ·w′Σw. Alphas are point-in-time factor-model estimates, not a forward guarantee — this tab is an illustration of the construction methods, not investment advice.