Stock Analysis & Trending Equities Methodology Guide

Overview

This page serves as the complete mathematical specification, quantitative dictionary, and architectural guide for SOPHIE's Equities & Trending Analysis Suite (/stock/trending, /stock/[ticker], /quant-trending, and the /stock/stock-analysis topic hubs).

The platform evaluates individual equities across four foundational quantitative pillars:

1. Valuation Models (Multi-model intrinsic fair value synthesis)
2. Fundamental Quality (4-dimensional accounting & financial strength scoring)
3. Technical Momentum & Microstructure (5-strategy quantitative ensemble)
4. Market Sentiment (SEC Form 4 insider transactions & NLP news sentiment)

These pillars are integrated by SOPHIE's Master Synthesis Engine into an overall score ($0\text{--}100$) and evaluated alongside 5 AI Persona Bots modeling iconic investment methodologies (Warren Buffett, Charlie Munger, Cathie Wood, Stanley Druckenmiller, and Benjamin Graham).

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1. Trending Stocks & Quant Aggregation Architecture

Located in src/app/stock/trending/client.tsx, src/app/quant-trending/quant-trending-client.tsx, and src/components/quant-trending/trending-widget.tsx.

1.1 Trending Stock 3-Month Performance Metric

For any covered equity in the trending matrix, performance is measured against its 3-month lookback baseline:

$$\text{Change}_{\text{3M}} = \left( \frac{P_{\text{latest}} - P_{\text{closest}(t - 90\text{d})}}{P_{\text{closest}(t - 90\text{d})}} \right) \times 100$$

where $P_{\text{closest}(t - 90\text{d})}$ searches sorted historical business dates for the minimum timestamp differential $|t_{\text{price}} - (t_{\text{now}} - 90\text{d})|$.

1.2 Quant Trending Aggregation Engine

Aggregates and normalizes quantitative finance intelligence across five primary web and research feeds:

• ArXiv (q-fin): Quantitative finance preprints (pricing, market microstructure, portfolio management).
• GitHub: Open-source quantitative trading frameworks, backtesting libraries, and factor models.
• Reddit: Practitioner sentiment and discussions from r/algotrading and r/quant.
• Hacker News: High-frequency, infrastructure, and financial technology engineering discussions.
• Google News: Curated institutional and macroeconomic developments.

Heat Scoring & Sorting Hierarchy:

• Heat Score ($0\text{--}100$): Normalized composite measuring upvotes, citation velocity, star growth, and social engagement:
  • $\ge 75$: High Heat (Red)
  • $50\text{--}74$: Elevated Heat (Orange)
  • $25\text{--}49$: Moderate Heat (Yellow)
  • $< 25$: Baseline Activity (Blue)
• Deterministic Multi-Key Sorting:
  1. Date Sort (Default): $\text{ETL Fetch Timestamp} \downarrow \to \text{Publish Timestamp} \downarrow \to \text{Heat Score} \downarrow$
  2. Heat Sort: $\text{Heat Score} \downarrow \to \text{ETL Fetch Timestamp} \downarrow \to \text{Publish Timestamp} \downarrow$

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2. Market Statistics & Volatility Metrics

Located in StockCompanyInfo (src/components/stock/stock-company-info.tsx).

2.1 52-Week Price Extremes

$$\text{High}_{\text{52W}} = \max_{t \in [T-252, T]} \text{High}_t, \quad \text{Low}_{\text{52W}} = \min_{t \in [T-252, T]} \text{Low}_t$$

2.2 Annualized Historical Volatility

Calculated from 252 trading days of historical daily returns:

$$r_t = \frac{P_t}{P_{t-1}} - 1 \quad (\text{or } \ln(P_t / P_{t-1}))$$ $$\sigma_{\text{annual}} = \text{stdev}(r_t) \times \sqrt{252} \times 100$$

2.3 Forward Dividend & Yield Derivation

Extrapolated from reporting period financial statements:

$$\text{Forward Annual Dividend} = \text{EPS} \times \text{Payout Ratio}$$ $$\text{Dividend Yield} = \frac{\text{Payout Ratio}}{\text{P/E Ratio}} = \frac{\text{Forward Dividend}}{P_{\text{current}}}$$

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3. Valuation Analysis Engine (Fair Value Synthesis)

Located in StockValuation (src/components/stock/stock-valuation.tsx).

Rather than relying on a single valuation model (which is vulnerable to model-specific biases), SOPHIE executes an ensemble of four distinct valuation methodologies and computes a weighted average intrinsic value:

$$V_{\text{weighted}} = 0.35 \cdot V_{\text{DCF}} + 0.35 \cdot V_{\text{Owner}} + 0.20 \cdot V_{\text{EV/EBITDA}} + 0.10 \cdot V_{\text{RI}}$$

3.1 Model 1: Discounted Cash Flow (DCF — 35% Weight)

Projects free cash flows over a 5-year discrete horizon and discounts them to present value:

$$V_{\text{DCF}} = \sum_{t=1}^{5} \frac{\text{FCF}_0 \cdot (1 + g)^t}{(1 + r)^t} + \frac{\text{FCF}_5 \cdot (1 + g_n)}{(r - g_n) \cdot (1 + r)^5}$$

• Baseline parameters: Discrete growth rate $g = 5.0\%$, discount rate / WACC $r = 10.0\%$, perpetual terminal growth rate $g_n = 2.5\%$.

3.2 Model 2: Owner Earnings (Warren Buffett Method — 35% Weight)

Measures the true cash flow accruable to shareholders after maintaining competitive position:

$$\text{Owner Earnings} = \text{Net Income} + \text{Depreciation \& Amortization} - \text{Maintenance Capex}$$ $$V_{\text{Owner}} = \frac{\text{Owner Earnings} \times (1 + g_{\text{conservative}})}{r - g_{\text{conservative}}} \times (1 - \text{MarginOfSafety})$$

3.3 Model 3: EV/EBITDA Multiple (Relative Valuation — 20% Weight)

Capital-structure neutral enterprise valuation benchmarked against industry peers and historical medians:

$$\text{Target EV} = \text{Median}\left(\frac{\text{EV}}{\text{EBITDA}}\right)_{\text{peers}} \times \text{EBITDA}_{\text{TTM}}$$ $$V_{\text{EV/EBITDA}} = \text{Target EV} - \text{Total Debt} - \text{Preferred Stock} + \text{Cash \& Equivalents}$$

3.4 Model 4: Residual Income / Economic Profit (10% Weight)

Evaluates whether the company creates value in excess of its cost of equity capital:

$$V_{\text{RI}} = \text{Book Value}_0 + \sum_{t=1}^{T} \frac{\text{Net Income}_t - (r_e \times \text{Book Value}_{t-1})}{(1 + r_e)^t}$$

where $r_e$ is the required cost of equity.

3.5 Valuation Gap & Signal Generation

$$\text{Valuation Gap} = \frac{V_{\text{intrinsic}} - \text{Market Cap}}{\text{Market Cap}} \quad (\text{or } \frac{P_{\text{fair}} - P_{\text{market}}}{P_{\text{market}}})$$

• Bullish (Undervalued): $\text{Valuation Gap} > +15\%$
• Bearish (Overvalued): $\text{Valuation Gap} < -15\%$
• Neutral (Fairly Valued): $-15\% \le \text{Valuation Gap} \le +15\%$
• Confidence Level (%): $$\text{Confidence} = \min\left(100, \frac{|\text{Valuation Gap}|}{0.30} \times 100\right)$$ (A $30\%$ or greater gap corresponds to maximum $100\%$ confidence).

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4. Fundamental Quality Engine (4-Dimensional Scoring)

Located in StockFundamentalsAnalysis (src/components/stock/stock-fundamentals-analysis.tsx).

The fundamental engine decomposes company financial statements into four orthogonal dimensions, evaluating 12 core accounting metrics against institutional threshold benchmarks.

Dimension & Overall Signal Logic:

• Dimension Score ($0\text{--}3$): Count of individual metrics meeting or exceeding their target threshold.
• Dimension Signal: Bullish ($\ge 2/3$ metrics), Bearish ($\le 0/3$ or majority failing), Neutral ($1/3$).
• Overall Fundamental Signal:
  • Bullish: Count(Bullish Dimensions) $>$ Count(Bearish Dimensions)
  • Bearish: Count(Bearish Dimensions) $>$ Count(Bullish Dimensions)
  • Neutral: Equal bullish and bearish dimension counts

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5. Technical Analysis Engine (5-Strategy Ensemble)

Located in StockTechnicalsAnalysis (src/components/stock/stock-technicals-analysis.tsx).

The technical engine combines 5 distinct quantitative strategies across different market microstructures to eliminate curve-fitting and single-indicator whipsaws:

$$\text{Score}_{\text{technical}} = 0.25 \cdot S_{\text{trend}} + 0.20 \cdot S_{\text{mr}} + 0.25 \cdot S_{\text{mom}} + 0.15 \cdot S_{\text{vol}} + 0.15 \cdot S_{\text{stat\_arb}}$$

5.1 Strategy 1: Trend Following (25% Weight)

• Exponential Moving Average (EMA) Ribbons: 8-day, 21-day, and 55-day EMAs: $$\text{EMA}_t(N) = P_t \cdot \alpha + \text{EMA}_{t-1}(N) \cdot (1 - \alpha), \quad \alpha = \frac{2}{N+1}$$ Bullish crossover alignment: $\text{EMA}_8 > \text{EMA}_{21} > \text{EMA}_{55}$.
• Average Directional Index (ADX): Measures trend strength. $\text{ADX} > 25.0$ confirms a persistent trending regime.
• Directional Movement (+DI / -DI): $+\text{DI} > -\text{DI}$ confirms upward directional bias.
• Normalized Trend Score: Scaled to $[-1.0, +1.0]$.

5.2 Strategy 2: Mean Reversion (20% Weight)

• Price Z-Score: Measures standard deviations from 20-day moving average: $$Z = \frac{P_t - \mu_{20}}{\sigma_{20}}$$ $Z < -2.0 \implies$ Statistically oversold (bullish reversal); $Z > +2.0 \implies$ Statistically overbought (bearish reversal).
• Bollinger Bands: $\text{Upper} = \mu_{20} + 2\sigma_{20}, \quad \text{Lower} = \mu_{20} - 2\sigma_{20}$.
• Relative Strength Index (RSI 14d & 28d): $$\text{RSI} = 100 - \frac{100}{1 + \text{RS}}, \quad \text{RS} = \frac{\text{EMA}(\text{Gains}, 14)}{\text{EMA}(\text{Losses}, 14)}$$ $\text{RSI} < 30 \implies$ Oversold; $\text{RSI} > 70 \implies$ Overbought.

5.3 Strategy 3: Multi-Horizon Momentum (25% Weight)

• Multi-Period Returns: $\text{Mom}_{\text{1M}}, \text{Mom}_{\text{3M}}, \text{Mom}_{\text{6M}}$.
  • Strong positive momentum: $> +5.0\%$
  • Strong negative momentum: $< -5.0\%$
• Volume Ratio: $$\text{Volume Ratio} = \frac{\text{Volume}_t}{\frac{1}{21}\sum_{k=0}^{20} \text{Volume}_{t-k}}$$ $\text{Ratio} > 1.50$ confirms institutional accumulation / high-conviction breakout.

5.4 Strategy 4: Volatility & Regime Detection (15% Weight)

• 21-Day Annualized Historical Volatility ($\text{HV}_{21}$): $$\text{HV}_{21} = \text{stdev}(r_{t-20 \dots t}) \times \sqrt{252} \times 100$$
• Volatility Regime Ratio: Current $\text{HV}_{21}$ divided by long-term median volatility ($<0.8$ low volatility, $>1.2$ high volatility).
• Volatility Z-Score: Standard deviations of current volatility relative to trailing 1-year mean.
• Average True Range Ratio ($\text{ATR Ratio}$): $\text{ATR}_{14} / P_t$, measuring normalized session dispersion.

5.5 Strategy 5: Statistical Time-Series Properties (15% Weight)

• Hurst Exponent ($H$): Measures the long-term memory and self-similarity of price series via Rescaled Range ($R/S$) analysis: $$(R/S)_n \propto c \cdot n^H$$
  • $H < 0.40$: Strong mean-reverting (anti-persistent)
  • $0.40 \le H \le 0.45$: Moderate mean-reverting
  • $0.45 < H < 0.55$: Random walk / Geometric Brownian Motion
  • $0.55 \le H \le 0.60$: Weak trending
  • $H > 0.60$: Strong trending (persistent)
• Return Skewness: Third standardized moment of returns $\mathbb{E}[((r - \mu)/\sigma)^3]$. Positive skew indicates upside tail probability; negative skew indicates crash/gap vulnerability.
• Return Kurtosis: Fourth standardized moment $\mathbb{E}[((r - \mu)/\sigma)^4]$. Kurtosis $> 5.0$ confirms heavy fat tails (leptokurtic risk).

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6. Market Sentiment Analysis Engine

Located in StockSentimentAnalysis (src/components/stock/stock-sentiment.tsx).

6.1 SEC Form 4 Insider Trading Signal (30% Weight)

Extracts legal insider transactions filed with the SEC:

• Asymmetry Rule: Insider purchases carry high positive signal weight (executives voluntarily deploy personal capital). Insider sales carry lower negative weight (routinely driven by tax planning, option exercises, or scheduled 10b5-1 plans).
• Transaction Metrics:
  • Net Insider Transaction Value ($\text{Value}_{\text{buys}} - |\text{Value}_{\text{sales}}|$)
  • Bullish vs. Bearish transaction count ratio

6.2 NLP News Sentiment Analysis (70% Weight)

Parses recent media and corporate disclosures using financial NLP models, scoring articles into Bullish, Bearish, or Neutral buckets.

6.3 Sentiment Synthesis:

$$\text{Weighted Bullish} = 0.30 \cdot \text{InsiderBuyScore} + 0.70 \cdot \text{NewsBullishScore}$$ $$\text{Weighted Bearish} = 0.30 \cdot \text{InsiderSellScore} + 0.70 \cdot \text{NewsBearishScore}$$ $$\text{Bullish Share} = \left(\frac{\text{Weighted Bullish}}{\text{Weighted Bullish} + \text{Weighted Bearish}}\right) \times 100\%$$

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7. AI Multi-Agent Investment Bot Framework

Located in StockAgentSuggestions (src/components/stock/stock-agent-suggestions.tsx).

SOPHIE implements 5 autonomous AI personas modeled on iconic investment philosophies:

7.1 Warren Buffett Bot (Quality Value & Economic Moats)

• Core Principles: Focuses on business predictability, capital allocation, and sustainable moats.
• Mandatory Criteria:
  • Return on Equity $\text{ROE} > 15\%$ consistently across cycles
  • Operating Margin $> 15\%$ reflecting pricing power
  • Conservative debt structure and strong liquidity
  • Valuation via Owner Earnings with a built-in Margin of Safety

7.2 Charlie Munger Bot (Multidisciplinary Mental Models & ROIC)

• Core Principles: Employs mental models (inversion, microeconomic incentives, psychological bias).
• Mandatory Criteria:
  • Return on Invested Capital ($\text{ROIC} > 15\%$)
  • Pricing power and low capital reinvestment requirements
  • Shareholder-aligned capital allocation (shrinking share count via accretive share repurchases)
  • Inversion: systematically checking for catastrophic business vulnerabilities

7.3 Cathie Wood Bot (Disruptive Innovation & Exponential Growth)

• Core Principles: Thematic investing in multi-trillion-dollar technological secular shifts (AI, genomics, robotics, blockchain).
• Mandatory Criteria:
  • Revenue growth acceleration and expanding Total Addressable Market (TAM)
  • High R&D intensity and gross margin expansion
  • Operating leverage potential over a 5-year exponential adoption S-curve
  • High-growth multi-stage DCF modeling

7.4 Stanley Druckenmiller Bot (Macro Momentum & Asymmetric Risk/Reward)

• Core Principles: Top-down macro alignment paired with aggressive bottom-up earnings momentum and disciplined risk control.
• Mandatory Criteria:
  • High-velocity growth: Revenue growth $> 30\%$ and EPS growth $> 30\%$
  • Price momentum $> 50\%$ with strong institutional sponsorship
  • Strict capital preservation: Debt-to-Equity $< 0.30$
  • Multiples: Screening for compressed EV/EBITDA and EV/EBIT relative to growth velocity

7.5 Benjamin Graham Bot (Deep Value & Quantitative Net-Net)

• Core Principles: The father of value investing; strict quantitative balance sheet conservatism without qualitative speculation.
• Mandatory Criteria:
  • Net-Net Working Capital (NNWC): $\text{Current Assets} - \text{Total Liabilities} - \text{Preferred Stock}$
  • Graham Number: Fair value ceiling calculated as: $$V_{\text{Graham}} = \sqrt{22.5 \times \text{EPS} \times \text{Book Value Per Share}}$$
  • Current Ratio $> 2.0$ and Debt Ratio $< 0.50$
  • Unbroken dividend payment record and multi-year positive earnings

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8. SOPHIE Master Synthesis & Composite Scoring

Located in StockAnalysisSummary (src/components/stock/stock-analysis-summary.tsx).

SOPHIE synthesizes all quantitative models, fundamental data, technical indicators, sentiment feeds, and agent opinions into a unified score and multi-horizon roadmap:

8.1 Composite Rating Score ($0\text{--}100$)

• $80\text{--}100$ (Emerald): Strong Bullish conviction across valuation, fundamentals, and momentum.
• $60\text{--}79$ (Blue): Moderate Bullish conviction.
• $40\text{--}59$ (Amber): Neutral / Mixed signals across pillars.
• $< 40$ (Rose): Bearish conviction / Significant multi-factor weakness.

8.2 Multi-Horizon Forecast Outlooks

• Short-Term Horizon (Days to Weeks): Driven by Technical Strategy Ensemble (EMAs, RSI, Z-Score) and NLP News Sentiment.
• Medium-Term Horizon (Months to 1 Year): Driven by Valuation Multiples (DCF, EV/EBITDA), Earnings Growth, and Analyst Target Dispersion.
• Long-Term Horizon (Multi-Year): Driven by Fundamental Quality (ROE, Moat Strength, FCF Conversion, Debt-to-Equity).

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9. Comprehensive Formula & Indicator Lookup Table

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Related Wiki Articles & Research

• Analyst Consensus Target Prices — Dispersion vs. average target prices
• SEC Form 4 Insider Trading Signals — Interpreting insider buys vs. sells
• Charlie Munger Worldly Wisdom — Multidisciplinary mental models in finance
• Stanley Druckenmiller Q3 2025 Positioning — Macro momentum and risk management
• Alphabet GOOGL DCF Valuation — Case study in DCF modeling