Equities

# Equities

This skill is a decision procedure: which valuation metric to use for which company, which index methodology fits which mandate, and the order of operations for analyzing a stock. It assumes the user can look up definitions; the value here is choosing the right tool.

## Choosing the Valuation Metric

Match the metric to the sector and capital structure — using the wrong one is the most common equity-analysis error.

| Situation | Use | Avoid | Why |
|-----------|-----|-------|-----|
| Financials (banks, insurers) | P/B, P/TBV, ROE vs P/B | EV/EBITDA | Debt is raw material, not financing — EV and EBITDA are meaningless; book value is marked closer to fair value |
| Capital-intensive (industrials, telecom, energy) | EV/EBITDA, EV/EBIT | P/E alone | Neutralizes depreciation policy and leverage differences across peers |
| Mature dividend payers (utilities, staples) | Dividend yield + payout sustainability, P/E | PEG | Growth is low and stable; income and coverage matter most |
| High-growth, low/no earnings | EV/Sales, PEG (if earnings exist), unit economics | P/E, P/B | Earnings are depressed by reinvestment; book value is mostly intangibles |
| Cyclicals (autos, semis, materials) | Mid-cycle or normalized P/E, P/B at trough | Spot P/E | P/E is lowest at the cycle peak and highest at the trough — spot P/E inverts the buy/sell signal |
| Negative earnings, positive cash flow | EV/EBITDA, P/FCF | P/E, earnings yield | Ratio is undefined or misleading with negative denominator |
| REITs and listed real estate | P/FFO, P/AFFO, NAV | P/E | GAAP depreciation distorts earnings for property — handled in detail by the real-assets skill |
| Cross-border / different leverage | EV-based multiples | Equity multiples | Enterprise value normalizes for capital structure |

Cross-checks that apply everywhere:
- Use forward (next-12-month) estimates for the numerator decision when the business is changing; trailing figures when estimate quality is poor.
- Compare against the company's own history and a true peer set, not the whole market.
- Translate any multiple into its implied assumptions (growth, margin, required return) before declaring cheap/expensive — a low multiple usually encodes a real problem.

## Choosing the Index Methodology

| Mandate | Methodology | Trade-off to flag |
|---------|-------------|-------------------|
| Cheap, tax-efficient market exposure | Cap-weighted (S&P 500, total market) | Momentum-chasing by construction; concentration in mega-caps — a single sector can exceed 30% |
| Reduce concentration / small-cap tilt | Equal-weighted | Higher turnover and rebalancing cost; structural size and contrarian tilt |
| Break the price-weight link | Fundamental-weighted (revenue, earnings, book) | Effectively a value tilt with extra steps; compare cost vs an explicit value fund |
| Explicit factor exposure | Factor/style index (value, momentum, quality, low vol) | Verify the factor definition and rebalance rules; factor timing rarely works |
| Avoid | Price-weighted (DJIA-style) | Weight proportional to share price is economically arbitrary — legacy only |

Selection rules: default to cap-weighted for core beta; add equal- or fundamental-weighted only when the user explicitly wants the embedded tilt and accepts the turnover; treat any "smart beta" product as a factor portfolio and evaluate its factor loadings, not its marketing name.

## Security Analysis Sequence

1. **Classify the business** — sector (GICS or equivalent), cyclical vs defensive, capital intensity, leverage. This determines the valuation toolkit (table above).
2. **Quality screen** — revenue trend, margin trend, ROIC vs cost of capital, balance-sheet risk (net debt/EBITDA, interest coverage), share count trajectory (dilution vs buybacks).
3. **Earnings basis** — pick trailing vs forward EPS, check for one-offs, use diluted share count. For cyclicals, normalize to mid-cycle.
4. **Value with the matched metric** — primary multiple from the table, one cross-check multiple, and where dividends are central a dividend-based check (Gordon growth: P = D1 / (r - g), valid only when g < r).
5. **Factor and style context** — regress (or eyeball) exposures to market beta, size, value, momentum, quality. Distinguish stock-specific thesis from a factor bet you could buy more cheaply via an index.
6. **Portfolio fit** — marginal effect on sector concentration and factor tilts; total return (price + dividends) is the comparison basis, never price return alone.

## Key Formulas

| Formula | Expression | Use Case |
|---------|-----------|----------|
| EV/EBITDA | (Market Cap + Debt - Cash) / EBITDA | Capital-structure-neutral valuation |
| Earnings Yield | EPS / Price | Compare equity vs bond yields |
| PEG | (P/E) / Earnings Growth Rate (in %) | Growth-adjusted valuation |
| Gordon Growth | P = D1 / (r - g) | Dividend-based intrinsic value |
| CAPM | E(R) = R_f + beta × (E(R_m) - R_f) | Required return input for valuation |
| Total Return | Price Return + Dividend Return | Performance comparison basis |

## Worked Example: Metric Selection and Valuation

**Given:** An industrial company with market cap $500M, total debt $100M, cash $50M, EBITDA $75M, EPS $7.50, price $150.
**Decide and calculate:**
1. Capital-intensive industrial → primary metric is EV/EBITDA (table above), with P/E as cross-check.
2. EV = $500M + $100M - $50M = $550M. EV/EBITDA = $550M / $75M = **7.33x**.
3. Cross-check: P/E = $150 / $7.50 = 20.0x; earnings yield = 7.50 / 150 = **5.0%**.
4. Interpretation: 7.33x EV/EBITDA is modest for an industrial if margins are stable — compare against the peer set and the company's own 5-10 year range. The 20x P/E looks richer than the EV multiple because the company carries little net debt; the EV multiple is the better cross-peer comparison.

## Common Pitfalls
- Applying EV/EBITDA to banks or P/E to REITs — metric/sector mismatch is the dominant error this skill exists to prevent
- Buying cyclicals on low trailing P/E at the cycle peak (the "value trap" inversion)
- Treating a fundamental-weighted or smart-beta index as alpha rather than a packaged factor tilt
- Confusing price return with total return — dividends compound to a large share of long-run equity returns
- Survivorship bias in backtested factor or screen results

## Cross-References
- **historical-risk**: beta, volatility, and Sharpe ratio fundamentals
- **fund-vehicles**: equity fund selection (ETFs, mutual funds, SMAs)
- **currencies-and-fx**: international equity currency effects
- **asset-allocation**: equity allocation within multi-asset portfolios
- **real-assets**: REIT valuation (P/FFO, NAV) is owned by that skill
- **qualitative-valuation** and **quantitative-valuation**: deeper single-company valuation workflows

## Running the Script

```bash
uv run scripts/equities.py            # run the demo (uses PEP 723 inline deps)
uv run scripts/equities.py --verify   # check demo outputs against the worked example (exit 1 on mismatch)
python3 scripts/equities.py            # alternative (requires: pip install numpy)
```

The demo prints valuation metrics (including the worked example's EV/EBITDA and earnings yield), a factor regression on synthetic data, and sector concentration analysis. Run `--help` for a list of the classes and functions. For programmatic use, import the module rather than running it — the demo only executes under `python equities.py`.