1 Primary Data: CRSP Monthly Stock File
We use the Center for Research in Security Prices (CRSP) monthly stock files from January 1996 to December 2023. The CRSP universe includes all listed common stocks on the NYSE, Nasdaq, and AMEX exchanges. Key variables include:
- PERMNO: Unique stock identifier
- Date: Monthly observation date
- Market Capitalization: Shares outstanding × price
- primaryexch : primary exchange
- SIC Code: Optional industry classification
1.1 Market-Cap Based Valuation Perspective
Unlike fixed-income instruments, public equities derive their economic value primarily from their tradeability. While dividends contribute to realized returns, they are secondary to a stock’s market capitalization path, which reflects its ability to attract and retain capital under uncertainty.
We therefore adopt a market cap–based valuation approach, using capitalization time series as the core proxy for equity value and flow dynamics.
1.2 Delisting Treatment: Terminal Value = Zero
When a stock is delisted:
- Its market capitalization becomes zero, and its final gross return is set to 0, implying net return of –1.
\[ R_{\text{gross}} = 0, \quad R_{\text{net}} = -1 \]
This reflects the reality that delisted equities become practically untradeable and lose all resale value for investors. In contrast to fixed-income instruments, equities have no residual recovery claim.
1.3 IPO Treatment: External Entry State
- Newly listed stocks (IPOs) are initially placed in an external state (state 0).
- From their first full month after IPO:
- Their market capitalization is ranked within the universe.
- They are assigned to a decile group (state 1–10) based on market cap percentile.
1.4 Survivorship Bias Adjustment
To avoid survivorship bias:
- We retain all stocks, including those that were delisted during the sample period.
- This prevents the overestimation of returns and misrepresentation of capital mobility that arises from survivor-only datasets.
1.5 State Classification Framework
For transition matrix estimation and mixture modeling (Section 4), we define the following percentile-based state mapping:
| State | Market Cap Percentile Range | Description |
|---|---|---|
| 10 | 90%–100% | Top 10% (largest-cap stocks) |
| 9 | 80%–90% | |
| … | … | |
| 1 | 0%–10% | Bottom 10% (smallest-cap stocks) |
| 0 | External | Delisted stocks (absorbing state) or IPOs before full inclusion |
This unconventional but analytically convenient mapping allows for intuitive modeling of:
- Upward mobility as a transition to higher state numbers
- Capital lock-in at the top (persistence in State 10)
- Exit fragility for lower states (transition to State 0)
1.6 Structural Implication
This mapping enables a semi-absorbing, non-reversible Markov transition model, where:
- Delisted stocks enter the absorbing state (0) permanently.
- Stocks that remain listed transition among states 1–10, based on their market cap percentile ranks at each time \(t\).
- New entrants (IPOs) begin in state 0 and join the ranked universe from their second month onward.
This design forms the empirical backbone for transition matrix analysis, mixture decomposition, and long-run mobility asymmetry in Section 4.