Survivorship Bias Free Universe Construction

When to Use

Use this skill when a backtest needs the set of instruments that were actually tradable on a historical date, and needs to settle positions in the ones that stopped trading. Evaluating a strategy against only today's constituents drops every company that went bankrupt, was acquired, or was dropped from the exchange — Enron, Lehman Brothers, Wirecard, the old General Motors — and the strategy is credited with never having held them.

Two failure modes, and the second is the expensive one:

The magnitude is strategy-specific, not a constant. Brown, Goetzmann, Ibbotson and Ross (1992) concluded that survivorship bias definitely affects results but that its size "is an empirical question"; published estimates for equity performance studies run roughly 20–80 bp/year (Brown and Goetzmann, 1995) and 71–91 bp on three-factor alphas (Elton, Gruber and Blake, 1996). Measure it on your own universe with the ghost audit below rather than quoting a headline number.

When NOT to Use

• Not an index-membership model. Listing and delisting bound tradability, not index membership — a name can be listed and out of the index. The addition/deletion event log and its half-open [add_date, del_date) interval belong to point-in-time-index-constituent-tracking.
• Not an announcement-timing auditor. This resolves when a security traded, not when its fate became knowable. A rebalance that must not act on an unannounced change needs the knowledge axis — use backtest-look-ahead-in-universe-selection.
• Not a corporate-action price adjuster. Splits and dividends are corporate-action-adjusted-backtesting. last_traded_price must arrive on the same basis as the position quantity.
• Not a source of point-in-time data. A clean audit means the metadata you supplied is internally consistent. Metadata reverse-engineered from a current-membership table produces a survivorship-biased universe that audits clean.
• Not for live universe construction. As-of machinery reconstructs the past; a live rebalance reads current listings directly.
• Not books-and-records arithmetic. Cash values are IEEE-754 floats.

Prerequisites

• A listing record per security: symbol, listing_date, delisting_date, delisting_reason, and a terminal value.
• A stable security_id — CRSP PERMNO, CUSIP, SEDOL, FIGI. It defaults to the symbol, which is safe only for a universe in which no ticker is ever recycled.
• Knowledge of which delisting date your vendor stores. This engine wants the last date the security traded (CRSP DLSTDT convention), inclusive.
• For each delisted name, exactly one of: a known terminal cash price per share, or a delisting return to apply to the last traded price.
• Optionally, today's membership list, to run the ghost audit.

Workflow

1. Reconcile the date convention before ingesting anything. Membership here is inclusive at both ends: listing_date <= T <= delisting_date, because delisting_date is the last day the security traded. Decision point — an index deletion date is not a last trading date. S&P DJI makes changes effective prior to the open on the effective date, so an index deletion date is half-open and the name is already gone that morning. Subtract one trading session before loading it here, or every deleted name lingers a session too long. Twitter alone has four defensible "delisting dates": merger effective 2022-10-27, last NYSE trade 2022-10-27 (close $53.70), trading suspended before the open 2022-10-28, Form 25-NSE effective 2022-11-08. Only the second belongs in this field.

2. Register by security, never by ticker. Populate security_id. The old General Motors Corporation traded as GM until its 2009 bankruptcy (moving to GMGMQ, then MTLQQ effective 2009-07-15); the new General Motors Company took GM at its 2010-11-18 IPO. Decision point — a duplicate security_id raises rather than overwriting. A ticker-keyed registry silently discards one of every recycled pair, which deletes the failed issuer from history — the exact bias this skill exists to remove, reintroduced by the tool meant to remove it.

3. Query the point-in-time universe. Call get_active_universe(T) per bar, or get_active_securities(T) to keep ids. Use resolve_symbol(sym, T) to answer "which company was GM in 2008". Decision point — a ticker held by two live securities on one date raises. Picking one silently is how a backtest ends up holding the wrong company's returns.

4. Settle the terminal value when a position reaches delisting_date. Two modes, exactly one per security:

   • delisting_settlement_price — known cash per share. Merger consideration ($54.20 for TWTR, which is not the $53.70 last close), liquidation distribution, tender price.
   • delisting_return — a fraction applied to last_traded_price, for when the terminal value is unknown.

   Decision point — a delisted security with no terminal value fails registration. The previous default of 0.0 settled a forgotten merger consideration at nothing: a silent, total, fabricated loss on a name that paid cash.

   Decision point — bankruptcy is not automatically zero. Lehman's common left the NYSE in September 2008 and went on trading over the counter as LEHMQ at non-zero prices for years; the position was sellable even though holders were eventually wiped out. When the delisting return is genuinely missing, impute it: −30% for NYSE/AMEX (Shumway 1997) or −55% for Nasdaq (Shumway and Warther 1999), available as module constants. Never let an imputation overwrite an observed delisting return.

   Decision point — settling an ACTIVE security raises. The old behaviour returned qty × 0.0 with the message "Active instrument.", booking a silent 100% loss on a healthy position.

5. Audit coverage over the backtest window. audit_survivorship_bias(start, end, current_static_universe=..., min_expected_attrition_rate=...). Decision point — the denominator is names live in the window, not everything registered. Counting names that never traded in the window inflates the denominator with securities the backtest could not have held and deflates the attrition rate the audit exists to report. Decision point — ghost_count is None means not audited, never zero. Pass today's membership to count names your history has and today's index does not; a snapshot-built universe scores zero by construction. Read it as a lower bound — the check compares tickers, so a recycled ticker hides its delisted issuer.

Full procedure: see references/workflows.md. Standards and sourcing: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

• Applying a current snapshot backwards: querying today's S&P 500 and running it across ten years of history. The ghost audit returns zero for exactly this universe, which is the tell.
• Keying the registry by ticker: two issuers that shared a symbol collapse into one, and the delisted one disappears from every historical universe. Ticker reuse is routine, not exotic — GM was reassigned within 18 months.
• Defaulting a missing settlement price to zero: a merger that paid $54.20/share settles at $0 and the backtest records a 100% loss on a profitable exit. Silent, and indistinguishable from a real bankruptcy in the P&L.
• Treating bankruptcy as an instant zero: the delisting return from the last exchange price is what the position actually realized. Zero is a modelling choice that must be stated, not the default truth.
• Imputing over an observed delisting return: the −30%/−55% figures replace a missing performance-related delisting return. Applying them where CRSP reports an actual DLRET overwrites data with an estimate — and they are estimates from US equity samples of the 1962–1993 era, not constants for other venues or asset classes.
• Mixing the two delisting-date conventions: loading an index deletion date as a last trading date holds every deleted name one extra session, every time.
• Certifying bias protection on a single delisted name: "at least one delisted instrument" is satisfiable by one name in a universe of 500. Set an attrition threshold you are willing to defend, and record it with the audit.
• Deleting rather than settling: dropping the position when the ticker stops printing removes the loss. The name is in the universe and the bias is still there.

Verification

• Register AAPL (active), LEH (last traded 2008-09-16, bankruptcy) and TWTR (last traded 2022-10-27, merger at $54.20). Confirm get_active_universe(2008-01-01) is ['AAPL', 'LEH'] and get_active_universe(2020-01-01) is ['AAPL', 'TWTR'].
• Boundary: TWTR must be in the 2022-10-27 universe and out of the 2022-10-28 one. Off by one in either direction is a real bug — a whole session of a name that traded, or a session holding a name that did not.
• Register both General Motors issuers under distinct security_ids and confirm the registry holds 2 records, GM is in the 2008 universe, resolve_symbol('GM', 2008-01-01) is the Corporation and resolve_symbol('GM', 2015-01-01) is the Company, and resolve_symbol('GM', 2010-01-01) is None.
• Settlement values, derived independently: TWTR 100 shares → $5,420.00 (100 × $54.20), not $5,370.00 (100 × the $53.70 last close). LEH 100 shares at a $3.65 last price with the −30% imputation → $255.50.
• Negative checks — each must raise UniverseError: settling an ACTIVE security; registering a delisted security with no terminal value; registering one with both; delisting_date before listing_date; a delisting reason with no date; a date with reason ACTIVE; a negative settlement price; a delisting_return below −1.0 (while exactly −1.0 is accepted); a non-finite price or quantity; a datetime.datetime where a date is required; a duplicate security_id; settling a recycled ticker by ticker rather than by id; settling by a string that is both one security's id and another's ticker (check both registration orders); an inverted audit window.
• Audit: over 2008-01-01..2008-12-31 with those three names, universe_in_period is 2 (TWTR listed in 2013), never_live_in_period is 1, and attrition_rate is 0.50 — not the 0.333 a registry-wide denominator reports.
• Ghost audit: with current_static_universe=['AAPL'] over 2008..2023, ghost_count is 2. With no snapshot supplied it is None, and must be rendered "not audited".
• Run python -m unittest discover -s skills/survivorship-bias-free-universe-construction/scripts and confirm 100% pass rate (51 tests).

Related Skills

• point-in-time-index-constituent-tracking
• backtest-look-ahead-in-universe-selection
• corporate-action-adjusted-backtesting
• reference-data-symbol-mapping-across-vendors
• lookahead-bias-elimination
• walk-forward-validation-setup