What changes when a backtest keeps only the securities that survived?

Freeze membership before seeing later outcomes

Consider a fictional one-period buy-and-hold exercise. At the start, four fully paid positions, A through D, each receive $1,000. Initial capital is $4,000. There are no contributions, withdrawals, transaction costs or distributions other than the exit proceeds stated below. Cash received from an early exit earns zero until the measurement endpoint.

This is a complete invented ledger, not a dataset of real companies. A and B remain listed at the endpoint. C exits with known final proceeds of $0. D exits with known cash proceeds of $500. The event labels describe the teaching scenario; they do not imply that every delisting has either outcome.

Reconcile the complete starting portfolio

At the endpoint, A is worth $1,200 and B $1,100. Add C’s stipulated $0 and D’s $500 held cash. Terminal wealth is 1,200 + 1,100 + 0 + 500 = $2,800. The initial-universe portfolio return is 2,800 / 4,000 − 1 = −30%.

The four position returns are +20%, +10%, −100% and −50%. Because the positions began with equal capital and the exercise preserves exit cash to the endpoint, their arithmetic average is also −30%. Both methods reconcile. Treating D’s cash proceeds as a still-trading quote would confuse an exit record with a market-price observation.

Show exactly what the survivor-only calculation selects

If the analyst retrospectively retains only A and B, the selected subset starts with $2,000 and ends with $2,300. Its return is +15%. That differs by 45 percentage points from the original portfolio’s −30%, but it describes a different universe and capital denominator.

The subset’s two individual returns were not recalculated incorrectly. The problem is presenting an ex-post membership choice as though it had been available at the start. The classic Brown, Goetzmann, Ibbotson and Ross paper analyzes how survival-based truncation can distort performance inference. This toy stock ledger illustrates selection arithmetic; it does not reproduce the paper’s mutual-fund results or estimate a market-wide bias.

Keep an unknown payout visible in a second control

Now remove only D’s terminal-payout information. Three of four outcomes are known, and $1,000 of initial exposure has an unresolved terminal value. Reporting −30% would require inventing the missing $500; inserting $0 would invent a total loss instead.

If an analyst separately stipulates a teaching bound that D’s proceeds lie between $0 and $1,000, total wealth lies between $2,300 and $3,300 and return between −42.5% and −17.5%. That range follows from an extra assumption, not from a missing record itself. Without a justified bound, report the unknown rather than dropping the position or manufacturing precision.

Method, sources, and limits

The original ledger and conditional range were checked on 27 October 2026. Actual reconstruction may require identifier histories, membership dates, corporate actions and verified exit cash flows. AI assisted this draft; separate AI verification is required before publication and is not human financial-expert review. No strategy return, product dataset completeness or future performance is established.