Forward Split Adjustment: carry later observations onto an earlier share basis

A stock split changes the size of the unit called one share. It does not, by itself, create the price collapse or volume surge that an unadjusted chart appears to show. Forward split adjustment lets you express observations after a split on a selected earlier share basis, while keeping the raw history intact.

This is mainly useful for controlled reconciliation: comparing a later record with a pre-split ledger, reproducing an older report, or testing that two adjustment directions are true inverses before rounding. It is not the usual choice for a current-basis chart; backward split adjustment serves that different purpose.

Define the factor direction first

Split feeds do not all name factors in the same direction. Here the ratio is:

$$r_e = \frac{N_e}{O_e}$$

where $N_e$ is the number of new shares and $O_e$ is the number of old shares for event $e$. A four-for-one forward split therefore has $N_e=4$, $O_e=1$, and $r_e=4$. This package rejects $r_e \le 1$ because unit factors and reverse splits belong to different contracts.

The target basis is the share unit in force at targetBasisAt. For an observation at time $t$, the eligible event set is:

$$E(t)=\{e \mid \text{targetBasisAt} < \text{effectiveAt}_e \le t\}$$

The cumulative price factor and reciprocal quantity factor are:

$$F_P(t)=\prod_{e\in E(t)}r_e, \qquad F_Q(t)=\frac{1}{F_P(t)}$$

Then:

$$P_t^{\text{earlier}}=P_t^{\text{raw}}F_P(t), \qquad Q_t^{\text{earlier}}=Q_t^{\text{raw}}F_Q(t)$$

$Q$ may be share-count volume or shares outstanding. Do not apply the quantity rule to trade count, currency notional, or an already adjusted field.

Why the boundary is inclusive

The event's effectiveAt is the first instant at which the input dataset says observations use the new share basis. Therefore an observation exactly at that instant is transformed; one before it is not. This is a package convention, not a claim that every vendor stamps daily or intraday records the same way.

The anchor is equally important. Events effective at or before targetBasisAt already belong to the chosen basis and must not be applied again. Multiple later splits compound in effective-time order. Because multiplication is commutative, simultaneous simple split factors produce the same arithmetic factor, but their event IDs are still retained for audit.

Takeaway: knowledge time chooses the event revision; effective time chooses which observations the selected revision transforms.

Work the synthetic example

Assume a validated four-for-one event and choose the pre-split share unit as the target basis. The numbers below are synthetic teaching values, not Apple prices.

At the boundary, $30\times4=120$ and $4{,}000/4=1{,}000$. Before rounding, price times share quantity is invariant:

$$(P_tF_P)(Q_t/F_P)=P_tQ_t$$

That identity catches arithmetic errors. It cannot prove that the ratio, timestamp, or event source is correct.

A real event, without fictional market data

Apple's July 30, 2020 issuer announcement said its board approved a four-for-one split, holders of record on August 24 would receive three additional shares per share held, and trading would begin on a split-adjusted basis on August 31 (Apple Newsroom). The related filing was accepted by EDGAR on July 30 at 18:55:04 (SEC filing detail).

A later Form 8-K records another boundary: at 5 p.m. Pacific daylight time on August 28, each outstanding share would automatically split into four (SEC Form 8-K). Apple's 2020 Form 10-K then states that share, restricted-stock-unit, and per-share information was retroactively adjusted for the split (SEC Form 10-K).

These are sourced facts. The teaching calculation $30\times4=120$ is a derived illustration of the declared ratio, not a report of Apple's traded prices. No provider series is used as authority. The case shows why a single field called splitDate is inadequate: announcement, record date, legal effect, new-basis trading date, provider publication, and local ingestion can differ.

For this package's daily synthetic fixture, effectiveAt = 2020-08-31T00:00:00Z is an explicit dataset convention representing the start of the August 31 daily label. It is not asserted to be Nasdaq's market-open timestamp.

Revisions and point-in-time lineage

Corporate-action records can be corrected or cancelled. The implementation groups revisions by eventId, verifies a linear supersedesRevisionId chain, and selects the latest revision whose publishedAt is no later than knowledgeAt. A known cancellation removes the transformation but remains visible in selectedRevisions. A later correction cannot leak into an earlier knowledge cutoff.

This does not make a forward-adjusted series a historical traded series. It creates a derived comparison basis as of a declared knowledge cutoff. Preserve both raw and adjusted values, the selected revision, event source, anchor, effective boundary, and generation time.

Rounding and reversibility

Without rounding, the inverse is direct: divide adjusted price by $F_P$ and divide adjusted quantity by $F_Q$. Public output may be rounded from zero to twelve decimal places. Once rounded, exact reversal is not guaranteed, so the result emits a warning. Production systems should retain unrounded decimal values internally and apply security- and venue-specific precision at a documented boundary.

Implementation contract

The Python and TypeScript implementations accept:

• UTC targetBasisAt and knowledgeAt instants ending in Z;
• strictly increasing observations with positive prices, non-negative share volume, and positive shares outstanding;
• effective-dated event revisions with explicit new and old share counts;
• an optional output precision, where null means no public rounding.

They return the raw and adjusted fields, both cumulative factor directions, applied event IDs, selected point-in-time revisions, the exact boundary rule, and rounding warnings. They reject malformed timestamps, duplicate observations, broken revision chains, non-forward ratios, and impossible quantities.

Explore the state changes

The guided playground provides four deterministic scenarios: one four-for-one boundary, two compounding splits, a known cancellation, and an invalid unit ratio. Step or play through 24 synthetic observations; Back reverses exactly one step and Reset restores the canonical state.

What this method does not prove

• A smooth series does not validate the event source.
• Price-volume invariance does not validate the boundary.
• An issuer event does not validate a vendor's adjusted-price history.
• Forward adjustment does not create a historical traded price.
• A split-only factor does not cover dividends, rights, spin-offs, mergers, cash-in-lieu, taxes, or fractional entitlements.
• Tests establish the package contract, not investment usefulness or provider parity.

Summary

Define $r$ as new shares per old share, declare an earlier target basis, and apply only active, knowable events with targetBasisAt < effectiveAt <= observation.timestamp. Multiply price by the compounded factor, divide share quantities by it, keep revision lineage, and round only at the public boundary.

Continue with Cash-Dividend Total-Return Adjustment for a cash distribution, or revisit Backward Split Adjustment when the target is a later share basis.

Asset map

Source roles and limitations are recorded in ../REFERENCES.md. This material is educational, not investment, legal, accounting, or tax advice.