Splits, Dividends and Adjusted Data

A price series is supposed to be a record of what happened. For any instrument that has ever split its shares or paid a dividend, the series in your database is not that record — it is a reconstruction, and somebody made choices while building it. This lesson is about which choices, what each one preserves, what each one destroys, and how to tell which version you are holding.

Two corporate actions, one problem

Stock splits

A split multiplies the number of shares outstanding and divides the price by the same factor. A holder of 100 shares at 120 becomes a holder of 200 shares at 60. Nothing of economic substance has changed: the position is worth 12,000 before and after.

The price series, however, now contains a 50 per cent overnight fall that never happened. Every percentage-change calculation across that boundary is wrong. Every volatility measure that spans it is wrong. A breakout rule sees a catastrophic gap; a mean-reversion rule sees the opportunity of a lifetime.

AmiBroker describes splits in the notation x->y, meaning that x shares before the split become y after it. An ordinary split into five pieces is 1->5; a reverse split that consolidates two shares into one is 2->1.

Cash dividends

A cash dividend transfers value out of the company to shareholders. On the ex-dividend date the share trades without the right to the upcoming payment, and the price adjusts downward by roughly the dividend amount — a two-unit dividend on a hundred-unit share produces, other things equal, a fall of about two units that is not a loss to anyone who held the share.

The gap is smaller than a split’s, which is exactly why it is more dangerous: it is not obviously an artefact. It looks like an ordinary down day, and it recurs every quarter.

Back-adjustment: what it actually computes

The standard fix is to rewrite history. Choose a reference point — normally the present — and multiply all earlier prices by whatever factor makes the series continuous across each action.

AmiBroker’s ASCII importer implements exactly this, and reading how it does it is the clearest available description of the mechanism. When a data file supplies both CLOSE and ADJCLOSE, the importer:

1. computes a factor as ADJCLOSE / CLOSE for each bar;
2. multiplies OPEN, HIGH, LOW and CLOSE by that factor;
3. divides VOLUME by the same factor.

For a 2-for-1 split, the factor on pre-split bars is 0.5: prices are halved and volume is doubled, restating the earlier history in post-split shares.

One 2-for-1 split, three versions of the same history (synthetic)

Synthetic prices. Adjustment removes the false −49.2% and leaves every other percentage change untouched.

Bar	D−2	D−1	Split day	D+1	D+2
Unadjusted Close	118.00	120.00	61.00	62.40	61.80
Unadjusted Volume	400,000	450,000	900,000	850,000	700,000
Adjustment factor	0.5	0.5	1.0	1.0	1.0
Adjusted Close	59.00	60.00	61.00	62.40	61.80
Adjusted Volume	800,000	900,000	900,000	850,000	700,000
Daily % change, unadjusted	—	+1.7	−49.2	+2.3	−1.0
Daily % change, adjusted	—	+1.7	+1.7	+2.3	−1.0

Synthetic prices. Adjustment removes the false −49.2% and leaves every other percentage change untouched.

What adjustment preserves, and what it destroys

Multiplying a contiguous block of history by a constant has a precise effect, and it is worth stating exactly, because most confusion about adjusted data comes from being vague about it.

Preserved: every percentage change within the adjusted block. If Tuesday was 1.7 per cent above Monday before adjustment, it is 1.7 per cent above Monday afterwards. Ratios, returns, and any indicator built purely on ratios are unaffected.

Changed: the single percentage change across the boundary — which is the whole point.

Destroyed: the price levels themselves. After adjustment, the number in the Close field for a bar five years ago is not a price anyone ever paid or saw quoted. It is a counterfactual: what that day would have been worth in today’s share terms.

!Important

This is the fact that makes adjusted data dangerous for a whole class of rules. “The stock broke 50” is a statement about a price that appeared on a screen. In an adjusted series that level may read as 12.50, or as 3.10 after twenty years of splits. Round numbers, psychological levels, tick sizes, minimum price filters and anything else referring to the absolute price are all measured against numbers that were never real.

Price return versus total return

Dividend adjustment does something conceptually larger than split adjustment. A split adjustment restates a unit; a dividend adjustment changes what is being measured.

• A price-return series answers: what did one share cost over time?
• A total-return series answers: what would a holder who reinvested every dividend have ended up with?

Neither is more correct. They answer different questions, and the difference compounds. As pure arithmetic, an instrument paying a steady 3 per cent a year for thirty years would show a total-return series ending about 1.03³⁰ ≈ 2.4 times higher than its price-return series, from dividends alone. The gap is not a rounding detail; for income-oriented instruments it can be most of the story.

?Reality check

“Buy and hold returned X per cent” is a claim you will see constantly, and it is incomplete until someone says which series it was measured on. A backtest of a trading strategy computed on price-return data and compared against a total-return benchmark is not a fair comparison, and neither is the reverse. Whenever you compare two return figures, check that both sides use the same convention before you believe the difference.

What adjustment does to volume and gaps

Two secondary effects catch people out.

Volume is rescaled too. AmiBroker’s importer divides volume by the adjustment factor, so pre-split volume is restated in post-split shares. That is the arithmetically consistent choice — it keeps price × volume roughly constant — but it means historical volume figures in an adjusted database are not the share counts that were reported at the time. A rule that says “at least one million shares traded” is being applied to a restated number.

Gaps change in absolute terms but not in percentage terms. A two-unit overnight gap in unadjusted data becomes a one-unit gap after a 2-for-1 adjustment. If your gap rule is expressed in currency units, adjustment silently changes its meaning across the whole history. If it is expressed as a percentage, or in multiples of ATR, it does not. That is a strong argument for writing rules in relative terms wherever the choice exists.

Precision: the quiet failure mode

Back-adjustment repeatedly multiplies old prices by factors below one. Over a long history with several splits, the adjusted prices of the earliest bars become very small numbers, and small numbers stored with limited precision lose relative accuracy.

AmiBroker’s documentation is unusually candid about the practical version of this problem. Historical Yahoo data supplies only two decimal digits in the adjusted-close field, so the computed factor gets progressively less accurate as the adjusted close approaches zero. The importer’s $RECALCSPLITS option exists specifically to mitigate it: instead of trusting the ratio directly, it watches for the ratio changing by more than ten per cent between consecutive bars, treats that as a split, guesses the true ratio by matching a simple fraction X/Y with X and Y from 1 to 9, and applies that clean ratio backwards until the next split is detected. A companion option, $ROUNDADJ, rounds the resulting adjusted prices to a stated number of decimal places.

⌀Data quality warning

The importer also locks the split ratio once the adjusted close falls below 0.05. Below that level the two-decimal source data no longer carries enough information to compute a meaningful factor. If you are studying the deep history of an instrument that has split many times, treat the oldest section of an adjusted series as approximate and check it against an independent source before drawing conclusions from it.

What AmiBroker gives you to work with

Adjusting inside the database

Symbol → Split applies a split to the currently selected symbol. AmiBroker attempts to guess the date and ratio from the quotations; if it cannot, it asks. Ratios are entered in the x->y form described earlier.

⚠Warning

The guide states plainly that the split operation cannot be undone. The same is true of Symbol → Delete and of deleting quotations. Back up the database folder — the whole folder, since an AmiBroker database is a directory rather than a file — before performing any of them on data you cannot easily reacquire.

Choosing what gets imported

If your data arrives as text, the format definition decides which version you get. The importer format that AmiQuote uses for historical downloads ships with a field list along these lines:

$FORMAT Date_DMY,Open,High,Low,Close,Skip,Volume
$SEPARATOR ,
$AUTOADD 1

The Skip field in that sixth position is the adjusted close, and skipping it means the adjusted close is read and thrown away. The consequence is worth stating explicitly, because it surprises almost everyone: the default import gives you split-adjusted prices, not dividend-adjusted prices. To obtain a total-return series you replace Skip with AdjClose, at which point the importer computes the factor described earlier and applies it to all four prices and to volume.

$FORMAT Date_DMY,Open,High,Low,Close,AdjClose,Volume

Two cautions attach to editing that file. First, an upgrade of the downloader may rewrite it, so verify it after every upgrade rather than assuming your edit survived. Second, vendors change their column order: AmiBroker published a corrected format file after one such change swapped the close and adjusted-close columns, and a format definition that no longer matches the file produces prices that are wrong without being obviously wrong.

Keeping both versions at once

There is a neat trick for the common situation where you want adjusted prices for returns and unadjusted prices for levels. The importer command $RAWCLOSE2OI 1 writes the raw close, multiplied by 100, into the open-interest field. For equity data that field is otherwise unused, so you get the unadjusted close carried alongside the adjusted series and readable from AFL.

Fragment — not a complete formula

// With $RAWCLOSE2OI used at import time, OpenInt carries raw close x 100.
RawClose = OpenInt / 100;
AdjustedToRawRatio = Close / RawClose;

The cost is that you have spent the open-interest field, so do not do this on futures or options data, where it holds something real.

Finding splits that were never applied

Tools → Database Purify includes a Report possible splits check. It scans for gaps between the previous close and the current open that exceed a percentage threshold you set, estimates a plausible split factor for each, and lists the dates as candidate unadjusted splits. It is a detector, not a repairer — it tells you where to look, and you decide.

That distinction matters. A large overnight gap can be a split, a merger, a reverse split, a currency redenomination, a data error, or genuine news. Only the first two are fixed by applying a ratio.

Which series for which question

Question you are asking	Series to use	Why
What return would a holder have earned?	Total return (dividend-adjusted)	Dividends are part of the return; ignoring them understates it
Did a price break a specific level?	Unadjusted, or split-adjusted only	The level must be a price that actually existed
Is this instrument above its 200-day average?	Either, consistently	The comparison is relative, so adjustment cancels
Was daily volatility elevated?	Split-adjusted at least	Unadjusted split gaps contaminate volatility badly
Did the stock trade at least a million shares?	Unadjusted volume	Adjusted volume is restated, not reported
Comparing a strategy with buy-and-hold	Same convention on both sides	Otherwise the comparison measures the convention

✕Common mistake

The most damaging error in this area is mixing conventions inside one study: computing signals on an adjusted series and then assuming fills at unadjusted prices, or comparing a price-return strategy result against a total-return index. Neither produces an error message. Both produce a number that is wrong by an amount nobody can see. Write down which convention your data uses, once, at the top of the formula, and check it whenever the data source changes.

Recap

Splits and dividends both put discontinuities into a price series, and back-adjustment removes them by rewriting earlier prices. Adjustment preserves every percentage change except the one it is fixing, and destroys the price levels. Dividend adjustment goes further and converts a price series into a total-return series, answering a different question. Volume is rescaled with prices; absolute gap sizes change while percentage gaps do not; and precision degrades in the deep history of heavily split instruments. AmiBroker exposes all of these decisions — in the importer’s ADJCLOSE handling, in $RECALCSPLITS and $ROUNDADJ, in $RAWCLOSE2OI, and in the Database Purify split detector — which means they are yours to make rather than yours to discover afterwards.

The next lesson turns from deliberate rewriting to accidental damage: the defects that get into a series without anyone intending them.

Check your understanding

Question 1. A stock split 2-for-1. In a correctly split-adjusted series, what happened to the volume figures for bars before the split?

• They are unchanged, since volume is not a price
• They were halved, to match the halved prices
• They were doubled, restating them in post-split shares
• They were set to zero for the split day only

Show the answer and why

Answer: They were doubled, restating them in post-split shares

The importer divides volume by the same factor it multiplies prices by. With a factor of 0.5 the prices halve and the volume doubles, which keeps price times volume roughly constant and restates the share count in current terms.

Question 2. You import Yahoo-style history with the default format definition, which skips the adjusted-close column. What kind of series do you end up with?

• Fully unadjusted prices
• Split-adjusted prices, but not dividend-adjusted
• A total-return series
• Prices adjusted for dividends but not splits

Show the answer and why

Answer: Split-adjusted prices, but not dividend-adjusted

The source close column is already split-adjusted; the separate adjusted-close column is what carries the dividend adjustment. Skipping that column therefore yields split-adjusted, price-return data — which is not what many people assume they are getting.

Question 3. Which of these rules would be damaged by switching from unadjusted to adjusted data? Select all that apply.

• Buy when the close exceeds 50
• Buy when the close exceeds its 200-day moving average
• Reject symbols priced under 5
• Buy when the daily gap exceeds 2 currency units

Show the answer and why

Answer: Buy when the close exceeds 50, Reject symbols priced under 5, Buy when the daily gap exceeds 2 currency units

Anything expressed in absolute price or currency units is measured against restated numbers after adjustment. The moving-average comparison is a ratio between two series that were adjusted by the same factor, so it is unaffected.

Question 4. Database Purify reports a possible split on a date where the price gapped 40 per cent overnight. What have you learned?

• That a split occurred and should be applied
• That the data is corrupt and the bar should be deleted
• That something discontinuous happened on that date, which now needs identifying
• That the detection threshold is set too low

Show the answer and why

Answer: That something discontinuous happened on that date, which now needs identifying

The tool detects gaps and estimates a plausible ratio; it cannot distinguish a split from a merger, a redenomination, a bad print or genuine news. The output is a list of dates to investigate, and applying a ratio blindly would corrupt a series that was correct.

Check my answersClear