Guide · Research method · Updated 2026-09-23

An adjusted price history is computed, not recorded, and it changes every time a company acts

A back-adjusted chart shows prices at which the stock never traded. That is the output of a calculation with inputs, a convention and a date, none of which the chart displays. This guide works the calculation for each corporate action from the National Stock Exchange's own files.

A price change that was not a return

A return is the change in the value of a holding. On an ex-date the quoted price changes for a second reason: the claim that one share represents has changed. After a five-for-one split each old share is five new ones, so a close of 3,956.70 followed by an open of 791.40 describes a holder who lost nothing. An unadjusted series records that session as a fall of 80 per cent, and every statistic computed across the ex-date inherits it.

The exchange's daily files do not correct it, and should not be expected to: they record what traded. Even the previous-close field of the full security bhavcopy carried the unadjusted close on the ex-date in 446 of the 447 split and bonus ex-dates from January 2022 to September 2026 that matched the files, so a return computed from the exchange's own previous-close column shows the phantom move too.

One observation did all of that. Annualised volatility is overstated 5.7 times because the split session alone contributes 28 times as much to the variance as the other 243 sessions combined. The drawdown and the worst day are the split itself. A Sharpe ratio, a beta, a stop rule or a breakdown signal computed over that year would be reporting the corporate action rather than the market. The guide to backtest integrity and the walkthrough of a pandas backtest both warn against differencing raw prices; what follows is the arithmetic, including the parts that warning leaves out.

One multiplier per action, and what each one holds constant

Adjustment multiplies every price before the ex-date by a single number m, chosen so that the value of a holding is the same on both sides of the event. NSE Clearing, the clearing corporation, states the principle for derivatives in exactly those terms on its corporate actions page: the value of a position on the cum and ex dates should remain the same as far as possible, so that an option that was in the money stays in the money. A price history needs the same property for the same reason.

Three details decide whether the arithmetic comes out right. First, direction: the exchange quotes split and bonus factors the other way up, as (A + B) / B or old face value over new, and divides strikes by them, while for a rights issue it quotes (P - E) / P and multiplies strikes by it. Both describe the same m. Second, order: "Bonus 1:2" on the exchange's list means one new share for every two held, so m is two thirds, not one half. Third, a reference price: the dividend and rights factors need P, the close on the last cum date, and a vendor that uses a different P holds a different factor.

A demerger has no arithmetic factor at all. Two claims exist where one did, and for a stock with derivatives the exchange discovers the parent's ex-date price in a special pre-open call auction rather than setting it by formula. The factor is whatever that discovery implies, which is why data sources disagree about it; the demerger cost base guide covers the same event from the tax side.

Rights: the factor depends on the price paid, not only on the ratio

A rights issue is a bonus issue with a bill attached. The holder receives A new shares for every B held and pays S for each. If S were zero it would be a bonus. If S equalled the market price nothing would pass to the holder and no adjustment would be needed. Every real rights issue sits between those limits, which is why no function of A and B alone can be the factor.

What passes to the holder is the discount on the new shares. Per entitlement it is P - S. Per existing share, once the new shares are counted, it is E = A (P - S) / (A + B). Subtract E from the last cum close and the result is the theoretical ex-rights price, the price at which the enlarged share count is worth exactly the old count plus the cash paid in: TERP = (B × P + A × S) / (A + B) = P - E, and m = TERP / P. The rights issue explainer sets out why that blend is not a gift; here it is a number to compute.

The exchange works exactly this arithmetic in the annexure to its derivatives circular for a rights issue. For a 3:25 issue at 1,800.00 in a large-cap name that went ex on 17 November 2025, the circular of 13 November computed the factor on an indicative price of 2,488.20 and printed 0.970366. On the actual last cum close the same method gives the following.

Two cross-checks show the arithmetic describes something real. The entitlement itself traded as a separate security, as SEBI's circular of 22 January 2020 on dematerialised rights entitlements provides. On its first session, 25 November 2025, it closed at 514.30 while the share closed at 2,332.90, which is 96.5 per cent of the 532.90 that the share price minus the issue price says one entitlement is worth. The market priced the right close to the value the formula assigns to it.

The second check is on the formula as published. The annexure multiplies the benefit per entitlement by A before dividing by A + B. The clearing corporation's summary page, as it read on 23 September 2026, writes the benefit per share as (P - S) / (A + B), without the A. For this issue that expression gives 0.989828 instead of 0.969485; it is right only when A is 1. Copy the method from a worked annexure, not from a summary line.

The single event is typical rather than special. Every rights issue on the exchange's list from 2022 to 2026 whose terms parse, whose issue price sat below the last cum close and whose closes are in the files gives 170 events, with a median discount of 30 per cent to P.

The ratio-only error has a closed form. Using m = B / (A + B) where the correct m is TERP / P overstates the ex-date return by a factor (B × P + A × S) / (B × P), a phantom gain of (A / B) × (S / P). It is largest when the issue is generous and the discount small, exactly the issues that look least like a bonus. The unadjusted series errs the other way by E / P, a phantom fall that grows with the discount. Only the theoretical ex-rights price leaves an ex-date that looks like an ordinary session: 15 of 170 events exceeded the largest move of the previous 60 days, against 115 under the ratio and 71 unadjusted. Five further issues were priced at or above the last cum close. There the entitlement had no intrinsic value and the formula no longer describes anything a holder would do, so they are kept out of the table rather than forced through it.

Every adjusted series is exact at one date

Adjustment can run in either direction. Back-adjustment multiplies everything before each ex-date by m, so the latest prices are the traded ones and history is restated in today's share units. Forward-adjustment divides everything from each ex-date on by m, so the earliest prices are the traded ones and the present is restated in the original share units. Both remove the step and both carry identical daily returns. They differ only in which end of the series is true.

The difference matters at the next action. A forward-adjusted series only ever appends: a new ex-date changes nothing before it, so a file saved last year agrees with today's on every date they share, at the cost of a present-day price that no screen shows. A back-adjusted series is anchored to the day it was built, and every new split, bonus, rights issue or, in a dividend-adjusted file, every dividend multiplies all earlier prices again. The history is not revised because anyone found an error. It is revised because a company acted.

What one year of corporate actions rewrote

Measured over the twelve months to 18 September 2026, for the 210 stocks with derivatives on that date: 10 had a split, bonus or rights issue, and 184 went ex-dividend at least once, 309 dividend ex-dates in all. A back-adjusted file that includes dividends, for any of those 185 names, disagrees with the same file downloaded a year earlier at every date before the action; one adjusted only for splits, bonuses and rights disagrees for 10.

For a rule that refers to a price level, the consequence can be measured directly. Take the closes of 31 December 2024 and apply a minimum-price rule twice: to a file built on that day, where the adjusted close is the traded close, and to one built on 18 September 2026.

At a threshold of 5,000 the same rule on the same day selects 8 fewer names out of 30, not because any 2024 price changed but because 2025 and 2026 happened. Once dividends are included, 189 of the 206 closes of that day differ between the two files. A backtest that used such a rule last year cannot be rerun from today's download and produce last year's trades.

What survives is narrower than it looks, and it can be stated exactly. A return between two dates before a new action is a ratio of two prices multiplied by the same m, so under multiplicative adjustment it does not change. Rounding is the one leak in the arithmetic itself, and it is small: rounding both versions to the paise changed 1,349 of the 48,185 daily returns of 2024 in these stocks by more than half a basis point, and none by more than 0.03 percentage points. Return-only statistics can be reproduced from a later download. Anything that touches a level, a volume or a convention cannot. That is the practical reason the guide to publishing a checkable result asks for the snapshot date.

Right for returns, wrong for levels

An adjusted series answers one question: what a holder earned between two dates. It is the wrong input for any rule that refers to where the price actually stood.

Round numbers and levels. Traders watching 2,500 in the rights name in the week before its ex-date were watching a level that sits at 2,423.71 in today's back-adjusted file, while the file's own 2,500 corresponds to a traded price of 2,578.69 that nobody saw. A round level stays round only when m is a simple number such as a half or a fifth; a rights or dividend factor such as 0.969485 turns every round level into an arbitrary one.

Tick sizes and one-tick costs. Since 15 April 2025 the exchange sets tick size from the traded close, from 0.01 below 250 up to 5.00 above 20,000, reviewed monthly under circular NSE/CMTR/67133. A cost model of one tick of slippage run on adjusted prices charges the wrong tick: applying the current schedule to the closes of 31 December 2024, 14 of the 206 stocks land in a different tick band in today's back-adjusted file from the one their traded close implies.

Filters, quantities, lots and rupee stops. A minimum price or a penny-stock screen selects a different universe from every back-adjusted download, as the table above shows. A share count sized from an adjusted price, a contract value, and a stop or target written in rupees rather than in multiples of volatility all refer to the traded price on the day.

The working rule: compute returns, volatility and return-based signals on the adjusted series, and evaluate every level, filter, quantity and cost against the price that actually traded that day, which means keeping the traded series beside the adjusted one.

Volume needs the same factor, applied the other way

Price and quantity are two halves of one number. Traded value, price times quantity, is untouched by a split: the same rupees change hands. So when prices before the ex-date are multiplied by m, quantities before it must be divided by m. A series that adjusts price and not quantity is internally inconsistent, and a volume signal read from it is reading the share count.

The example is not unusual. Across the 419 split and bonus ex-dates in the files with at least 50 sessions before and 20 after, the published quantity stepped up by a median factor of 2.71 across the ex-date. With the factor applied the median step was 0.83, in line with the 0.84 step in traded value, which needs no adjustment. In 202 of the 419 events the published series showed activity rising while adjusted quantity fell. A rule that flags a session when quantity exceeds twice its 50-session average fired a median of 5 times in the 20 sessions after the ex-date on published quantity and 1 on adjusted quantity; 94 events fired on at least 10 of those 20 sessions, against 3 once adjusted.

The dividend question

A dividend is the one action where declining to adjust can be correct. The ex-date fall is real: cash leaves the company and arrives with the holder. Whether a series should show that fall depends on what it is meant to measure.

An unadjusted series measures price return, what the quote did, and it belongs next to a price index. A series multiplied by (P - D) / P at each dividend approximates total return, treating each dividend as reinvested at the ex-date, and it belongs next to a total return index. The index provider publishes both. Its methodology document of September 2026 computes the total return index as the previous value times the day's price index plus the indexed dividend, over the previous price index, which reinvests each dividend after the close of its ex-date; the Nifty50 Dividend Points index, per its factsheet of 31 August 2026, carries those dividends as a running total that resets after each March expiry. Even the price index is not purely a price series: the same document adjusts it for any dividend at or above 2 per cent of the share price and keeps such dividends out of the total return. Mixing the two conventions is the common error, and it is not small.

Reconstructed from the exchange's own index files, the Nifty 50 compounded at 11.18 per cent a year in price over the ten financial years to March 2026 and at 12.54 per cent with dividends reinvested, a gap of between 1.01 and 1.67 percentage points in every one of those years. A dividend-adjusted stock series measured against the price index is handed that gap as outperformance. The guide to dividend investing explains why the ex-date fall is a transfer rather than a loss.

The derivatives market takes a third position. SEBI's circular CIR/MRD/DoP-1/P/00108/2018 of 5 July 2018 adjusted stock option strikes for dividends at or above 5 per cent of the share price, and its circular of 28 June 2022 lowered that line to 2 per cent, which is where the clearing corporation's page stands today. An adjusted strike is reduced by the whole dividend. Below the line nothing is adjusted, and the futures price is left to carry the expected dividend within its cost of carry. Over the twelve months to 18 September 2026 the 210 stocks with derivatives had 309 dividend ex-dates with a median size of 0.49 per cent of the last cum close; 28 of them, 9 per cent, were at or above 2 per cent. A page still quoting a 5 per cent line predates June 2022.

Subtraction is right for a strike and wrong for a history. Take an illustrative old price of 400, a cum close of 1,000, a dividend of 50 and an ex-date close of 950. Multiplying the old price by 0.95 gives 380 and a holding-period return of 150.0 per cent, which is exactly the total return. Subtracting 50 gives 350 and a return of 171.4 per cent, an invented 21.4 points. Repeated over decades of dividends, subtraction drives early prices towards zero and can take them below it.

A derived artefact needs a provenance

None of this makes adjusted data unreliable. It makes it derived: the output of a function of four inputs, the traded prices, a list of actions, a set of conventions and a date. Two researchers with identical traded prices can hold different adjusted series and both be correct. A result built on one is checkable only when it states:

The source of the traded prices and of the action list. The convention: back or forward, multiplicative or subtractive, which actions were applied, whether dividends below any threshold were included, how demergers were handled, and which reference price fed the dividend and rights factors. The snapshot date of any back-adjusted file. The split of uses: which statistics used adjusted values, which used traded values, and whether volume was adjusted.

The durable practice is to store the traded file and the action list, never only the adjusted output, and to compute the adjusted series as a function of the snapshot date when the analysis runs. Any earlier result can then be regenerated as of its own date, and a disagreement with another figure traced to a named input. Treating data as something to be specified rather than simply downloaded is part of the research method the curriculum teaches, because a result is only as reproducible as its inputs.