Guide · Research method · Updated 2026-09-23

A continuous futures series is a construction, and each way of stitching it breaks a different measurement

Open a long chart of index futures and you are looking at decisions somebody made for you. A monthly contract is listed about 90 days before it expires, does about 76 per cent of its trading as the near month, and then stops existing. The exchange publishes a price for every contract on every session and never a continuous one, because there is not one.

This page builds the three standard joins from one set of settlement prices, measures how far apart they land, and states the result as what each one invalidates, because a construction that is right for one measurement is wrong for another by design.

Three live contracts and no continuous price

On every one of the 528 sessions from 1 August 2024 to 18 September 2026, the large cap benchmark index carried exactly three futures contracts, near, next and far, each with its own price. The price used here, and the one every open position is marked to, is the daily settlement price: the volume weighted average price of the contract's last thirty minutes or, for a contract that did not trade in that window, a theoretical price computed from the index as F = S e^rt, under NSE Clearing's published settlement mechanism for equity derivatives. On each of the 25 expiries in the sample, the expiring contract settled at the index's closing level exactly.

On thinner products the settlement price is often not a traded one. The next month contract on the financial services index settled away from its own close on 108 of 528 sessions, and on the next rung large cap index on 30. The file shows what those prices are. On 18 September 2026 all 5 index futures contracts that did not trade settled at prices implying one identical rate, 6.32 per cent, through that formula, while the traded ones implied anything from -0.76 to 9.89; the financial services index's October contract carried a last trade of 25,452.20 and settled at 25,682.85. A roll that fires early on such a contract stitches the series across a formula, not a trade.

So a long series answers two questions on every session: which contract to show, the roll rule, and how to join it to its successor, the stitching method. Everything downstream inherits both, and neither is visible on the chart.

The gap at every roll is carry, not a move

At a roll the next contract is priced above the expiring one by roughly a month of carry: the cost of funding the index for the extra month, less what it distributes. Why that is an arbitrage bound rather than a forecast is set out in the forward price is not a forecast; this page takes the gap as given and measures what it does to a series.

At the close of the session before each expiry, the next contract settled above the expiring one at 160 of 164 rolls since 30 January 2013, by 0.410 per cent on average, within a range of -0.145 to 0.904 per cent. The four exceptions fell in May 2020, June 2020, July 2020 and May 2022. The last two years show the same on every index with listed futures.

An unadjusted series adds that gap to the first session after every roll. Over the last 25 rolls on the large cap index, its move on that session exceeded the held contract's own move by 0.49 per cent on average, in the same direction every time. On 25 August 2026 the chart rose 1.08 per cent; the contract actually held rose 0.61.

Three constructions, defined exactly

Unadjusted. On each session, the settlement price of whichever contract the roll rule says is held. Every value on it printed. Every roll inserts a step equal to the gap, and nothing on the chart distinguishes that step from a market move.

Difference adjusted. Leave the latest contract untouched. At each roll, add the gap, new minus old at the same close, to every earlier price. Each session's change in points then equals the change of the contract actually held, so the point path is exact, and every level before the latest roll is moved by the sum of all later gaps.

Ratio adjusted. Leave the latest contract untouched and multiply every earlier price by new over old at each roll. Each session's percentage change then equals the held contract's, so the return path is exact, and every earlier level and every distance in points is scaled by the product of all later ratios.

The adjusted series are not rival approximations of one true series; they describe two different positions. The difference series is the profit and loss of a fixed number of contracts rolled lot for lot, which is what an account holding one lot experiences. The ratio series is the return of an exposure reset at each roll to the account's value, as if every roll reinvested the whole balance. The unadjusted series describes no position at all: it records where the near contract traded. Adjusting forward instead, keeping the oldest contract real, preserves the same properties and makes today's price the fictional one.

Four answers from one set of prices

The long leg joins 164 monthly rolls from 30 January 2013 to 18 September 2026. A position rolled at a fixed rule transacts only at roll sessions, so its result follows exactly from the settlement prices on those sessions: buy the next contract at each roll, sell it at the following one.

These are not rounding differences. The unadjusted series rose 285.76 per cent against the index's own 285.52, because the near contract converges to the index at every expiry and, across the two years measured daily, never stood more than 0.91 per cent from it. The lot held and rolled made 7,794.55 points on a first price of 6,094.90. The rest is 9,523.65 points of roll gaps, paid by the long in the price of each new contract. That is not an economic loss, since a futures buyer does not pay for the index and can hold the money at interest, and the carry is the price of that. It is simply not a return of the futures.

The adjusted series disagree with each other for another reason. The ratio series compounds, as that reinvested exposure would, to 97.3 per cent. The difference series gets the points exactly right, all 7,794.55 of them, then divides them by a starting level of 15,583.95 that never traded. Over the last two years the gap between chart and position is large enough to change a sign.

On the banking sector index the unadjusted series says the futures rose 9.2 per cent in two years, and on the financial services index 8.7. A lot held and rolled through the same sessions lost 5.1 and 5.2 per cent of its first price. Both statements come from the same file.

Far from the present, the levels are fiction

Two distortions grow with distance. On the difference series a real one per cent move in January 2013 reads as 0.39 per cent, because the point move is right and the level under it is 2.57 times too high: volatility, percentage stops and drawdowns measured there are all compressed. On the ratio series a real 100 point move reads as 196: point stops, point targets and any range quoted in points are all inflated.

The standard warning about the difference method is that it can go negative. That is true of the method, which adds a running total with no floor: where the next contract usually trades below the expiring one, back-adjustment pushes the history down until, far enough back, it crosses zero. Indian index futures rolled into a dearer contract at 160 of 164 rolls, so here the failure runs the other way. The history is lifted, never sunk, and the damage lands on every percentage computed on it.

Back-adjustment also rewrites itself. Anchored to the latest contract, each new roll moves the entire history by that roll's gap: the most recent roll in the sample moved every earlier value of the difference series by 114.50 points. Two downloads either side of a roll disagree at every historical session.

One stop rule, three answers

A rule that references a price level shows the damage directly. Take the simplest: buy at the close, exit at the first close 2 per cent below the entry price, otherwise exit after 20 sessions. Run it from every session of a window on each series, and once on the position itself, one lot of the held contract rolled lot for lot with the stop measured from the price actually paid. Then repeat with a stop a fixed number of points below entry, about 2 per cent of each window's average price: 500 points for 2024 to 2026 and 160 for 2016, a decade back.

Near the present the adjustments average about 6 per cent and the series disagree by a few points. A decade back they do not. In 2016 the difference series stood at 1.99 times the traded price on average, so its 2 per cent stop was really a 4.0 per cent stop, and it fired on 21.1 per cent of entries against 48.6 for the position. The ratio series ran the percentage stop correctly and the point stop wrongly: 160 adjusted points were about 101 real ones, and it stopped out 59.5 per cent of entries against 48.6. The unadjusted series was wrong both ways, and its mean 20 session result of +0.53 per cent against the position's +0.22 is the carry again, since almost every window that long contains a roll.

That qualifies the rule of thumb that ratio-adjusted data is unfit for stop studies. It holds only for stops in points. For a stop in percent the ratio series is right and the difference series is the one that fails, by a margin that grows every year back.

The decision, stated as what each series invalidates

Nothing in that table is a preference. Each construction preserves one property by giving up the others, so a study that needs two properties needs two series or, better, a simulation on the contracts themselves with each roll executed as a trade. Generating a signal from percentage moves on the ratio series and booking its profit and loss in points on the difference series is legitimate. Reading a level off either of them is not.

The roll date is a second, hidden choice

Adjustment removes the gap. It does not remove the choice of which contract is held on which session, and that choice moves the answer too. Nine roll rules on the same 25 cycles of the large cap index:

The spread across rules is 471.55 points on the same position over the same two years, 1.9 per cent of its first price, and almost all of it comes from one decision: whether the series holds the expiring contract through its final session. At the close of the session before expiry the expiring contract stood 18.22 points above the index on average, and the final session settles it at the index close. A series rolling at the expiry close books that convergence, 455.45 points across 25 rolls, which one rolling a session earlier never holds. Rolling three or five sessions early lands in between, because over those sessions the next contract's premium shrank faster: by 25.17 points on average from five sessions out, against 13.39 for the expiring contract.

Liquidity rules are less neutral than they sound. The next contract's volume overtook the expiring one's before the final session in only 3 of 25 cycles; in the other 22 it led only on expiry day, so a volume crossover rule behaves almost exactly like rolling at the expiry close. Open interest moved earlier, leading at the session before expiry in 19 cycles and two sessions before in 6. What the published rollover figures built on that open interest can and cannot say is covered in what rollover measures.

The 2025 expiry move, and the roll rules it broke

The regulator's circular SEBI/HO/MRD/MRD-TPD-1/P/CIR/2025/76 of 26 May 2025 limited each exchange's equity derivatives expiries to one weekday, Tuesday or Thursday, and put every contract other than benchmark index options, index futures included, on a minimum one month tenor expiring in the last week of the month on that day. NSE chose Tuesday: its circular 103/2025 of 17 June 2025 moved contracts expiring on or after 1 September 2025 to Tuesday, monthly contracts to the last Tuesday, and circular 111/2025 of 25 June 2025 left contracts expiring on or before 31 August 2025 unchanged. The file agrees: all 13 monthly expiries in the sample before the change fell on a Thursday, and 11 of the 12 after it on a Tuesday, with 30 March 2026 a Monday because the Tuesday was a holiday.

For a continuous series the change sorts roll rules into two kinds. A rule counted in sessions back from expiry kept its meaning. A rule anchored to the calendar did not: rolling on the Monday of expiry week moved from three sessions before expiry to one, rolling on the Friday before the expiry week from four to two, and rolling five calendar days before expiry from four sessions to three. A rule hard coded for the old calendar, rolling on the last Wednesday of the month, fell after the contract had already expired in nine of the twelve months since and rolled early in the other three. Any statistic pooled across the change, such as the behaviour of the three sessions before expiry, is two samples: before a Thursday expiry those sessions normally fall inside one week, and before a Tuesday expiry they always straddle a weekend.

The transition also left a trap in the data. In the exchange's own file, the large cap index's September 2025 contract carries an expiry of 25 September 2025 on 25 sessions and 30 September 2025 on the next 41. It was re-dated at the close of 31 July 2025, the date circular 111/2025 set for realigning long dated contracts, and its price ran on without a break. The banking sector index's January to March 2025 contracts were re-dated the same way at the close of 1 January 2025, in the earlier move to Thursday under circular 154/2024. A stitcher that keys contracts by the expiry date field sees a contract vanish and another appear with no trade between them, and a time to expiry read from that field jumps by five days overnight. Keying by expiry month, and taking the date from the contract's last session, avoids both.

A result on a continuous series names its construction

Every figure above came from one set of files. The same position over the same two years reads -6.61 per cent on the unadjusted series and between -17.38 and -18.99 per cent on the ratio series depending on the roll rule. A result that does not state both choices cannot be checked, which is the general case made in publishing a result someone else can check. For continuous futures the minimum disclosure is short.

The habit that follows is to keep the raw contract file rather than any adjusted series, and to rebuild the series from it with the rules written down. The raw file does not change when the next roll arrives. Every back-adjusted series built from it does, the same way a stock history adjusted for corporate actions is rewritten at each new action, a problem covered in backtesting integrity.

What each construction is actually for

The unadjusted series is the record of where contracts traded. The difference series is the ledger of a lot held and rolled. The ratio series is the return of a balance reinvested at every roll, and the only one on which percentages from different years compare. None of them is the futures price, because past the life of one contract there is no such thing. Choosing among them is not a data question but a question about what the study measures, answered before the data is loaded, which is the part of method no charting setting supplies.