--- title: "Mean reversion vs momentum: a test on Nifty closes" description: "Autocorrelation and the variance ratio on dated Nifty closes, two counted rules, and why four quarters cannot name a regime or choose a style." source_url: "https://www.rupeecase.com/learn/path-18/module-18-9-mean-reversion-vs-momentum" --- [Path 18 9 of 14](/learn/path-18/)Mean reversion against momentum[Next 18.10](/learn/path-18/module-18-10-implied-correlation) From 1 Jul 2025 to 17 Jul 2026 the Nifty ended lower than it began, and in that time its day to day behaviour changed sign. In the quarter to 3 Oct 2025 a rise tended to be followed by a small rise. In the quarter to 16 Apr 2026 a rise tended to be followed by a small fall. Over the whole stretch the pull was close to nothing at all. Ask a momentum trader and a mean reversion trader to read the same file and each can find a quarter that proves them right. This lesson tests what the file supports with two plain measures, [autocorrelation](/learn/glossary#autocorrelation) and the variance ratio, shows how little four quarters can tell you, and explains why the two styles are less opposed than they sound. Every figure comes from NSE end of day files, dated and not live. 3By the end you can 1. Say how momentum and mean reversion differ by horizon and by object, a price or a spread. 2. Read an autocorrelation and a variance ratio next to their noise bands. 3. Explain why a short window cannot name a regime and what a fair test must fix first. Watch in the terminal: what are the four lead figures? A short tutorial on sample data. ## The idea, plainly ### Two bets about the last move Momentum says a price that has been rising tends to keep rising over the next holding period, and a falling one to keep falling. Mean reversion says a price stretched away from an average tends to come back. They are not opposite beliefs about markets in general. They are bets at different horizons and on different objects. Studies of many markets report momentum over months in prices, and reversal over days to a week for some stocks and indices. Mean reversion in the strict sense belongs to a spread between two prices that share a home, which the [cointegration module](/learn/path-18/module-18-7-cointegration-toolkit) tests. A single index level is much closer to a random walk. Run the same unit root test on the Nifty close and it cannot reject a wandering path, where the daily returns reject it easily. ### Measuring the pull Autocorrelation asks whether today's return is related to the return k days ago. A positive value points to momentum, a negative one to reversion. The variance ratio asks the same thing over longer horizons. If returns were unrelated, the variance of a q day return would be q times the variance of a one day return. A ratio above one says moves tend to run, and a ratio below one says they tend to reverse. The maths: autocorrelation and the variance ratio For daily log returns r, with the sample mean removed: AC(k) = cov(r_t, r_t-k) / var(r) VR(q) = var(q day sum) / (q x var(1 day)) With n returns and no true pull, AC(1) has a spread of about 1 over the square root of n. For 258 returns that is about 0.06, so a value inside about two spreads of zero cannot be told from noise. The variance ratio has a wider spread that grows with q, because overlapping q day sums share most of their days. Read a five day ratio below one next to that wider spread, not next to zero. 3 terms this section turns on From the module glossary; every term is in the Learn glossary too. Source: Module 18.9, Mean reversion against momentum. ### Why the options desk cares The two styles are also two payoffs. Someone long options, such as a gamma scalper, gains when moves run beyond what the option price assumed. Someone selling options earns the premium when moves stay inside it, and loses when a trend carries the index past the strikes. So a regime question is a risk question for both sides. A seller who assumes reversion carries the risk of a sustained run, and a buyer who assumes momentum pays decay while the index ranges. The [variance risk premium module](/learn/path-16/module-16-13-variance-risk-premium) puts a price on that trade. ## Worked example: four quarters of the Nifty The file gives 259 sessions from 1 Jul 2025 to 17 Jul 2026. Here is the path first. It has a flat stretch, a rise, a long fall and a rebound, so a story of any style can be told about some part of it. One path with a flat stretch, a rise, a fall and a rebound Daily close of the Nifty 50 from 1 Jul 2025 to 17 Jul 2026. Each style can find a stretch that suits it, and the path alone does not choose between them. Source: NSE end of day data, computed by RupeeCase. As of 17 Jul 2026. ### Autocorrelation by quarter Split the returns into four blocks of about 65 sessions and measure the lag one autocorrelation in each. The sign of the pull flipped once, inside the noise Each bar uses about sixty five daily returns, so one standard error is about one over the square root of sixty five, and a value inside two of them is not distinguishable from zero. The whole window gave a value close to zero. Source: NSE end of day index closes, computed by RupeeCase. As of 17 Jul 2026. Read one more paragraph, 66 words Three quarters lean toward momentum and one toward reversion, and every bar sits inside the noise band of two spreads, about 0.25 either side of zero. The highest is a little past one spread. A regime change would need a shift larger than the band, held for longer than a quarter. Four blocks cannot show one. They show that a short window can flatter either style. ### The variance ratio The variance ratio looks at the same returns summed over several days. Below one means moves tended to reverse over that horizon. All four ratios sit a little below one, which is within their noise Variance of the summed return over q days divided by q times the variance of the one day return, for the whole window, with overlapping sums. A random walk gives one. The five day ratio is less than one spread away from it. Source: NSE end of day index closes, computed by RupeeCase. As of 17 Jul 2026. All four sit a little under one, a mild lean toward reversal. The five day ratio is the lowest, and it is still only about one spread below one. This is the honest answer to the question this lesson began with: a faint reversal tilt that this sample cannot separate from no pull at all. ### Two simple rules, counted A rule turns the idea into a count. The first rule looks at the last 20 sessions. If the index rose, momentum says the next five sessions rise. The second looks at how far the close sits from its 20 session average, in usual sizes. If it sits more than one and a half above, reversion says the next five sessions fall. Nothing is traded and no return is claimed. The question is only how often the next five sessions agreed. The two rules agreed with the next week about as often as a coin would The first two bars test momentum, with the second also the reversion reading. The last two test the stretch rule on closes far above and far below the 20 session average. Overlapping windows; illustration of method, not a return claim. Source: NSE end of day index closes, computed by RupeeCase. As of 17 Jul 2026. Read one more paragraph, 104 words After a 20 session rise, the next five sessions rose less than half the time, which leans against momentum. After a stretch above the average they fell about two times in three, which leans for reversion. After a stretch below, they rose only two times in five, which leans against it. The two stretch cases pull in opposite directions, and put together they agree with the rule on about half the cases. The windows overlap, so only about a fifth of the cases are independent looks. A sample this size and this shape is a demonstration of method. It does not choose a style. ### What a fair test must fix first Each of the choices above could have been made differently, and each changes the count. A fair test writes them down before it looks: the lookback, the holding period, the threshold for a stretch, the data used to choose them and the data used to judge them. It also includes costs. A reversion rule trades often, because it acts on every stretch. Every round trip of a futures leg pays STT of 0.05% on the sale and the other statutory charges in the [cost module](/learn/path-12/module-12-6-cost-of-an-fo-trade), so a small average gain per trade can vanish. A momentum rule trades less but holds through the fall that ends a trend. Neither cost shows in a count of ups and downs. The same goes for slippage, the gap between the price you see and the price you get, which grows when a rule fires on exactly the days when everyone else is moving too. Add it to the cost before judging an edge that is smaller than a fraction of a percent per trade. Read one more paragraph, 67 words Published studies add that the effects differ by market, period and horizon, and that many fade once costs are included. Indian studies exist, and the one paper in the sources reports momentum across many futures markets over months. None of that is a result for the Nifty on these dates. The only claim this lesson tests is the narrow one in its charts, on the dates shown. ### Read the chart yourself Look at the path above and find the longest stretch where the index kept moving one way. Ask what lookback and holding period would have called it momentum, and which would have called its end a reversal. If two choices of the same rule give opposite answers on the same stretch, the rule has a free parameter that the data did not fix. That parameter should be written down before the test, and the test run on a period that did not shape it. Watch in the terminal: which numbers am I looking at? A short tutorial on sample data. ## The common mistake The claim: Indian markets are mean reverting, so every sharp move gets reversed within the week. The sample points the other way as often as it points this way. The five day variance ratio was a little below one, which fits the claim, yet it sat within one spread of no pull. Three quarters had a positive autocorrelation, which fits the opposite claim. After a stretch below the average the next week rose only two times in five. A single regime label, either way, needs far more data than four quarters. Ask for the lookback, the holding period and the threshold before the test, the count of cases including the misses, and a result that survives on a period that was not used to build it. ## Key takeaways * Momentum and reversion are bets at different horizons, not opposite worldviews. * A single index is near a random walk; a spread can have a home. * Read autocorrelation and variance ratios against their noise bands. * Four quarters can flatter either style without proving it. * Fix the lookback, holding period and threshold before the test. Two terms to hold on to from 18.9 From the module glossary. Source: Module 18.9, Mean reversion against momentum. **Before you trade.** Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. [Read the SEBI study](https://www.sebi.gov.in/reports-and-statistics/research/aug-2026/study-profitability-of-individual-traders-in-the-equity-derivatives-segment-fy25-fy26-_103835.html) What does Mean reversion against momentum cover?Both styles can find a quarter that suits them. Two plain measures say how much the file supports either. It works through The idea, plainly, Worked example: four quarters of the Nifty, The common mistake, Key takeaways. It is module 18.9 of Path 18, Arbitrage and Relative Value, about 10 minutes of reading, free. AF&O on RupeeCase ## Hedging only, in development F&O at RupeeCase will do one job: protect a portfolio you already own, by a rule published before it runs. No speculation, no naked option selling, no leveraged bets. It is not available yet. [How hedging will work](/hedging)[Sign up for RupeeCase](https://invest.rupeecase.com/signup) [No hedgeFalls with the marketWith a putA floor, for a premiumIllustration with made up numbers, not a product and not a recommendation.](/hedging) QQuick check ## 10 questions, 7 to pass. Each attempt draws 10 of the 15 questions in this module's bank, and a retake draws a fresh set. A pass gives this module's Certificate of Completion. Your result stays on this device and counts towards the Path 18 certificate. 7 of 10 correct passes module 18.9 Every answer is explained when you check; a retake is always free. Source: RupeeCase Learn quiz rules (70% to pass). Passed ### Certificate ID Download PNGPrint or save as PDF[Check the ID](/learn/certificates/verify) Self paced and unproctored. A record of completing free education by RupeeCase; not a NISM certificate and not endorsed by NISM, NSE, BSE or SEBI. It qualifies no one to deal, advise or publish research. CCheck yourself ## Path 18 so far. Your quick check results on this device, stop by stop. Stop 9 of 14 on Path 18 Arbitrage and Relative Value: every live stop, this module ringed. Source: RupeeCase Learn, Path 18. 1. [18.1Cash futures arbitrage and the Nifty 50 Arbitrage indexNot yet](/learn/path-18/module-18-1-cash-futures-arbitrage) 2. [18.2Conversions and reversalsNot yet](/learn/path-18/module-18-2-conversions-and-reversals) 3. [18.3Pair trading intuition: correlation is not cointegrationNot yet](/learn/path-18/module-18-3-pair-trading-intuition) 4. [18.4Futures calendar arbitrage and roll dynamicsNot yet](/learn/path-18/module-18-4-futures-calendar-arbitrage) 5. [18.5Box spreads with European index optionsNot yet](/learn/path-18/module-18-5-box-spreads) 6. [18.6Parity deviations in practice: what the frictions costNot yet](/learn/path-18/module-18-6-parity-deviations) 7. [18.7Cointegration toolkit: Engle Granger, ADF, half life and z scoreNot yet](/learn/path-18/module-18-7-cointegration-toolkit) 8. [18.8Pair trading with Indian stock futuresNot yet](/learn/path-18/module-18-8-pair-trading-with-stock-futures) 9. [18.9Mean reversion against momentumNot yet](/learn/path-18/module-18-9-mean-reversion-vs-momentum#quiz) 10. [18.10Implied correlationNot yet](/learn/path-18/module-18-10-implied-correlation) 11. [18.11Dispersion trades: construction and risksNot yet](/learn/path-18/module-18-11-dispersion-trades) 12. [18.12The correlation risk premiumNot yet](/learn/path-18/module-18-12-correlation-risk-premium) 13. [18.13Baskets, PCA stat arb and Johansen testsNot yet](/learn/path-18/module-18-13-pca-stat-arb) 14. [18.14Kalman filter hedge ratiosNot yet](/learn/path-18/module-18-14-kalman-filter-hedge-ratios) 15. [TPath test, 30 questionsNot yet](/learn/path-18/module-18-14-kalman-filter-hedge-ratios#pathTestSection) Path 18 in reading time: 143 minutes over 14 modules Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 18. Explore next ## Put the module to work. * [Free module 14.16Gamma scalping10 min read](/learn/path-14/module-14-16-gamma-scalping) * [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder) * [Free module 18.3Pair trading intuition: correlation is not cointegration8 min read](/learn/path-18/module-18-3-pair-trading-intuition) * [Free module 19.2Strategy metrics: CAGR, Sharpe, Sortino, drawdown and expectancy9 min read](/learn/path-19/module-19-2-strategy-metrics) * [Free module 18.7Cointegration toolkit: Engle Granger, ADF, half life and z score10 min read](/learn/path-18/module-18-7-cointegration-toolkit) * [Free module 18.8Pair trading with Indian stock futures10 min read](/learn/path-18/module-18-8-pair-trading-with-stock-futures) Community ## Join my WhatsApp group. Scan the code, fillFill one short form, and join my WhatsApp group. Slides, sources, factsheets and the rebalance logs live there, and members join a daily Google Meet with me. New to RupeeCase? [Getting started](/getting-started) [See the terminal](/terminal) [Sign up for RupeeCase](https://invest.rupeecase.com/signup) [Join the WhatsApp group](https://forms.gle/C6HMtM1Z2GfeocQV7) [One form, one group](https://forms.gle/C6HMtM1Z2GfeocQV7)Scan with your phone camera SSources ## Go to the source. 5 sources, NSE the most cited The publisher of each source listed below. Source: Module 18.9 source list. 1. [NSE Indices, Nifty 50](https://www.niftyindices.com/indices/equity/broad-based-indices/nifty-50) NSE 2. [NSE, Nifty 50 index overview](https://www.nseindia.com/products-services/indices-nifty50-index) NSE 3. [SEBI Investor, Understanding derivatives](https://investor.sebi.gov.in/understanding_derivatives.html) SEBI 4. [NISM, Series VIII Equity Derivatives certification examination](https://www.nism.ac.in/revamp-nism/equity-derivatives/) NISM 5. [Moskowitz, T., Ooi, Y. and Pedersen, L. (2012), Time series momentum, Journal of Financial Economics](https://doi.org/10.1016/j.jfineco.2011.11.003) Paper GTerms ## 5 terms from this module. MomentumThe tendency of a price that has risen over a lookback to keep rising over the next holding period. Mean reversionThe tendency of a price or spread stretched from its average to move back toward it. [Autocorrelation](/learn/glossary#autocorrelation)The link between a return and the return k days earlier. Positive points to momentum, negative to reversal. Variance ratioThe variance of a q day return over q times the variance of a one day return. One means no pull. RegimeA stretch of time in which a market behaves in one stable way. Naming one takes more data than a few quarters. [All 230 terms in the glossary](/learn/glossary) [Question people askMean reversion or momentum: what is the difference?A short answer with a dated chart](/learn/questions/mean-reversion-vs-momentum)[Related module18.3 Pair trading intuition: correlation is not cointegration8 min, Intermediate](/learn/path-18/module-18-3-pair-trading-intuition)[Related module19.2 Strategy metrics: CAGR, Sharpe, Sortino, drawdown and expectancy9 min, Intermediate](/learn/path-19/module-19-2-strategy-metrics)[Pillar guideDerivatives and Quant115 modules across paths 12 to 19](/learn/derivatives) Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.