4A.12 Case studies

Case 1: Gap-and-crap and breakout failures on the Nifty, 2011–2026#

The claims "Gap-and-crap": a stock that gaps up strongly at the open tends to sell off through the day and close below its open, trapping late buyers. "Most breakouts fail": a close above resistance tends to be followed by a fall back below it.

Data and method Yahoo ^NSEI daily bars, 1 Feb 2011 to 4 Nov 2026 (3,866 days). Gap and intraday return as in 4A.4. Null: driftless intraday Brownian motion with trailing 20-day Parkinson volatility (Proposition 4A.4). Breakout: the first day on which the Nifty closes above the highest high of the previous 20 days (M04's Donchian level). Failure: any of the next five closes is below that level. Null for failure: Monte Carlo of Gaussian random walks with the trailing 20-day close-to-close volatility, started at the actual distance above the level (4,000 paths per event).

Results

Event	n	Statistic	Observed	Random-walk null
Gap up > 0.5%	612	close below open	48.7%	50%
		close below previous close	17.8%	17.3%
		mean open-to-close return	−0.046% (s.e. 0.041%)	0
Gap up > 1%	148	close below open	52.0%	50%
		close below previous close	12.8%	9.5%
		mean open-to-close return	−0.166% (s.e. 0.110%)	0
Gap down > 1%	120	close above open	56.7%	50%
20-day closing breakout	243	fails within 5 days	52.7% (s.e. 3.2%)	60.7% (driftless, trailing vol)

Analysis At the index level there is no reliable gap-and-crap effect. The largest up-gaps show a small intraday give-back (−0.17%, $t\approx-1.5$) that is not significant, and the probability of closing below the previous close is close to the random-walk prediction once you remember (4A.4) that big-gap days are about 30% more volatile than the trailing estimate. The breakout result looks at first like the opposite of folklore: breakouts failed less often than the driftless null (52.7% against 60.7%). Two adjustments explain most of it. Adding Nifty's average daily drift (+0.035%) to the null lowers the predicted failure rate to 57.4%. Using the volatility actually realised over the next five days (about 13% lower than the trailing estimate, because volatility tends to fall in uptrends: the leverage effect of M02) lowers it to 51.2%, which matches the observed rate. The mean five-day return after a breakout was +0.01%, against +0.17% for all days (difference not significant). Conclusion: on the Nifty, "most breakouts fail" and "breakouts work" are both descriptions of a random walk with a small drift and changing volatility.

Case 2: 4 June 2024, the trade-management view#

Context M01 · 1.11 Case 4 holds the dated timeline and its sources; M02 · 2.10.3 measures the move in standard deviations. The numbers used here: after exit polls, the Nifty closed at a record 23,263.90 on 3 Jun 2024; on results day, 4 Jun, it closed at 21,884.50 (−5.93%), with an intraday low of 21,281.45 (−8.5%). Yahoo's bar for 4 Jun shows an open of 23,179.50, which was also the day's high: the gap was only −0.36%, and the fall happened during the session as counting progressed. India VIX had implied a result-day standard deviation of about 6.3% (M02's calculation), against an ordinary daily volatility of 0.72%.

A long position managed by ordinary rules Suppose a trader was long one lot of Nifty futures (lot size 25 at the time; it became 75 on 20 Nov 2024 and 65 from the January 2026 contracts) from the 3 Jun close, with a 2% stop (465 points, 2.8 ordinary daily standard deviations away).

• Ordinary-day probability of the stop being hit within the day, by (4A.9) with $\sigma=0.72\%$: $2\Phi(-2.02/0.72)=0.5\%$. Event-day probability with the implied 6.3%: $2\Phi(-2.02/6.3)=75\%$. The stop that was "safe" by ATR was close to a coin flip under the option market's own forecast.
• Fill. Because the gap was small, the stop triggered in the continuous session. An SL-limit order risked not filling in a fast fall; an SL-market order filled at or below the trigger depending on the speed of the market at that moment (M01 · 1.4). If filled at 22,798.6, the loss was 465 points, ₹11,632 per lot, 1R.
• Closing-basis stop. A trader who used "exit on a close below the stop" exited at 21,884.50: a loss of 1,379.4 points, 2.96R. The discrete-monitoring correction (4A.10) says closing-basis stops overshoot by about $0.58\sigma$ on average; on an event day with $\sigma\approx6\%$, the expected overshoot is about 3.5%, roughly what happened.
• Widening the stop in the afternoon, when the index was down 8%, meant holding through a day of extreme volatility with no information about the next day's drift. The next day the Nifty rose 3.36%; whether widening "worked" on that occasion says nothing about the rule (Proposition 4A.14 is about expectations).

Event-aware sizing The correct correction is ex ante, not at 14:00 on the day. If the risk budget is 1% of capital and the plausible loss is two event standard deviations (12.6%), the notional should be about $1\%/12.6\%\approx8\%$ of capital, against $1\%/2\%=50\%$ under the ordinary 2% stop: a sixfold cut. Alternatively, keep the position and buy a put, so that the loss is capped by contract rather than by a stop that the event can jump (M12 · 12.6).

Case 3: A documented test of chart patterns: Lo, Mamaysky and Wang (2000)#

The paper Andrew Lo, Harry Mamaysky and Jiang Wang, "Foundations of technical analysis: computational algorithms, statistical inference, and empirical implementation", Journal of Finance 55(4), 2000, 1705–1765 (NBER Working Paper 7613).

What they did They addressed the objection that chart patterns are too subjective to test. Prices are first smoothed by nonparametric kernel regression, which removes noise without imposing a shape. Local extrema of the smoothed series are then located, and ten classic patterns are defined as explicit inequalities on five consecutive extrema: head-and-shoulders and inverse head-and-shoulders, broadening tops and bottoms, triangle tops and bottoms, rectangle tops and bottoms, and double tops and bottoms. This is the programme of 4A.2 applied to the whole pattern catalogue. They applied it to a large sample of US stocks from 1962 to 1996, and compared the distribution of daily returns after each pattern with the unconditional distribution, using goodness-of-fit tests (Kolmogorov–Smirnov and chi-square on deciles), with Monte Carlo checks of the tests' size.

What they found Several patterns, head-and-shoulders among them, are associated with conditional return distributions that differ from the unconditional ones: the patterns carry some incremental information (by our reading of the paper, more clearly for Nasdaq than for NYSE/AMEX stocks). The authors stress that statistical informativeness is not profitability: their tests compare distributions, not trading returns after costs, and patterns optimal for detecting anomalies need not be optimal for trading.

Reading it with this module's tools

• The design is right. Algorithmic pattern definitions (like Definition 4A.3) remove the hindsight of drawing patterns on finished charts, and a distributional comparison against the unconditional benchmark is the correct null (Proposition 4A.1 says what noise alone produces).
• The effect is about distributions. A pattern can change the variance or the shape of next-day returns without changing their mean. For a trader, only the mean after costs matters for expectancy (Proposition 4A.9); a variance change matters for sizing and stops.
• Multiple testing and decay. Ten patterns, several smoothing choices and two exchanges are many trials. The sample ends in 1996, before decimalisation and the post-publication decay documented for many anomalies (M04 · 4.7.1). Treat the result as "patterns are not pure noise in this sample", not as a trading system.
• Compare with candlesticks. The careful candlestick tests (4A.1) found no value even at the distributional level. The weight of evidence is that well-defined, multi-swing patterns contain a little information, single-bar patterns almost none, and neither has been shown to survive Indian costs.