The NSE results pull Das's three post-limit-close predictions toward different price bands. The next-day mean response matches best at the 10% band. Yet pooled same-boundary persistence at that band is 0.2674, beyond the model's ceiling of 0.1681 when the tail index is 3. That ceiling is the highest persistence permitted by the wide-band asymptote under any retention coefficient. Das gives the ceiling and himself removes the 2%, 5% and 10% bands from calibration. This leaves an awkward question: why place the 20% calibration beside the mean-response comparison across four bands? The third prediction says opposite-limit reversal decays as C to the power minus nu. The appendix computes it from the data, though no plot compares it with theory.
We could not test any of this ourselves. The signal requires point-in-time NSE band schedules and Indian exchange closes. A US-equity run cannot substitute, since US equities lack a fixed daily close limit and therefore lack the mechanism.
The mechanism itself is clean. An exchange band clips each daily return at plus or minus C. Das calls the unconstrained return, meaning the move that would have printed without the band, the latent variable X_t. The observed return is R_t = clip(X_t, -C, C). What remains censored is the hidden excess L_t = X_t - R_t, the portion of the move absent from the tape. Tomorrow's latent return combines a fresh i.i.d. shock with lambda times today's hidden excess. This retention term supplies all temporal dependence in the construction. The shocks are symmetric, independent across days and have regularly varying tails of index nu. Clipping creates the state variable; retention moves it forward.
The stationary law behaves neatly. With lambda below 1, the recursion is a contraction. The shock tail index remains unchanged, while the tail amplitude is multiplied by 1/(1 - lambda^nu). Monte Carlo trajectories of 10^10 steps use Student-t shocks at scale 0.01. After multiplication by (1 - lambda^nu), the tails for lambda = 0.4, 0.6 and 0.8 collapse onto one another.
Continuation wins in the wide-band limit
The trading claim comes from the wide-band limit, where C is large beside the shock scale and limit closes are scarce. One dominant shock then produces the limit close. It may have arrived j days earlier, provided it was large enough to endure j rounds of clipping and retention. Its minimum size is C times B_j, where B_j sums lambda to the power minus m for m up to j.
Three results follow. The conditional mean return on the next day keeps the same sign and rises linearly with band width. Same-limit persistence approaches a finite constant, 1 minus the weight assigned to age-zero histories, because another close at the same boundary requires only the residual excess to survive. A close at the opposite limit on the following day requires a second tail event, so reversal falls as C to the power minus nu. Simulations reproduce this separation over the simulated range. No retention threshold appears: when lambda is small, the normalized response behaves as lambda/(nu - 1), meaning any positive retention generates same-sign drift.
The empirical sample contains NSE stocks from November 2007 to June 2026. Das obtains the records from NSE archives through the nselib package and studies bands of 2%, 5%, 10% and 20%. A band-history consistency check leaves a base universe of 757 symbols. Five exclusions reduce the sample from 1,163,004 daily observations to 898,689, with the count for each exclusion reported.
Das sets nu = 3 using 13 global index return series. Maximum-likelihood degrees of freedom extend from 2.41 for KOSPI to 3.99 for Nikkei 225, average 3.15, and have Kolmogorov-Smirnov distances at or below 0.029. Lambda then comes from one figure. At the 20% band, 217 of 1,494 limit closes repeat at the same boundary, producing lambda_eff of about 0.942. Neither parameter is estimated from the mean responses, as Das explicitly says.
One band survives calibration
Das has a genuine defence, though its reach is limited. Pooled persistence equals 0.7885 at 2%, 0.4478 at 5%, 0.2674 at 10% and 0.1452 at 20%. The first three values exceed 0.1681. Das correctly excludes them from inversion and states that no admissible lambda lets the wide-band asymptote describe them. Calibration therefore rests on the only sample observations that do not reject the asymptotics. The estimate reaches 0.942, close enough to 1 that almost all hidden excess must remain overnight to produce a 14.5% repeat rate. Meanwhile, the 5% band contains 19,825 events, compared with 1,494 at 20%.
Calibration uses 1,494 of 23,711 events, 6%.
Fig. 6 then grades the model across all four bands, including the three barred by the bound.
Direction creates another weakness, one Das also acknowledges. At 20%, upper-circuit persistence is 163/1230 = 0.1325, while lower-circuit persistence is 54/264 = 0.2045. The lower value by itself exceeds the ceiling. Das attributes the gap to panic, margin calls and forced liquidations, concluding that downward limits retain more memory than upward limits. Direction-dependent lambda cannot repair the bound. Lower-circuit persistence remains 0.2045, above the 0.1681 ceiling, under every admissible retention coefficient regardless of the upper-direction value. Das further concedes that the empirical upper-limit response at 20% falls substantially below the prediction. The abstract describes the data as "qualitatively consistent" with the predicted same-sign response "and its increase across wider price bands".
Qualitative is accurate, and carries much of the argument. We did not find standard errors or confidence intervals for the empirical means m_+(C) and m_-(C). Nor is there a test against a null of zero next-day drift. The evidence consists of box plots overlaid with the theory line. Bootstrap machinery appears elsewhere in the paper, using 2,000 moving-block resamples with block length 20 days, though it is used for tail index estimates rather than response means. We also found no adjustment for symbols whose events cluster on the same date. Such clustering matters when market-wide selling sends dozens of stocks to lower circuit together.
How much does tolerance move the 2% result?
The event definition is unusually precise. An upper-circuit day requires the close to reach at least the limit price times (1 - 0.25%), applied one-sided. A separate ceiling removes returns that exceed the band by more than 0.01C. Further filters impose a low-price floor of INR 10 and a four-calendar-day trading continuity rule. Events are also removed when the recorded band changes the next day, and around disclosed bonus and split ex-dates.
These tolerances vary with the band. For the 20% band, the classification window in return space extends from about 19.70% to 20.2%. Its half-percentage-point span equals 2.5% of the band. At the 2% band, the window extends from about 1.745% to 2.02%, spanning 0.275 points, or nearly 14% of the band. The narrow-band definition is more than five times looser, precisely where persistence exceeds the theoretical ceiling by a factor of nearly five. Looseness alone does not account for 0.7885. Still, an implementer selecting tau = 0.1% in place of 0.25% would identify a different collection of 83 upper-circuit and 144 lower-circuit events at 2%. The paper's most striking empirical figure would change with it.
Reconstruction would leave us with three judgment calls. We could not determine which symbol-days comprise the 1,163,004 initial rows. Das retains corporate actions beyond splits and bonuses because only those two have a determinate exchange-disclosed ratio, leaving us to decide whether the others should remain. Symbols with internally inconsistent band-change disclosures pose the final choice, since removing them entirely creates the 757-symbol universe. The paper says the data are available from the author on request.
The trade remains elusive
There is no Sharpe and no cost estimate, and neither is claimed. This statistical physics paper stops at conditional means and frequencies. A stock pinned at its upper circuit cannot be purchased at that price, which defines the lock in the first place. Even a genuine same-sign response may therefore resist capture. The setup still has structural appeal: censoring explains why some information is provably absent from the close.
Confidence intervals for the conditional mean responses, separated by band and direction, would change my reading. So would the same test in a second price-limited market. Das himself proposes direction-dependent retention. The intervals and second market are our additions. With one parameter drawn from global index tails and another estimated from 1,494 events, the two-parameter model reproduces the sign of next-day drift at four band widths and its rise with band width. At three of those widths, it also violates its own persistence bound.