All strategies · Longbow Weekly · Longbow Learned · RANK500

Three Nifty 500 weekly strategies, re-tested without survivorship bias and combined

Longbow Weekly, Longbow Learned and RANK500 v2 · pre-registered in research/combo/STRATEGY_COMBO.md before any result · 31 Oct 2026 · research only, no orders · the sealed period (October 2025 onward) was not used

1. The three strategies in one table

2. Data: what changed and why it matters

The earlier tests used Dhan price history, which only exists for stocks that are still tradable, together with the actual Nifty 500 member lists. A stock that was in the index and later went bust or was delisted has no price history, so it was silently absent: 40% of member names in 2010 and 20% in 2020. This flatters any strategy, and most of all a momentum strategy that keeps buying what has gone up. The 4% a year allowance we used was an estimate.

Now: prices and the universe come from the NSE cash-market daily file (bhavcopy), 2004 to 2026, for every EQ/BE/BZ name that traded, delisted and merged ones included (4,283 tickers; 519 renames joined through the ISIN code). Returns use close ÷ previous close, which NSE adjusts for splits and bonuses on the ex-date; one-day moves beyond ±50% are treated as data errors. The universe is point-in-time: at each month-end, the 500 names with the largest 60-day median traded value (price at least ₹10, at least 120 sessions listed), effective the next session. This is not the Nifty 500 list (which would need the historical lists matched to tickers for every delisted name; not available), so it measures the style on the liquid top 500, survivorship-free. Share of the real Nifty 500 list that is also in this universe, by year:

Decomposition (Longbow Weekly, frozen design, 2016 to September 2025, 2x costs): Dhan history with real index lists: about 25%. Same bhavcopy prices with the real index lists (only names with a matching ticker; 321 names a week): 25.9%. Turnover-top-500 universe including every delisted name (420 names a week): 17.3%. So the data source is not the cause (bhavcopy reproduces the Dhan result); the drop comes from the stocks that were missing, plus the fact that the new universe also holds liquid non-members. The truth for the index itself lies between 17% and 26%; the survivorship-free figure is the cautious one. Index over the same window: 13.3%.

Published numbers against the re-test

The earlier figures deducted a 4% allowance; this study deducts none because the delisted names are inside the data. Costs are the strategies' own schedules (W and M: delivery charges plus 0.2% a side; R: its liquidity-tiered slippage).

3. Re-test of the frozen designs

Longbow Weekly (W), 2007 to September 2025

Random selection through the same filter and engine (30 runs, 1x costs) earned a median of 8.0% and a 90th percentile of 10.4% a year over the full history, so the ranking is worth about 11 points over random picks (1x). W beat the index in 42% of calendar years; the years it won by more than 10 points were 2007, 2008, 2011, 2014, 2017, 2020, 2021, 2023.

Longbow Learned (M), 2012 to September 2025

Random numbers blended with the same rule earned a median of 7.5% and a 90th percentile of 9.8% (1x). M beats W by about 4.3% a year on the common window and has a similar drawdown, but alpha against the index is not statistically reliable (t about 1.4 at 1x, 0.8 at 2x).

RANK500 v2 (R), 2010 to September 2025

Random selection through the same rules earned a median of 2.8% (90th percentile 4.8%) a year at 1x; R earned 15.7%. Development years are weak and deep (2011: R lost 48% against 28% for the index, trough on 20 December 2011, then gained 45% in 2012; the earlier Dhan-based development run showed a 26% drawdown; the cause of the difference was not isolated). Validation years are strong, in the small-cap boom of 2020 to 2023. This is the regime dependence flagged in the original report, now measured.

Optimisation (small, development only, then validated once)

A grid of 24 settings each for W and M (names 10/15/20/30 × rebalance every 2/4/8 weeks × market filter on/off) was run on development at 2x costs only. Rule fixed beforehand: highest development Sharpe among settings with drawdown ≤ 30%, at least 2 turns a year and ahead of the index in ≥ 60% of years; the winner replaces the frozen design only if it also wins validation by more than 1 point of CAGR without a worse drawdown.

W (no setting met the years-ahead condition, so the Sharpe ranking alone chose):

M (16 of 24 settings had a drawdown ≤ 30%):

Outcome: both selected settings rebalance every 8 weeks (annual turnover 3.0 for W and 3.3 for M against 4.5 and 4.1), so costs bite less. W: the selected setting (20 names, every 8 weeks, filter on) beats the frozen design in validation at 2x costs by 3.2 points with a smaller drawdown, so the replacement rule is met; note that no W setting met the years-ahead condition, so the choice rested on Sharpe alone. M: the selected setting ties the frozen design in validation (same CAGR, slightly deeper drawdown), so the rule is not met and the frozen design stays. Applied to the live paper runs: nothing (a frozen paper spec is not changed mid-run). The W variant is recorded as a candidate v2 to run in a separate paper book if wanted.

4. Trade details

Every trade, fill and audit check is on the three strategy pages (trade log, execution audit). Audit notes for the re-test: the independent rupee ledger reconciles to the simulator within 0.3% (W) and 0.01% (M); two fills in about 9,800 (W) and 7,400 (M) have an open outside the recorded day's range (bhavcopy data glitches) and are flagged FAIL, and the M book briefly held 16 names against the limit of 15 at some rebalances; both are left visible.

5. Do they complement each other?

• W and M: redundant. Pearson 0.89, Spearman 0.79; rolling 52-week correlation never below 0.55. They hold mostly the same names, switch to cash on the same filter, and are 26% of the time together more than 10% below their peaks. Running both doubles one bet. M is the better of the two on this data (higher return, less time in drawdown: 34% of weeks against 46%).
• R against W/M: moderately diversifying. Pearson 0.46 and 0.42; rolling range 0.18 to 0.84. In the index's worst 10% of weeks W and M are at -0.06 and -0.04 with the index (cash through the filter) while R sits at 0.80. R has no market filter and takes the full fall. The sleeves therefore protect each other's weak spots only partly: when the filter is off and the market is falling, W and M are safe and R is not; when the filter whipsaws in a rising market W and M miss gains that R keeps.
• Drawdowns overlap little between R and the others: R and M together more than 10% below peak 5% of weeks, R and W 13%.

6. Combining them, and Kelly

Weights are fitted on development (2012 to 2017) and applied untouched to validation (2018 to September 2025). Long-only, total weight at most 100% (no leverage), the remainder in cash at repo minus 1.5%, sleeves rebalanced weekly to target, sleeve-to-sleeve rebalancing costs ignored.

Kelly criterion

The Kelly criterion picks the weights that maximise the expected logarithm of wealth, i.e. long-run growth. For one strategy with weekly excess return mean μ and variance σ² it is f* = μ / σ² (stake as a multiple of capital). Estimates on the common window: W 3.9, M 4.5, R 5.1, the index itself 3.9. All are far above 1: Kelly would borrow several times capital. That is not advice to leverage; it says each of these has a high Sharpe relative to its variance in this sample, and that the sample's mean is the thing estimated worst (a 14-year mean of weekly returns has a standard error of the same order as the mean). With the no-leverage constraint the three-sleeve Kelly solution is fully invested; fitted on 2012-2017 it puts 0 / 13 / 87% in W / M / R, fitted on all years 0 / 47 / 53%. A bootstrap of the Kelly weights (300 resamples in blocks of 8 weeks) gives mean weights W 4%, M 52%, R 44% with 5th to 95th percentile ranges W 0%-11%, M 0%-100%, R 0%-100%: R and M are always the main holdings, W is usually zero (it is dominated by M), and the split between R and M is not determined by the data.

Fractional Kelly: half Kelly (half the Kelly weights, the rest in cash) delivers about 13.6% a year with a 14.8% drawdown on the common window; quarter Kelly 9.3% and 7.5%. These hold a large cash share; they are what Kelly practitioners use because full Kelly assumes the estimated edge is exact and the return distribution is stable, neither of which holds here (and 2011 shows the drawdowns this style can have).

7. Insights and recommendation

1. Survivorship was a large part of the earlier edge for the two Longbow strategies and a smaller part for RANK500. The honest expectation at 2x costs is now roughly 0 to 6 points a year over the index depending on the window (W: 4 points over 2007 to 2025 and 4 over 2016 to 2025, level with the index over 2012 to 2025; M: 4 points over 2012 to 2025, 6 over 2018 to 2025), with drawdowns about the index's (30-37%), not the 12 to 18 points earlier published. RANK500's validation edge is mostly in the 2020 to 2023 small-cap boom.
2. Do not run W and M together as separate bets. If one is kept, keep M (same cost, better numbers) and treat W as its baseline. Both paper runs are already live; leave them running unchanged as the A/B and decide after 52 weeks.
3. Use R as the second sleeve. It is the only one whose returns are not mostly the other's. Its weaknesses (no market filter, illiquid names, a bad 2011-2013) are different from the Longbow weaknesses (cash drag in strong markets).
4. Capital split to paper-test: equal weight of M and R (50/50), W at zero, fully invested at most. Without any fitting this mix returned 22.5% a year with a 19.8% drawdown on 2012 to 2025 (validation Sharpe 1.03), the best out-of-sample Sharpe of the mixes tried and close to the fitted ones, and it does not depend on a fragile optimisation. Equal weight of all three delivers 21.0% a year with a 21.5% drawdown on the common window; Kelly-fitted weights did not beat it out of sample on Sharpe (0.91 against 0.97 in validation).
5. Real money, if ever: start with at most a quarter to a half of the Kelly-implied exposure, because the edge estimate is the least certain input; require 52 weeks of forward paper results first (already the rule). Keep the allocation at or below 100% of capital; never lever up on the strength of a Kelly number.
6. What was optimised and what was not: only turnover-reducing settings (every 8 weeks; 20 names) look worth watching; nothing else in the grid is distinguishable from noise. RANK500's frozen v2 was not re-optimised.

8. Limits of this study

• The universe is "top 500 by turnover", not the index. Results describe the style on liquid names including delisted ones; the index itself lies between the earlier and the new figures.
• Bhavcopy closes are NSE closing prices; ticker changes without a shared ISIN break a history (the name then looks like a new listing); adjustments rely on NSE's previous-close adjustment, and ±50% days are discarded.
• Periods overlap between development and validation of the machine-learning models (retrained rolling); the sealed period was not used (spent for all three).
• Kelly weights are in-sample estimates from 14 years of weekly data; the bootstrap shows how wide they are.
• Three strategies share one data pipeline and one market; correlation in a crisis can be higher than in the whole sample (the index's worst weeks in this sample include March 2020, where the filter helped W and M).

Files: research/combo/ (build_sf.py, run_wm.py, run_r.py, compare.py, report_combo.py, results/), data/rank500_sf/, data/research/panel_sf.parquet.

Research and education only. Hypothetical and back-tested results have inherent limitations and do not guarantee future results. Not investment advice; the publisher is not presented as a SEBI-registered investment adviser or research analyst.