algorithmic-trading-anthology-july-2026-seasonality-voided-by-audit

Conclusion: Voided

Withdrawn after audit. Repeating the same trades on exchange-traded funds, which hold real contracts and pay real costs, cut return-for-risk from 0.80 to 0.34. The pattern was largely an artefact of how free price histories stitch expiring contracts together.

Figure 1 · Growth of $1

2008–2026 · net of 15bp round-trip costs

What one dollar became, after costs: $8.48 by 2026. Shown against Control, S&P 500, rebased to the same starting dollar.

Return for risk

1.16

range 0.74 to 1.60

Ann. return

12.0%

volatility 10.4%

Max drawdown

12.8%

over 213 months

Beats the search

97.6%

chance, after correction

Method

Hypothesis

Agricultural futures carry persistent calendar-month seasonality that can be harvested cross-sectionally.

Rule

UNIVERSE = 15 agricultural futures

MIN_YEARS = 8

N_SIDE = 4

function positions(bar):

m = month(bar.next)

for symbol in UNIVERSE:

history = returns(symbol) in month m, years before bar.year

if count(history) < MIN_YEARS:

continue # not enough seasons to judge

score[symbol] = mean(history)

return long_short(score, N_SIDE, bar)

function long_short(score, n, bar):

longs = top n symbols by score

shorts = bottom n symbols by score

return equal_risk(longs, bar) - equal_risk(shorts, bar)

# ── execution ────────────────────────────────────────────────────────

COST_PER_TRADE = 15 bps of the notional that changes hands

function on_bar(bar, book):

if not bar.is_month_end:

return # decisions are made monthly only

target = positions(bar) # the rule above

target = scale_to_gross(target, 1.0)

rebalance(book, target, bar)

function scale_to_gross(w, limit):

gross = sum(abs(w)) # total capital at work

if gross == 0:

return w # flat is a valid target

return w * limit / gross # leverage fixed, never implicit

function rebalance(book, target, bar):

for symbol in union(book.symbols, target.symbols):

delta = target[symbol] - book.weight(symbol)

if delta > 0:

buy(symbol, delta, fill = next_bar.close)

else if delta < 0:

sell(symbol, -delta, fill = next_bar.close)

book.charge(COST_PER_TRADE * abs(delta))

# Orders are filled at the next month's close, never the one the decision

# was made on. There is no stop_loss(), take_profit(), limit order or

# position cap: a holding changes only when positions() returns a

# different target at the next month end.

Analysis

Initial result

Sharpe 1.16, confidence interval [0.74, 1.60], design half 1.26 and holdout 1.10, best five months only 17.6% of profit. It survived deflation against all 560 trials the project had run — the harshest correction available here.

That result warranted scrutiny, and the concern has a specific form. A futures contract expires every few months, so a long price history is really many short ones stitched together. The stitches happen on a calendar. A strategy that trades the calendar could easily be trading the stitches.

So the same four commodities were checked against exchange-traded funds that hold the real contracts and pay the real cost of rolling from one to the next.

Audit against investable funds

Table A · Spliced futures against the investable ETF

monthly return difference, same underlying commodity

Pair	Months	Mean annual gap	ANOVA p (calendar structure)
ZW=F / WEAT	178	+10.9%	< 0.0001
ZC=F / CORN	193	+3.9%	< 0.0001
SB=F / CANE	178	+2.3%	< 0.0001
ZS=F / SOYB	178	−0.8%	< 0.0001

All four show calendar-month structure in the gap. December corn: t = +8.8. September wheat: t = +7.0. The spliced wheat series overstates investable returns by roughly eleven points a year.

Performance on investable instruments

A new rule was added afterwards: a result does not count if the returns could not actually have been earned. Changing the rules after seeing the answer is usually cheating, so this one is allowed to do only one thing — take results away. It can never hand one out.

What remains is not nothing. The investable version is weakly positive, and in line with what others have reported for crop seasonality. Fifteen years of fund history is simply too little to prove it either way. That is a limit of the data, not a verdict on the idea.

Table B · Where the edge went

identical seasonal long/short signal, 2011-10 onward

Earned on	Months	Ann. return	Sharpe	t
Spliced futures (what the backtest saw)	178	+17.7%	+0.80	3.09
ETFs (what an investor could hold)	178	+5.5%	+0.34	1.31

Correlation between the two return streams is 0.87 — these are the same trades. Most of the measured edge was the splice.

The strategy did not find seasonality in crops. It found seasonality in how the price series was assembled.

Evaluation

Table 1 · Performance

2008-10 – 2026-06 · 213 months, 213 invested

Measure	Value
Annualised return	12.0%
Annualised volatility	10.4%
Return for risk taken	1.16
95% range	0.74 to 1.60
t-statistic	4.90
Maximum drawdown	12.8%
Hit rate	64.3%
Annual turnover	19.39×
Return skew	(0.05)
Return kurtosis	2.99

+ 6 more rows− fewer rows

The range is measured by resampling the history in blocks, so runs of good and bad months stay intact.

Table 2 · Robustness

Diagnostic	Value	Reads as	Bad	Okay	Yay
Design half (pre-2015)	1.26	return for risk	≤ 0	0 – 0.40	≥ 0.40
Holdout half (2015+)	1.10	return for risk	≤ 0	0 – 0.40	≥ 0.40
Top-5-month share of profit	17.6%	how much rode on a few months — lower is better	≥ 40%	25 – 40%	< 25%
Top-2-year share of profit	24.7%	concentration	—	—	—
Distinct trading episodes	1	how many independent runs this really is	< 50	50 – 100	≥ 100
Chance the edge is real	100.0%	non-normality corrected	—	—	—
Chance it beats the whole search	97.6%	chance of beating the whole search by luck	—	—	—

bad/ok boundary is the pre-registered criterion · ok/good is a margin above it, not a criterion · blank where none was registered

+ 3 more rows− fewer rows

The last row asks whether the result would stand out from the hundred-odd ideas tried here, rather than being judged alone.

Table 3 · Pre-registered criteria

measured against C3_RP_LONG

Check	What it asks	Result
1	Reward large enough for the risk	pass
2	Confidence range clear of zero	pass
3	Profit not concentrated in a few months	pass
4	Worked in both halves of the history	pass
5	Beat buying and holding	pass
6	Stood out from the whole search	pass

+ 2 more rows− fewer rows

These six checks were written down before the strategy was run.

Table 4 · Net return by calendar year

after costs

Year	Net return
2008	1.0%
2009	13.3%
2010	17.8%
2011	1.9%
2012	14.2%
2013	14.1%
2014	25.2%
2015	21.4%
2016	(0.7%)
2017	(3.0%)
2018	3.4%
2019	9.5%
2020	18.2%
2021	7.1%
2022	26.6%
2023	12.8%
2024	26.3%
2025	9.1%
2026	(4.4%)

+ 15 more rows− fewer rows

Table 5 · Concentration detail

Measure	Value
Best years	2022:+27%, 2024:+26%, 2014:+25%
Worst year	2026:-4%

Reference

Instruments

last price and one-month change, live from Yahoo Finance

Symbol	Notes
ZW=F	Chicago SRW Wheat — continuous futures on CBOT, quoted in US cents.
KE=F	KC HRW Wheat — continuous futures on CBOT, quoted in US cents.
ZC=F	Corn — continuous futures on CBOT, quoted in US cents.
ZS=F	Soybeans — continuous futures on CBOT, quoted in US cents.
ZM=F	Soybean Meal — continuous futures on CBOT, in USD.
ZL=F	Soybean Oil — continuous futures on CBOT, quoted in US cents.
ZR=F	Rough Rice — continuous futures on CBOT, in USD.
SB=F	Sugar No. 11 — continuous futures on ICE Futures, quoted in US cents.
KC=F	Coffee C — continuous futures on ICE Futures, quoted in US cents.
CC=F	Cocoa — continuous futures on ICE Futures, in USD.
CT=F	Cotton No. 2 — continuous futures on ICE Futures, quoted in US cents.
OJ=F	Orange Juice — continuous futures on ICE Futures, quoted in US cents.
LE=F	Live Cattle — continuous futures on CME, quoted in US cents.
GF=F	Feeder Cattle — continuous futures on CME, quoted in US cents.

list truncated in the source record

Sample

2008-10 – 2026-06 · 213 months

Sources

NOAA Physical Sciences Laboratory. Climate indices. ONI, Niño 3.4, MEI v2, DMI, PDO, AMO, TNA, QBO, solar flux. psl.noaa.gov/data/climateindices/list

Queensland Department of Agriculture and Fisheries. Southern Oscillation Index. The Long Paddock. Monthly, 1876–. www.longpaddock.qld.gov.au/soi/soi-data-files

Yahoo Finance. Historical market prices. Adjusted close, month-end. Retrieved with yfinance. finance.yahoo.com

Revision history

Rev	Stage	Status	Change
01	Draft	—	Direction and pass/fail criteria fixed before the run
02	Tested	Validated	Passed every check, including the penalty for how many ideas were tried
03	Audited	Voided	Repeating the trades on real funds showed the returns could not actually have been earned