Fractional Differentiation for SPY Dip-Buying

Method

Rule / pseudocode

DATA ← adjusted observations for the stated instrument and horizon

RULE ← Buying SPY on >1% down days when the fractionally differenced price series (d=0.4, window=60) is positive achieves better OOS Sharpe than unfiltered dip-buy, by avoiding entries during structural downtrends.

METHOD ← Entry: Close on signal day: daily return < -1% AND frac_diff_60 > 0 · Exit: Close 3 trading days later · Train/test split: 70/30 by trade count (452 IS through 2020-04-21, 195 OOS) · Costs (bps): 10

FIT ← estimate or select parameters on each training window only

TEST ← apply the frozen rule to the next unseen window after stated costs

REPORT ← return, Sharpe, drawdown, trade count, significance and fold stability

VERDICT ← prefer robustness and sufficient observations over the headline return

_Fractional differentiation (Lopez de Prado) preserves long-range memory in price while achieving stationarity. A positive fractionally differenced series means the long-range trend is intact despite recent volatility — exactly the condition where mean reversion after a dip is most credible. This regime filter should improve the dip-buy signal by avoiding entries during structural downtrends._

Out-of-sample equity curve

Growth of $1 over the held-out test data the strategy never saw while it was being built, after 10 bps round-trip costs.

Out-of-sample performance

OOS Sharpe

0.09

Ann. return

Max drawdown

-29%

Win rate

13%

p-value

0.383

not significant

WF folds +

3/5

Measured on held-out data. A high Sharpe with a non-significant p-value means the result could still be luck — read them together.

Hypothesis

Buying SPY on >1% down days when the fractionally differenced price series (d=0.4, window=60) is positive achieves better OOS Sharpe than unfiltered dip-buy, by avoiding entries during structural downtrends.

Method

Entry: Close on signal day: daily return < -1% AND frac_diff_60 > 0 · Exit: Close 3 trading days later · Train/test split: 70/30 by trade count (452 IS through 2020-04-21, 195 OOS) · Costs (bps): 10

Results

Out-of-sample Sharpe was 0.09, versus 0.08 in-sample. A bootstrap test returned p = 0.383 (not significant). Walk-forward Sharpe stayed positive in 3 of 5 folds. Worst out-of-sample drawdown was -29.11%.

Analysis

This re-run corrects two material flaws in the original backtest. Trades are now non-overlapping: once a 3-day hold begins, no new entry is taken until the position closes, reducing IS trade count from 452 to 274 and OOS from 195 to 138. The headline Sharpe and drawdown figures derive from a daily mark-to-market equity curve (position 1.0 during the hold, 0 otherwise) with 10 basis points deducted at entry per trade. Significance is tested via a block-bootstrap on per-trade OOS returns against a zero-edge null, correcting the prior bug that resampled the raw positive-mean series and returned p ≈ 0.5 regardless of edge.

IS Sharpe collapsed from 0.853 to 0.084 once overlapping trades were removed, immediately confirming that the earlier result was an artefact of double-counting returns across concurrent positions. OOS Sharpe is 0.087, with annualised return of 1.18% against 13.63% volatility and a maximum drawdown of 29.1%. The equity curve peaked near 1.13 during the high-volatility dip-buying windows of 2020-2022 but gave back most of those gains in the 2025 sell-off, finishing only 7.7% above the OOS starting value over six-plus years — consistent with SPY's long-run drift being captured during a handful of volatile episodes rather than any systematic signal.

Walk-forward consistency sits at exactly 60%, the bare minimum of the PROMISING threshold, but the fold-level detail is unflattering: folds 1 and 2 are negative (-0.13 and -0.22), fold 3 reaches 0.99, fold 4 reaches 0.59, and fold 5 collapses to 0.07. Two consecutive losing folds at the outset of the OOS period, followed by a single strong fold that coincides with the COVID crash, drive most of the apparent positive WF result. The combined walk-forward Sharpe is 0.02 — indistinguishable from zero.

The corrected block-bootstrap p-value on the 138 non-overlapping OOS per-trade returns is 0.383, far above the 0.10 threshold required for any confidence in a real edge. Under a zero-edge null (returns demeaned before block resampling), the observed per-trade Sharpe of 0.53 sits comfortably within the distribution expected from noise alone. The original p = 0.496 was produced by the buggy test that resampled raw positive-mean returns and centred the null on the observed Sharpe; both runs agree on non-significance, but the corrected bootstrap now tests the right hypothesis.

With OOS Sharpe 0.087, p-value 0.383, and walk-forward dominated by two consecutive losing folds, this experiment is rejected. The fractionally differenced filter (d=0.4, window=60) is positive for SPY more than 98% of the time, making it effectively inoperative as a regime detector. Any positive return in the OOS period reflects SPY's structural upward drift captured during infrequent dip windows, not an exploitable short-term edge. The strategy is not viable for paper trading.

Provenance

Synthesized from 1u437da, 1tj2yu5. The buy-the-dip idea ([1u437da]) and the fractional differentiation insight ([1tj2yu5]) combine naturally: use fractionally differenced SPY price as a momentum state indicator, and only take dip-buy entries when the fractionally differenced trend is still positive. This filters out entries during genuine trend breaks vs. healthy pullbacks.

Evidence

Walk-forward Sharpe by fold

Each fold retrains on past data then tests on the next unseen window. Staying positive across folds is the real test of an edge.

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_Generated by labs-algo-trading. Automated research — not financial advice. Backtests overfit; treat verdicts as hypotheses._