KO–PEP Frozen-Reference Excursion Convergence

Hypothesis

Derived by the Research Lead from Anna Ananova, Rama Cont and Renyuan Xu's Model-free Analysis of Dynamic Trading Strategies: trade two-sided excursions of the KO–PEP regression spread and close on return to its frozen reference. Use synchronized 1-HOUR bars on USEQ instead of the paper's unavailable historical second-by-second NYSE midprices. Preserve its five-session regression window and use its reported 3.2-sigma KO–PEP threshold as the baseline, without treating that empirical optimum as verified performance. Add a cost-aware minimum excursion, a bounded spread-loss exit and a time stop. Estimate coefficients before each session only while flat; freeze coefficients, residual scale and quantities throughout each position. This is an adapted experiment, not a reproduction of the paper's empirical results. The supplied full text establishes the trading rules that the abstract alone leaves unspecified.

Keep the paper's actual equity pair rather than substituting a crypto spread. This fills the heavily underrepresented long-short direction and reduces single-instrument concentration. Corpus concentration is unavailable, so instrument novelty cannot be verified. Unlike the pending frozen-versus-rolling Engle–Granger comparison, this contract uses a single frozen OLS reference, no cointegration selection and an explicit excursion-amplitude cost floor. Only one mechanism is proposed: scenario resampling and local-time asymptotics are analytical tools, not distinct trading signals.

negative_expectancy: The cost floor is not the binding problem. On 138 closed legs (69 KO-PEP baskets, Aug 2024 to Aug 2026), avg_trade_return_pct was -0.194%, below the USEQ floor of +0.05%. PF was 0.84, Sharpe -0.65, return -3.25% and IC -0.098 (not significant). Zero commissions and about $830 of impact plus borrow explain only part of the loss. Most baskets ended at the 5-session time stop instead of converging to the frozen reference, so 3.2-sigma hourly excursions did not mean-revert within the hold window. The QA edge concern is borne out. Bounded tuning of loss_multiple, max_hold_sessions and min_capture_fraction cannot create a positive gross reversion. This rejects only the Research Lead's 1-hour, next-open adaptation on USEQ. It does not test Ananova/Cont/Xu's second-by-second midprice strategy, which remains untestable without tick-level NYSE data.

Implementation

Trades two-sided KO–PEP spread excursions using exactly synchronized hourly USEQ bars. Fits OLS over five prior sessions while flat, freezes the reference and quantities during each position, and exits on convergence, bounded spread loss or a session deadline.

Addresses the Layer 1.5 failure by explicitly declaring parameters.bar_interval as the fixed value 1-HOUR and using matching hourly bar types for both instruments. Includes all fixed research-plan values and the three tunable baseline values. Existing signal, entry, sizing and exit logic is preserved; only the class documentation changes in the source. No independent verification was run. The required outbox file could not be written because this session permits read-only filesystem access; the complete task-bound JSON is returned here.

Verification Results

The sandbox reports -3.25% return and -0.194% average net return per closed leg. The 0.6% theoretical spread-capture floor does not guarantee realized convergence profits; assess pair-level returns, next-open execution and costs in the full backtest.

Backtest Review

Sharpe

-0.65

Total return

-3.25%

Max drawdown

4.93%

Trades

138

Win rate

47.8%

Profit factor

0.84

The implementation matches the hypothesis: 69 pair trades with 69 long and 69 short legs, hedged at entry, using a session-frozen OLS reference, accounting that reconciles, and clean input audits on both legs.

Risk stayed small: max drawdown was 4.93% against the pre-registered 10% limit, and peak leverage was 0.42.

Expectancy is negative after costs. Each closed leg averaged -0.194% of notional, against a USEQ floor of +0.05% (preferred +0.10%). Profit factor was 0.84, Sharpe -0.65 (CI -1.99 to 0.81), and total return -3.25% over about 2 years. Commissions were zero. Modeled impact was $767 and borrow $67, so costs explain only part of the loss.

At pair level, 34 of 69 baskets were profitable. Net PnL was -$3,253, about -0.075% of combined notional per basket. Paying the spread to cross the 3.2-sigma threshold does not lead to profitable convergence.

About 36 of 69 pairs were held 6 or more calendar days, so most exits came from the 5-session time stop rather than convergence. Excursions on 1-hour bars do not revert to the frozen 5-session reference within the holding window.

The signal-research IC was -0.098 (t=-0.68, 49 observations), which carries no information. Losses appeared in both calm (-1.48%) and stressed (-2.06%) volatility regimes.

This matches a known failure pattern: an earlier USEQ KO/PEP pairs run died at fee_edge. The tunable ranges (loss_multiple 1-2, max_hold 3-10 sessions, min_capture 0.4-1.0%) only rescale the exits and the entry floor. They cannot turn a negative gross reversion into a profit.

Iteration History

Verification failed (Layer 1.5 — hypothesis/config consistency) [class=hypothesis_mismatch]: - optimization_plan fixes bar_interval at 1-HOUR

Outcome Summary

On 1-hour bars, 3.2-sigma KO-PEP excursions did not revert to a frozen 5-session reference within the hold window, so the loss comes from gross reversion rather than costs, and only the paper's second-by-second midprice version would be a real test of the idea.

The backtest review abandoned it for negative expectancy. Avg per-leg return of -0.194% was below the USEQ floor of +0.05%, signal IC was -0.098 (t=-0.68, not significant), and most baskets ended at the 5-session time stop instead of converging. Zero commissions and about $830 of impact plus borrow explain only part of the loss, so tuning the bounded parameters could not fix it.

An adaptation of Ananova/Cont/Xu's model-free pairs approach: trade 3.2-sigma two-sided excursions of the KO-PEP regression spread on 1-hour USEQ bars, using a 5-session OLS reference that stays frozen while a position is open, and exit on convergence to that reference, a bounded spread-loss stop or a time stop.

From Aug 2024 to Aug 2026 it closed 138 legs (69 hedged KO-PEP baskets) and returned -3.25%, with Sharpe -0.65 (CI -1.99 to 0.81), profit factor 0.84 and avg_trade_return_pct of -0.194%. Max drawdown was 4.93% and peak leverage 0.42.

Analysis

Model-free Analysis of Dynamic Trading Strategies