Pairs Trading: A Supply Chain Hazard Model for Cointegration Breaks

Abstract

A cointegrating relation is often treated as a statistical property of two price series, although the economic mechanism supporting that relation can change before a trailing price window recognizes the change. This paper examines a narrower hypothesis: deterioration or disappearance of an observed supplier-customer relationship can raise the hazard that a previously cointegrated equity pair loses its constant-parameter equilibrium. The economic channel is specific. A persistent commercial relationship can couple expected revenues, production costs, demand, investment, and firm-specific cash-flow expectations. When the relationship contracts materially, the shared component of the firms' valuation processes can weaken while a rolling cointegration test continues to contain months of pre-break observations.

Altsets quarterly supply chain data are used to construct two commercial state changes from Relationship Size, Supplier Revenue %, and Customer Cost %: persistent relationship disappearance and broad economic-weight deterioration. Six relationships provide calibrated break and control episodes. Hyundai Glovis to Boeing and Teijin to Caterpillar exhibit simultaneous declines across all three dependency measures, while Broadcom to Samsung Electronics and PepsiCo to Seven & i provide disappearance episodes after sustained observed relationships. AMD to Samsung and Samsung to Qualcomm supply stable and sub-threshold controls.

A survival specification then treats loss of rolling cointegration as the event and the commercial states as time-varying covariates. A controlled simulation quantifies the detection problem that motivates the design. With a 252-trading-day rolling Engle-Granger monitor, an abrupt removal of the common stochastic trend produces a median price-only alarm delay of 30 trading days; a 63-day gradual de-anchoring raises the median delay to 55 days. The paper therefore identifies a measurable distinction between commercial information and lagged price diagnostics: commercial deterioration can be tested as an early state variable for cointegration failure rather than as another pair-selection score.

Keywords: supply chain data; cointegration; structural breaks; survival analysis; pairs trading; hazard models; statistical arbitrage

Problem

Cointegration-based relative-value models rely on a stronger proposition than contemporaneous return correlation. If two log price series, $p^s_t$ and $p^c_t$, share a stochastic trend, a linear combination can remain stationary even though each price is individually nonstationary. The resulting spread can support an error-correction interpretation and, in trading applications, a mean-reversion rule. The difficulty appears after formation. A pair that passed a historical test can enter a new economic regime while a rolling test remains dominated by observations generated under the old regime. Gregory and Hansen formalized cointegration tests that admit unknown regime shifts and showed that conventional tests can lose power when the intercept or slope of the long-run relation changes. Gregory, Nason, and Watt similarly reported sharply reduced ADF rejection frequencies in the presence of structural breaks. The statistical problem is therefore temporal: evidence that supported the equilibrium yesterday can remain inside the estimation window after the mechanism supporting that equilibrium has changed.

Pairs-trading research has treated structural instability as a material operational risk. Gatev, Goetzmann, and Rouwenhorst's classic relative-value study matched equities through normalized price histories and attributed profitability to temporary divergence among close substitutes sharing a common return component. Later cointegration-based research has focused more explicitly on instability, including procedures intended to avoid entering pairs already undergoing a structural break. Those approaches remain primarily price conditioned. They ask whether prices have already become inconsistent with the historical relation. The hypothesis investigated here places an economically interpretable state variable before that question. If the common trend partly reflects a recurring supplier-customer mechanism, a change in the commercial relation can occur before enough post-break price observations accumulate to overturn a trailing cointegration test.

The commercial mechanism has support outside the statistical-arbitrage literature. Cohen and Frazzini documented return predictability across customer-supplier links, consistent with information about economically related firms entering prices with delay. Hertzel, Li, Officer, and Rodgers documented wealth effects extending along supply chains during financial distress, including adverse effects on suppliers of distressed firms. Accounting standards also treat concentrated commercial dependence as an economically meaningful risk object. FASB Statement 131 requires disclosure when a single external customer represents at least 10 percent of revenue and describes major customers as a significant concentration of risk. These findings motivate a conditional prediction rather than a generic claim that connected firms move together. When the measured economic weight of an existing link contracts sharply or the exact directed relationship disappears after a persistent history, the hazard of losing the old price equilibrium should rise relative to otherwise comparable connected pairs whose commercial state remains intact.

Prior Work

Structural-break econometrics supplies the statistical half of the problem. Gregory and Hansen allow the cointegrating intercept or slope to shift at an unknown date, while Hansen and Johansen develop recursive procedures for evaluating constancy of long-run parameters in cointegrated VAR systems. These methods are useful after price behavior begins to change because they distinguish a stable equilibrium from one whose parameters have moved. They do not specify an economic variable that should alter the prior probability of a break. A price monitor therefore treats tomorrow's parameter instability as conditionally similar whether the firms have just ended an important commercial relationship or have experienced no observable change in their bilateral activity. The proposed survival model changes that information set. Commercial deterioration becomes a time-varying covariate observed outside the price system, while rolling ADF evidence remains in the model as the conventional price-only state.

The distinction also separates this study from pair-selection research. A supply chain link is not used to assert that two firms should be cointegrated, and no pair enters the survival sample merely because an economic relationship exists. Entry requires the price criterion first. The commercial relationship becomes relevant only after a price equilibrium has already been established. This ordering prevents the economic link from becoming a substitute for statistical validation. It also creates a falsifiable null: after conditioning on rolling price evidence and conventional risk states, commercial disappearance and weight deterioration may carry no incremental information about subsequent cointegration failure. Such an outcome would imply that the observable commercial variables either change too slowly, are already capitalized in prices, or fail to correspond to the economic forces generating the statistical equilibrium.

The primary hypothesis is therefore directional. Conditional on a pair satisfying the formation cointegration rule, persistent relationship disappearance or a sufficiently broad decline in economic weight increases the subsequent hazard of constant-parameter cointegration failure. A secondary hypothesis concerns timing. If commercial information reaches the model before the trailing price window is sufficiently contaminated by post-break observations, the commercial warning time should precede the conventional rolling failure time. A third comparison separates disappearance from weight decline. Disappearance represents a discrete state change, while a decline can represent gradual reallocation of purchases, sales, or capacity. Theory suggests a larger hazard shift following disappearance, although re-entry episodes in the Altsets histories make permanence inappropriate as an assumption. The coefficients on the two event types should therefore be estimated separately rather than collapsed into a single churn variable.

Events

The Altsets panel used here contains quarterly point-in-time relationship histories from September 2021 through September 2026. Each directed supplier-customer observation can carry three economic measures: Relationship Size in dollars, the percentage of supplier revenue associated with the relationship, and the percentage of customer cost associated with the supplier. The three measures answer different economic questions. Relationship Size approximates the bilateral scale of the edge, Supplier Revenue % measures dependence from the seller's income side, and Customer Cost % measures dependence from the buyer's purchasing side. A deterioration event should therefore require broad movement rather than a single noisy metric.

For metric $m \in \{S,R,C\}$, define the retention ratio

where $S$ is Relationship Size, $R$ is Supplier Revenue %, $C$ is Customer Cost %, and the denominator uses up to eight prior quarterly observations.

A weight-break indicator $W_{i,k}$ switches on when at least two of the three retention ratios are at or below 0.60, equivalent to declines of at least 40 percent from their trailing peaks, after at least six observed quarters. A disappearance indicator $D_{i,k}$ requires two consecutive absent quarterly snapshots after a run of at least six consecutive observed quarters. The persistence conditions prevent a single snapshot from defining the event.

Six relationships create a compact event panel with two weight breaks, two disappearance episodes, one stable control, and one sub-threshold decline. The selection is intentionally heterogeneous because the hypothesis concerns whether the economic state of the bilateral relationship conditions survival of an already-cointegrated price relation, rather than whether a single industry generates a particular return pattern.

The two continuous weight-break episodes are unusually clean. Hyundai Glovis to Boeing crosses the 40 percent rule in March 2025 after Relationship Size, Supplier Revenue %, and Customer Cost % had fallen approximately 56 percent, 58 percent, and 58 percent from their trailing peaks. Teijin to Caterpillar crosses in June 2026 with corresponding declines of approximately 46 percent, 42 percent, and 45 percent.

Broadcom to Samsung provides a different state change. After nine consecutive observed quarters through June 2025, the directed relationship is absent for three quarterly snapshots and returns in June 2026 at a much smaller scale. Relative to March 2025, re-entry Relationship Size is about 54 percent lower, Supplier Revenue % about 68 percent lower, and Customer Cost % about 61 percent lower.

PepsiCo to Seven & i disappears after seven consecutive observed quarters and later reappears at greater measured scale. That later reappearance makes disappearance a state transition rather than an assumed permanent termination, which is why $D_{i,k}$ is treated as a time-varying exposure in the survival model.

The controls sharpen the threshold interpretation. AMD to Samsung remains nearly unchanged over the year beginning June 2025: Relationship Size rises about 0.9 percent, Supplier Revenue % stays at 1.27, and Customer Cost % moves from 0.27 to 0.28. Samsung to Qualcomm moves in the opposite direction but remains below the 40 percent event rule, with declines of approximately 25 percent in Relationship Size, 23 percent in Supplier Revenue %, and 28 percent in Customer Cost %.

A linear specification that treats every decline as equivalent would blur these cases. The proposed event definition permits a direct test of nonlinearity: a broad 20 to 30 percent contraction can be compared with the much larger Boeing and Caterpillar episodes without assuming that hazard rises proportionally with each percentage point of deterioration.

Hazard

For each commercial pair $i$, daily split- and dividend-adjusted equity prices are converted to a common currency before testing. Let $p^s_{i,t}$ and $p^c_{i,t}$ denote the log prices of the supplier and customer. The formation equation is

A pair enters the risk set only if an Engle-Granger test rejects the null of no cointegration at the 5 percent level over the preceding 504 trading days. The longer formation interval separates pair admission from the shorter monitoring window. Once admitted, cointegration is re-estimated over trailing 252-trading-day windows every five trading days. Constant-parameter failure occurs when the rolling test fails to reject no cointegration at the 5 percent level for three consecutive monitoring dates.

The three-monitor persistence rule converts isolated p-value noise into a sustained price-only alarm. Gregory-Hansen testing can then classify whether the episode is better described as a shifted cointegrating regime rather than complete loss of a long-run relation, while recursive parameter-constancy diagnostics provide a secondary description of hedge-ratio instability.

Let $T_i$ denote trading days from entry into the risk set until the persistent rolling failure. The central estimand is a Cox-type hazard with time-varying commercial states,

$D_i(t)$ indicates a qualifying relationship disappearance, $W_i(t)$ indicates broad weight deterioration, and $A_i(t)$ contains the contemporaneous price-only warning state, including the rolling Engle-Granger p-value and its recent change. $X_i(t)$ contains parsimonious confounders whose omission could create false attribution: realized volatility of each stock, the difference in market betas, broad-market stress, and exchange-rate volatility for cross-currency pairs.

The quantities $\exp(\beta_D)$ and $\exp(\beta_W)$ are the commercial-break hazard ratios. A coefficient near zero after conditioning on $A_i(t)$ would indicate that the commercial event adds little beyond price deterioration already visible in the rolling window. A positive coefficient would indicate incremental timing information.

The warning comparison follows directly from the event times. Let $\tau_i^C$ be the first qualifying commercial event and $\tau_i^P$ the persistent price-only failure. For episodes in which both occur, define

Positive $L_i$ is an early-warning interval. Negative $L_i$ indicates that the price relation failed before the commercial state changed. The distribution of $L_i$, rather than a trading return, answers the paper's central timing question.

The stable commercial controls provide a placebo: if a similar frequency of rolling failures occurs when $D_i=W_i=0$, then either the price relation is intrinsically unstable or conventional market variables explain the failure. The disappearance and weight-break coefficients also permit the required comparison between discrete termination-like events and gradual economic contraction without forcing the two processes into one severity score.

Lag

A controlled simulation isolates a mechanical reason that commercial information can lead a rolling price monitor. The experiment uses 504 pre-break trading days and 252 post-break days. Before the break, $x_t$ follows a random walk and

where

and the residual innovation standard deviation is 0.7 relative to a unit standard deviation for the common random-walk innovation.

Each simulated pair must pass the 5 percent Engle-Granger criterion over the full 504-day formation period. Monitoring then uses the same 252-day rolling window, five-day evaluation interval, and three-consecutive-failure rule defined above.

Three states are simulated across 300 paths each. The stable state keeps the cointegrating relation intact. The abrupt-break state makes $y_t$ an independent random walk at day zero. The gradual state reduces the loading of changes in $y$ on changes in $x$ linearly from one to zero over 63 trading days while the independent innovation component rises correspondingly.

The stable simulation produces one rolling alarm in 300 paths over the following 252 trading days, a 0.3 percent false-alarm frequency under this persistence rule. Under abrupt de-anchoring, all 300 paths eventually trigger the price-only alarm, yet the median alarm arrives 30 trading days after the economic break. The interquartile interval is approximately 19 to 56 trading days. Only 34.0 percent of the paths are flagged within 20 trading days, 61.0 percent within 40 days, and 77.7 percent within 60 days.

The delay is longer under gradual de-anchoring. Of 300 paths, 299 trigger within the one-year monitoring horizon; the median delay is 55 trading days, the interquartile interval is 40 to 85 days, and the 90th percentile is approximately 116 days. Only 4.0 percent are detected within 20 days and 30.3 percent within 40 days.

These calculations are diagnostic rather than an estimate of the real-world effect of commercial deterioration. The simulation establishes the amount of latency that can arise from the econometric monitor itself when the underlying equilibrium changes at a known date. A commercial event observed at day zero would lead the rolling test by a median of roughly six trading weeks in the abrupt specification and eleven weeks in the gradual specification.

The economic hypothesis remains responsible for linking actual relationship deterioration to actual structural failure. The simulation quantifies the opportunity for an early warning; the survival coefficient tests whether commercial events occupy that opportunity in observed markets.

The commercial threshold also has a useful failure test. Lowering the required decline from 40 percent to 35 percent moves the Hyundai Glovis to Boeing warning from March 2025 to December 2024 and the Teijin to Caterpillar warning from June 2026 to March 2026. Raising the threshold to 50 percent preserves the Boeing episode but removes the Caterpillar event.

The event definition therefore contains economically relevant sensitivity rather than an invariant classification. A credible empirical effect should survive reasonable movement around the 40 percent rule without depending entirely on the Caterpillar boundary case. The AMD and Qualcomm controls provide an additional challenge: if a model produces the same hazard response for Qualcomm's roughly 20 to 30 percent decline as for Boeing's roughly 56 to 58 percent decline, the proposed nonlinear economic mechanism has little empirical support.

Identification

The strongest alternative explanation is common exposure. Supplier and customer stocks can share industry factors, interest-rate sensitivity, commodity inputs, geographic demand, or broad risk-on and risk-off regimes even when the bilateral relationship contributes little to their price equilibrium. Cointegration failure could therefore coincide with commercial deterioration because both respond to the same macro shock.

The design addresses this in two places. First, the pair must be cointegrated before the commercial event, so the study concerns survival of an established statistical relation rather than contemporaneous comovement created after the shock. Second, the hazard model conditions on rolling price evidence and time-varying market states. Cross-currency pairs require common-currency prices or explicit FX controls; otherwise a currency regime can appear as a break in the equity relation. Sector membership and beta similarity should enter as stratification or matching variables rather than as automatic explanations for the commercial coefficient.

A second identification problem is reverse timing. Prices may anticipate a relationship termination before the quarterly commercial observation changes. If that occurs systematically, $L_i$ should be negative or close to zero, and $\beta_D$ should shrink once the rolling p-value trend enters the hazard specification. Such an outcome would reject the early-warning mechanism while still allowing commercial events to describe the same underlying economic transition ex post.

The timing test therefore carries more information than a simple association between relationship breaks and failed pairs. Commercial variables should improve the conditional hazard before the price-only criterion crosses its failure threshold. A survival model that records only eventual co-occurrence would be unable to distinguish economic anticipation from delayed statistical recognition.

A third issue concerns regime changes that preserve cointegration under new parameters. A customer can reduce purchases, a supplier can renegotiate terms, or the economic scale of a relationship can change without eliminating the common trend. Gregory-Hansen testing is useful here because conventional ADF failure in the presence of a level or slope break can reflect parameter instability rather than disappearance of cointegration altogether.

The survival endpoint is intentionally constant-parameter failure, since a fixed-spread relative-value model is already invalidated when its hedge ratio or equilibrium level changes materially. Post-event break-adjusted testing then partitions those failures into reparameterized equilibria and more complete de-anchoring. This avoids treating every commercial termination as a claim that the two equities must become statistically unrelated forever.

Interpretation

The selected Altsets histories already illustrate why a binary relationship flag is insufficient. Boeing and Caterpillar retain their supplier links while economic dependence contracts across all three measured dimensions. Broadcom and PepsiCo provide periods in which the exact directed relationship disappears after a sustained run. Qualcomm declines materially without reaching the event threshold, while AMD remains nearly unchanged.

These state differences are economically distinct inputs to a survival model. They also permit a result that a generic relationship-churn study cannot produce: an estimate of whether loss of commercial weight changes the conditional lifetime of a previously established price equilibrium after the model has already observed the contemporaneous price evidence.

The null outcomes are informative. If $\beta_D$ and $\beta_W$ are near zero, commercial links may explain cash-flow transmission without explaining persistence of cointegration. If the coefficients are positive before adding rolling price diagnostics and vanish afterward, prices are already incorporating the relevant relationship transition quickly enough that supply chain data add little warning time.

If only disappearance is associated with higher hazard, the equilibrium may tolerate substantial resizing while remaining anchored by an ongoing contract or recurring transaction channel. If weight decline predicts failure while disappearance does not, disappearance may mix economically different states, including temporary reporting or contracting gaps and later re-entry. The PepsiCo to Seven & i history makes that last possibility empirically plausible and argues for estimating disappearance and deterioration separately.

Conclusion

Cointegration failure is usually diagnosed from the same price system whose historical observations created the original signal. That creates a monitoring delay whenever the economic process changes faster than the rolling window. Supplier-customer histories provide an external state variable with a clear economic interpretation: the scale and direction of the commercial mechanism itself.

The proposed test therefore begins after cointegration has already been established and asks whether subsequent deterioration in Relationship Size, Supplier Revenue %, and Customer Cost %, or persistent disappearance of the directed edge, changes the hazard that the old equilibrium fails.

The Altsets episodes provide concrete event definitions rather than generic network exposure measures. Boeing and Caterpillar cross a broad three-metric deterioration threshold after long observed relationships; Broadcom and PepsiCo provide persistent disappearance episodes; AMD and Qualcomm provide stable and sub-threshold contrasts.

The controlled simulation establishes why timing can differ even under an unambiguous break: a 252-day rolling Engle-Granger monitor trails an abrupt break by a median of 30 trading days and a gradual 63-day de-anchoring by 55 days under the specified monitoring rule.

The empirical quantity of interest is consequently the incremental commercial-break hazard ratio and the distribution of commercial-to-price warning lead times. A positive estimate would identify an early-warning role for historical supply chain data in cointegration monitoring. A null estimate would place a useful boundary around the idea by showing that commercial state changes fail to improve on information already contained in rolling prices.

References

Altsets supply chain dataset.

Cohen, L., and A. Frazzini. 2008. "Economic Links and Predictable Returns." Journal of Finance 63(4), 1977-2011.

FASB. Statement of Financial Accounting Standards No. 131, "Disclosures about Segments of an Enterprise and Related Information." Major-customer disclosure and concentration-of-risk discussion.

Gatev, E., W. N. Goetzmann, and K. G. Rouwenhorst. 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule." Review of Financial Studies 19(3), 797-827.

Gregory, A. W., and B. E. Hansen. 1996. "Residual-Based Tests for Cointegration in Models with Regime Shifts." Journal of Econometrics 70(1), 99-126.

Gregory, A. W., J. M. Nason, and D. G. Watt. 1996. "Testing for Structural Breaks in Cointegrated Relationships." Journal of Econometrics 71(1-2), 321-341.

Hansen, H., and S. Johansen. 1999. "Some Tests for Parameter Constancy in Cointegrated VAR-Models." Econometrics Journal 2(2), 306-333.

Hertzel, M. G., Z. Li, M. S. Officer, and K. J. Rodgers. 2008. "Inter-Firm Linkages and the Wealth Effects of Financial Distress Along the Supply Chain." Journal of Financial Economics 87(2), 374-387.