Next-Day Return Prediction with Directional Supply Chain Exposure

Abstract

A supplier-customer edge is usually treated as a binary object in empirical asset-pricing work: two firms are connected or they are not. That representation discards the economic asymmetry inside the link. A customer representing 29% of a supplier's revenue and a customer representing 10% create different cash-flow exposures even though both generate the same adjacency indicator. This paper estimates a small event-response model in which firm-specific return shocks are transmitted according to directional economic exposure. The source firm's daily return is residualized against market and sector returns, and the connected firm's residual return is measured on the next trading day. For customer-originated shocks, Supplier Revenue % defines exposure; for supplier-originated shocks, Customer Cost % defines exposure. Relationship Size provides a symmetric dollar baseline. The eight-link panel produces an asymmetric result. Economic weighting materially improves the customer-to-supplier model relative to a binary edge, although the estimated function reflects attenuation of an opposite-signed response rather than monotonic positive propagation. Supplier-to-customer transmission is better described by an exposure threshold than by a linear weight: customers with higher cost exposure respond in the source shock's direction, while low-exposure customers do not. Dollar relationship size explains less of the cross-section than the direction-specific percentages. The exercise therefore rejects a simple rule in which stronger commercial links mechanically generate proportionally larger return spillovers.

Keywords: Information diffusion; Event studies; Lead-lag effects; Residual returns; Cross-firm predictability

Problem

The return-predictability literature has already established that economically related firms can contain information about one another. Cohen and Frazzini use major customer relationships to show that customer returns predict subsequent supplier returns, interpreting the effect through limited investor attention to economically linked firms. Their customer-momentum result is specifically about delayed incorporation of information across a commercial relationship rather than ordinary own-stock momentum. Menzly and Ozbas reach a related result at the industry level: returns cross-predict across economically related supplier and customer industries, and that predictability weakens as the population of informed investors increases. These results motivate a narrower measurement question. Once a relationship has been identified, should its contribution to cross-firm return transmission be represented by the same coefficient as every other relationship, or should the coefficient depend on how much cash flow actually runs through that edge?

The distinction becomes more important when direction changes. If firm $C$ is a large customer of supplier $S$, negative information about $C$'s demand can change expectations for $S$'s future revenue. The economically relevant denominator is then $S$'s revenue, because it measures how much of the supplier's sales base is associated with that customer. If instead an input supplier $S$ experiences a shock, the exposure of customer $C$ depends more naturally on the share of the customer's cost structure represented by that supplier. A dollar relationship of identical size can therefore create very different exposures on the two sides. Real-economy evidence supports treating production links as transmission mechanisms rather than undirected correlations. Barrot and Sauvagnat identify supplier shocks using natural disasters and document output and market-value effects on customers, particularly when inputs are difficult to replace. Carvalho, Nirei, Saito, and Tahbaz-Salehi document propagation both upstream and downstream after the Great East Japan Earthquake. The unresolved issue here is whether a similar directional structure can improve the measurement of short-horizon price-shock transmission.

The primary hypothesis is therefore conditional rather than universal. Let $w_{SC}$ denote the economic dependence of the receiving firm on the source firm. If commercial exposure affects the amount of source-firm information that is relevant to the receiving firm's expected cash flows, the response coefficient should vary with $w_{SC}$. A second hypothesis concerns asymmetry. Customer-to-supplier transmission should load on Supplier Revenue %, while supplier-to-customer transmission should load on Customer Cost %. There is no requirement that the two response functions have equal signs, slopes, or thresholds, because demand news and input news enter expected cash flows through different mechanisms. The falsifying result is straightforward: if a binary edge describes the responses as well as directional economic weights, or if permuting weights across relationships leaves the fit unchanged, then exposure adds little information to short-horizon return transmission.

Prior

Customer momentum is an especially relevant baseline because its economic logic is directional. Cohen and Frazzini's supplier return is forecast from the return of an economically important customer, and the authors show that the effect survives controls for the supplier's own momentum. That design establishes a lead-lag relation but leaves room for richer weighting. The principal-customer disclosure used in much of this literature already imposes an implicit economic threshold: a major customer receives a relationship indicator while smaller relationships may be absent. Once continuous revenue exposure is observable, the threshold can be replaced by an explicit weight. Menzly and Ozbas add an information-segmentation mechanism by showing that cross-predictability varies with analyst coverage and institutional ownership. The present exercise holds the attention mechanism in the background and asks a different question: conditional on a large idiosyncratic source return, does the next-period residual response vary systematically across connected firms according to the economic importance of the edge?

Production-network studies imply that equal weighting is unlikely to be structurally correct. Barrot and Sauvagnat show that shock propagation is stronger when inputs are specific, which makes substitution costly. Carvalho et al. show that a localized shock can travel in both directions and through indirect links, demonstrating that network orientation is economically meaningful. Neither result implies a linear mapping between an accounting exposure percentage and a one-day equity response, and the event study below does not impose that assumption as the only alternative. A median exposure split is estimated alongside the linear interaction. This distinction is useful because a 1 percentage point increase in exposure need not have the same effect at 1% and 25%. Bargaining power, inventories, substitution options, prior disclosure, and investor attention can create thresholds or saturation. A binary model, a continuous interaction, a two-bucket specification, and a dollar-size interaction are therefore compared on the same response observations.

Data

Altsets records directed commercial relationships with three quantities used here: Supplier Revenue %, Customer Cost %, and Relationship Size. The attached historical workbook stores these metrics by directed supplier-customer pair and observation date, which permits the relationship weight to be fixed using information preceding the return event rather than inferred from the subsequent market response. For an edge from supplier $S$ to customer $C$, Supplier Revenue % is used when the source shock originates at $C$, because the receiving firm is $S$; Customer Cost % is used when the source is $S$, because the receiving firm is $C$. Relationship Size enters separately as a dollar-valued alternative weight. The event exercise fixes exposures at the latest pre-event snapshot and never adjusts them using the observed target returns.

The synchronized return panel contains eight directed links. Four suppliers are connected to Arrow Electronics, creating a customer-to-supplier test with a wide range of supplier revenue dependence. Four customers are connected to Intel, creating the supplier-to-customer test. The choice produces variation in the economically correct directional percentage while keeping source shocks common within each direction. That is important econometrically: when every Arrow supplier is evaluated against the same Arrow shock, differences in the receiving-firm response cannot arise from different source returns. The same logic holds for Intel's customers. Altsets history also shows that the selected relationships are economically persistent rather than one-session classifications. For example, the pre-event Supplier Revenue % values for Silicon Laboratories, Analog Devices, and Diodes relative to Arrow remain near the central values observed through their preceding histories, while Intel-Dell remains the high-cost-exposure relationship within the Intel customer set.

The economic interpretation of the percentages is independently visible in company disclosures. Littelfuse reported that Arrow represented 9.5% of consolidated net sales in 2025, 9.4% in 2024, and 11.2% in 2023, closely matching the 9.85% pre-event Altsets supplier-revenue exposure used in the panel. Arrow itself reports a highly diversified customer base, with no single customer representing more than 2% of its 2025 consolidated sales, while its supplier relationships operate largely through cancellable distribution agreements and some businesses depend on a limited number of suppliers. Those disclosures illustrate why the two directional percentages should not be treated as interchangeable. A commercial edge can be material to a component manufacturer even when the same edge occupies a much smaller fraction of the distributor's aggregate economics.

Model

For firm $i$ on date $t$, the first-stage return equation removes broad market and sector movement:

Here $r_{m,t}$ is the market return and $r_{s,t}$ is the appropriate technology or semiconductor benchmark. The event variable is the residual return of the source firm, $x_e=\hat{\varepsilon}_{source,t_e}$. The response variable is the receiving firm's next-trading-day residual, $y_{j,e}=\hat{\varepsilon}_{j,t_e+1}$. The one-day delay targets gradual information incorporation rather than contemporaneous common-factor comovement. Because the empirical object is a small event panel, these residuals are treated as local factor-adjusted shocks rather than structural estimates of permanent factor betas.

The binary benchmark is

where $d$ identifies the propagation direction. Every connected recipient receives the same transmission coefficient. The exposure model replaces that restriction with

For customer-to-supplier events, $w_{j,e}$ is Supplier Revenue % expressed as a fraction. For supplier-to-customer events, $w_{j,e}$ is Customer Cost %. The quantity

is the exposure-weighted transmission response. It measures the receiving firm's expected residual-return response per percentage point of source residual return at a specified economic exposure. The model is intentionally simple. A positive $\tau_1$ indicates that the response coefficient becomes more positive as economic dependence rises, while a negative value indicates the reverse. The sign of $T_d(w)$ remains an empirical object because an equity-price shock can reflect information about margins, bargaining power, financing, product positioning, or another firm-specific state rather than a pure quantity shock.

Two alternatives test whether the continuous specification is forcing an inappropriate shape. The nonlinear model divides the four relationships in each direction at the median exposure:

The dollar baseline replaces $w_j$ with centered $\log(1+\text{Relationship Size}_j)$. This comparison separates directional dependence from the absolute commercial value of a link. A $3 billion relationship can be large in dollars and still represent a modest fraction of a large firm's economics; a $200 million relationship can represent a major customer for a smaller supplier. The paper's central comparison is therefore binary connectivity versus direction-specific percentage exposure, with dollar size functioning as a competing explanation rather than a second definition of the same variable.

Events

The Arrow panel uses two non-overlapping idiosyncratic source moves, a positive residual of 5.71 percentage points on September 11, 2026 and a negative residual of 3.57 points on September 21. The Intel panel uses a positive 3.98 point residual on September 16 and a negative 6.33 point residual on September 25. Each source observation is paired with the next-trading-day residual for all four receiving firms, yielding eight customer-to-supplier and eight supplier-to-customer responses. The full event-response matrix used in the estimation records the same source shock across every recipient in its direction and the predetermined Altsets weight for each relationship.

The dates also provide an external check that the source residuals need not be interpreted as unidentified market noise. Arrow's September move followed an expansion of its HPE Networking distribution portfolio, including expanded access to HPE Aruba and Juniper products, which Arrow itself described publicly during the preceding days. Intel's September 16 move coincided with Reuters reporting that Intel and SK Hynix were discussing U.S. memory-chip manufacturing arrangements, including possible use of Intel's Ohio capacity. The regressions do not code these stories as causal treatments, and the economic sign of the news is not imposed on the target firms. They serve only to establish that at least part of the selected residual variation occurred around firm-specific information capable of changing expectations about commercial activity.

Results

The binary customer-to-supplier model estimates a transmission coefficient of $-0.207$, with an in-sample residual RMSE of 1.343 percentage points. Adding Supplier Revenue % changes the fitted response to

and lowers RMSE to 1.115. The reduction is approximately 17%. The dollar relationship-size interaction produces an RMSE of 1.297, only a modest improvement over the binary edge, while a model that uses exposure weighting without a baseline term performs worse at 1.548. The shape is economically informative. At a 10% supplier-revenue exposure, the fitted coefficient is approximately $-0.38$; at 20%, approximately $-0.18$; and near 29%, approximately zero. Increasing dependence therefore attenuates an opposite-signed next-day response rather than generating a progressively larger positive response. The result differs from the naive hypothesis that the strongest customer relationship should mechanically create the largest same-direction return spillover.

The median-split model reaches nearly the same fit without imposing linearity. The exposure median is 17.785%. Relationships below the median have a fitted source-response coefficient of $-0.365$, while the high-exposure group has a coefficient of $-0.050$. RMSE is 1.115, effectively identical to the continuous interaction. The pair-level estimates tell the same story: the two lower-exposure suppliers display the strongest negative source-response slopes, while the highest-exposure supplier is near zero. A same-industry unconnected benchmark using Monolithic Power Systems and Teradyne produces a binary source-response coefficient of roughly $-0.188$, close to the connected binary estimate. Connectivity alone therefore provides little separation in this local event sample. Economic heterogeneity inside the connected group carries considerably more information than the connected indicator itself.

The supplier-to-customer panel behaves differently. Using the four selected Intel customer links, the binary coefficient is $0.091$, with RMSE of 1.395. The continuous cost-exposure model is

with RMSE of 1.378. The in-sample improvement over the binary model is only about 1%. Relationship Size yields RMSE of 1.380, similarly weak. The nonlinear split produces a more distinct result. The median Customer Cost % is 1.23%. Low-exposure customers have an estimated coefficient of $-0.030$, while the high-exposure group has a coefficient of $0.211$, and RMSE falls to 1.242. Within this small panel, supplier-originated shocks therefore look more consistent with a threshold response than with a smooth proportional function. Dell's 12.6% cost exposure and Super Micro's 1.54% exposure belong to the high group; Arrow and Best Buy fall below the threshold.

The difference between directions is more informative than either coefficient in isolation. Customer-originated shocks produce strong cross-sectional exposure structure, yet the structure appears as attenuation of a negative one-day relation. Supplier-originated shocks produce weaker linear structure but a clearer high-versus-low exposure break. This is compatible with distinct mechanisms. Customer news can change a supplier's expected revenue directly, but a distributor's own stock shock may also contain information about distribution margins, competitive position, financing, or channel bargaining power whose effect on suppliers need not share the same sign. Supplier shocks affect customers through input availability, cost, and substitution possibilities, which can generate a threshold when the input is economically large enough to influence the customer's expected cash flows. Barrot and Sauvagnat's evidence that propagation is stronger for specific inputs provides a real-economy analogue for this state dependence.

Checks

Leave-one-relationship-out prediction gives the strongest reason to resist a simple symmetric interpretation. In the customer-to-supplier panel, the binary model's out-of-pair RMSE is 1.500, while the continuous exposure model lowers it to 1.130. The improvement is approximately 25%, and the median-bucket specification produces 1.235. Thus the exposure interaction is not solely fitting one relationship while it remains in the estimation set. In the supplier-to-customer panel, the result reverses. Binary leave-one-pair-out RMSE is 1.518, the bucket model improves it to 1.364, while the continuous linear model becomes extremely unstable, with RMSE above 9. The linear cost-share slope therefore has little support as a portable coefficient in this sample. The threshold representation survives the cross-pair exercise much better.

A second failure test permutes exposure weights across the connected relationships while holding the source shocks and target responses fixed. For customer-to-supplier transmission, the actual Supplier Revenue % assignment generates the lowest raw-residual sum of squared errors among all 24 possible assignments of the four observed weights. After residuals are standardized by firm-specific volatility, the observed assignment falls to sixth among 24, so the ordering is sensitive to return scale. The supplier-to-customer assignment fares poorly in the comparable four-pair exercise: 20 of the 24 weight assignments fit at least as well as the observed linear cost weights. The permutation evidence therefore reinforces the model comparison. Customer-to-supplier exposure contains cross-sectional information in raw return units, though part of that information is associated with differences in recipient volatility. Supplier-to-customer exposure should not be summarized by a stable linear coefficient from this panel.

The result also changes the interpretation of Relationship Size. If the mechanism were simply that economically larger transactions generate larger market spillovers, log relationship value should absorb much of the improvement from directional percentages. It does not. Dollar size improves the customer-to-supplier RMSE from 1.343 to 1.297, compared with 1.115 for Supplier Revenue %. On the Intel side, both linear cost exposure and dollar size make only small in-sample improvements, while the cost-exposure bucket produces the larger change. The distinction is economically coherent. Relationship Size measures scale. Supplier Revenue % and Customer Cost % measure dependence. Scale and dependence coincide in some relationships, particularly Intel-Dell, but they diverge sharply in others. The event responses appear to distinguish those concepts.

Meaning

The empirical object estimated here is narrower than customer momentum. Cohen and Frazzini ask whether customer returns forecast supplier returns across a broad historical sample. This paper asks what happens inside the edge after a large source residual has already been identified. The small event panel provides little support for assigning every connected firm a common transmission coefficient. It also provides little support for replacing the binary indicator with a universal proportional weight. The economically useful specification is directional. Supplier revenue dependence contributes information when the source is the customer, while customer cost dependence is the natural variable when the source is the supplier. Even then, functional form matters.

The counterintuitive customer-to-supplier sign is especially useful for separating exposure from interpretation. Higher Supplier Revenue % moves the response coefficient toward zero, and the strongest-exposure suppliers exhibit much less reversal than the weaker-exposure suppliers. That pattern can arise if high-exposure commercial information is incorporated more quickly, leaving less next-day movement, while weakly exposed firms exhibit delayed reversal from common sector or attention effects. It can also arise because the source equity shock combines several firm-specific cash-flow components, only some of which travel through the customer relationship. The present design cannot distinguish those explanations. What it can establish is that the cross-section is structured: assigning the same binary coefficient to the four links discards information, while treating the directional percentage as a simple positive multiplier mischaracterizes the observed response.

The supplier-to-customer side points toward a different testable prediction. If customer cost exposure behaves as a threshold, future larger-sample work should estimate whether propagation changes sharply after an input becomes sufficiently important to the buyer's cost structure, perhaps conditional on input specificity or substitutability. Carvalho et al. document that real shocks can travel in both directions through production networks, while Barrot and Sauvagnat show that the properties of the input affect the strength of propagation. The eight-link event study gives a market-price counterpart to that logic: direction and economic dependence alter the response function, yet the same functional form should not be imposed on upstream and downstream propagation.

Conclusion

A binary supplier-customer indicator is an incomplete state variable for short-horizon cross-firm return transmission. In the customer-to-supplier panel, allowing the coefficient to vary with Supplier Revenue % reduces in-sample error by about 17% and leave-one-pair-out error by about 25% relative to the binary model. The improvement is considerably larger than the improvement obtained from Relationship Size. The estimated function, however, is not a simple positive exposure multiplier. Higher exposure attenuates an opposite-signed next-day response, with the highest-exposure link approaching a zero coefficient. The raw-weight permutation places the observed exposure assignment first among 24 possibilities, while volatility standardization weakens that ordering.

Supplier-to-customer propagation has a different shape. A linear Customer Cost % interaction adds little and fails badly under leave-one-pair-out prediction. A median split is more stable: low-cost-exposure customers have little or slightly negative transmission, while the higher-exposure group has a positive coefficient of roughly 0.21. The eight-link sample therefore supports an asymmetric and nonlinear interpretation of commercial shock transmission. Economic exposure improves measurement only when its direction and functional form match the mechanism being tested. The empirical result is consequently narrower, and more informative, than the statement that connected firms affect one another: the edge's economic denominator changes what can be measured, and the appropriate transmission function differs depending on which side of the relationship originates the shock.

References

Altsets supply chain dataset.

Cohen, Lauren, and Andrea Frazzini. "Economic Links and Predictable Returns." The Journal of Finance 63, no. 4, 2008, pp. 1977-2011.

Menzly, Lior, and Oguzhan Ozbas. "Market Segmentation and Cross-predictability of Returns." The Journal of Finance 65, no. 4, 2010, pp. 1555-1580.

Barrot, Jean-Noel, and Julien Sauvagnat. "Input Specificity and the Propagation of Idiosyncratic Shocks in Production Networks." The Quarterly Journal of Economics 131, no. 3, 2016, pp. 1543-1592.

Carvalho, Vasco M., Makoto Nirei, Yukiko U. Saito, and Alireza Tahbaz-Salehi. "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake." The Quarterly Journal of Economics 136, no. 2, 2021, pp. 1255-1321.

Arrow Electronics, Inc. Form 10-K for the year ended December 31, 2025.

Littelfuse, Inc. Form 10-K for the year ended December 27, 2025.