Factor-Adjusted Downside Beta in Supply Chain Equity Pairs

Abstract

Firm-level tail-risk research often compresses a production network into node-level quantities such as degree or centrality. That representation can discard the economic asymmetry of individual commercial relationships. This paper tests whether downside return dependence is better characterized by economically weighted directed edges than by a firm's global network position. Four relationships are studied through time: SK hynix -> Intel, Samsung Electronics -> Intel, Hyundai Glovis -> Boeing, and Boeing -> Korean Air. Altsets quarterly histories provide Supplier Revenue %, Customer Cost %, and Relationship Size, while daily equity returns from July 22 through September 29, 2026 provide a short cross-market experiment in which Korean source-firm closes precede U.S. focal-firm closes. A source-tail beta is estimated from the bottom quintile of source returns after removing contemporaneous U.S. market exposure, then aggregated using binary, Supplier Revenue %, direction-aware economic dependence, and Relationship Size weights. Intel and Boeing have similar global degree centrality, yet their selected edges exhibit sharply different tail coefficients. Intel's two supplier edges have positive market-adjusted downside betas, while both Boeing cases are negative. Economic weighting changes the within-firm aggregates much less than the sign difference across firms. More consequentially, Intel's positive coefficients nearly disappear after semiconductor-sector residualization. Local economic exposure therefore contains information that centrality omits, but a commercial edge is not sufficient evidence of transmission. Factor-purged tail dependence is the relevant object.

Keywords: supply chain data; downside beta; quantile dependence; directed networks; factor residualization; commercial exposure

Problem

A centrality statistic answers a structural question: how extensively is a firm connected to the surrounding network? Tail dependence poses a different question: conditional on an extreme loss at a particular counterparty, how much of the focal firm's return moves in the same direction? The distinction is economically material when contractual exposure is concentrated. Two firms can have similar degree while one depends heavily on a small supplier, another has many substitutable counterparties, and a third is economically important to a customer without depending materially on that customer for revenue. Network position and pair-level dependence are therefore capable of moving independently even when both are measured from the same graph. Existing supply-chain research has documented associations between network centrality and crash or tail risk. Shi et al. construct a weighted directed supply network for Chinese manufacturing firms and report lower stock-price crash risk among more central firms, while Zhuo et al. associate stronger supply-network structure with lower systemic tail risk. Those studies make node position the principal explanatory object.

The financial econometrics literature supplies several alternatives to unconditional correlation. Ang, Chen, and Xing study covariance specifically in declining markets and show why downside beta can differ from ordinary beta. Adrian and Brunnermeier's CoVaR conditions system risk on the distress state of a particular institution, formalizing the broader idea that dependence in an adverse state can contain information hidden by unconditional covariance. Barunik and Cech estimate common risks directly in return-distribution tails with panel quantile regression. These methods differ in estimand and application, but all reject the assumption that average-state dependence is necessarily sufficient for an adverse state.

A second literature establishes that commercial links can organize return dependence. Cohen and Frazzini show that information concerning principal customers is incorporated into economically linked firms' prices with delay, creating return predictability across customer-supplier pairs. Their result establishes a reason to study directed firm links rather than arbitrary pairwise correlation. It does not imply that every commercial relationship generates a positive tail coefficient, because common industry shocks, market exposure, timing, and idiosyncratic news can produce similar return patterns. Levi and Welch sharpen that identification issue in a different setting: much of the apparent incremental information in downside beta can disappear after ordinary market exposure is controlled. Their result makes factor residualization central to the present experiment rather than an auxiliary robustness exercise.

The hypothesis tested here is therefore narrower than the claim that stronger commercial relationships create greater comovement. Let $j$ denote the source firm and $f$ the focal firm. Conditional on $j$ entering its lower return tail, a direct transmission mechanism predicts a positive residual sensitivity $\beta^-_{j\rightarrow f}$, with larger economically relevant focal-side exposure increasing the importance of that coefficient in the focal firm's aggregate tail statistic. If the apparent coefficient instead arises from a common market or industry shock, it should shrink materially after those factors are removed. Global degree centrality should have limited ability to distinguish the two cases when focal firms occupy similar positions in the total graph. A negative tail coefficient is a direct failure of the same-direction transmission prediction for that pair and period.

The distinction between global topology and edge intensity also follows from network theory. Acemoglu, Ozdaglar, and Tahbaz-Salehi show that greater connectivity can absorb sufficiently small disturbances yet propagate sufficiently large negative shocks under other conditions. Their model concerns financial networks rather than supplier contracts, but it demonstrates why the number of links and the consequences of a particular shock need not have a monotonic relation. A node can be structurally connected and locally exposed at the same time. The empirical question is therefore whether a tail statistic constructed from actual directed economic weights separates what centrality aggregates away.

Design

The return model begins with a market residual rather than raw focal-company returns. For focal firm $f$,

where $r_{f,t}$ is the focal firm's daily close-to-close return, $r_{M,t}$ is the SPY return, and $u_{f,t}$ is the residual. The ordinary directed edge coefficient is

The downside coefficient restricts estimation to days when the source firm's return lies in its own lower quintile. Let $Q_j(0.20)$ denote the empirical 20th percentile of $r_j$. Then

This construction asks whether an unusually negative source return carries same-day information for the focal firm beyond the broad U.S. market move. It is deliberately simpler than CoVaR and does not require estimating an entire conditional loss distribution from ten tail observations. The tail filter performs the state conditioning; the regression coefficient measures the direction and scale of the focal residual response.

Commercial direction determines which Altsets percentage represents dependence from the focal firm's perspective. For an edge $e=(s,c)$, where $s$ is supplier and $c$ is customer, define historical focal dependence as

Customer Cost % is appropriate when a supplier shock is transmitted downstream into a customer because it measures the supplier's share of the customer's cost base. Supplier Revenue % is appropriate when a customer shock is transmitted upstream into a supplier because it measures the customer's share of the supplier's revenue. Using Supplier Revenue % mechanically on every edge would therefore assign the wrong economic side to supplier-to-customer transmission. Relationship Size supplies a third weighting object based on the absolute scale of the commercial edge.

For weighting scheme $m$, let $w_{ef}^{(m)}$ denote the historical edge weight and normalize within each focal sample,

The edge-weighted downside beta is

Four versions are calculated. Binary weighting assigns equal weight to each selected edge. Revenue weighting uses historical mean Supplier Revenue % regardless of direction and therefore provides the required conventional economic-weight comparison. Direction-aware weighting uses $d_{ef}$. Size weighting uses median historical Relationship Size in U.S. dollars. A weighting system adds information only when it changes the aggregation in an economically interpretable way; a different numerical result is insufficient.

The global comparator is degree centrality,

calculated from the resolved Altsets network containing both quantified and non-quantified directed commercial edges. The network contains 47,742 nodes and 169,939 unique directed pairs in the current pre-return snapshot. Intel has 187 distinct counterparties, including 115 incoming and 82 outgoing links, while Boeing has 173, including 108 incoming and 66 outgoing links. Their normalized degree centralities are 0.003917 and 0.003624. Intel's value is only 8.1% above Boeing's. The experiment therefore compares two focal companies that are relatively close on this global structural measure rather than choosing one highly central and one peripheral node.

Edges

The four relationships were selected because they allow direction, economic intensity, and cross-market timing to interact without expanding the exercise into a broad network regression. Altsets quarterly histories extend across different portions of 2021 through 2026 for these edges. Historical means are used for the two percentage metrics, while the median is used for Relationship Size to reduce the influence of individual scale observations. The three measures answer separate questions. Supplier Revenue % describes supplier-side sales dependence, Customer Cost % describes customer-side purchasing dependence, and Relationship Size describes absolute commercial scale.

The Intel pair illustrates why the three edge metrics cannot be treated as interchangeable. SK hynix accounts for an average 1.525% of supplier revenue on its Intel relationship, almost four times Samsung Electronics' 0.402%, yet Intel's average customer-cost exposure is similar across the two edges at 2.106% and 2.239%. Relationship Size is also comparatively close at median values of approximately $787 million and $896 million. Supplier Revenue weighting therefore concentrates 79.1% of Intel's two-edge weight on SK hynix, while Customer Cost weighting allocates only 48.5% to SK hynix and 51.5% to Samsung. An observed supplier loss propagating into Intel is economically closer to the latter weighting, since the focal variable is Intel's cost exposure.

Boeing creates the opposite direction case. Hyundai Glovis is a supplier to Boeing, so Boeing's relevant focal-side dependence is the 0.216% average Customer Cost share. Korean Air is a customer of Boeing, so the return experiment deliberately reverses the commercial edge and asks whether a poor Korean Air trading day is associated with Boeing's later U.S. return. The appropriate Boeing-side exposure is then the 0.629% Supplier Revenue share. Korean Air's average 35.243% Customer Cost value is economically large, but it measures Korean Air's dependence on Boeing, not Boeing's dependence on Korean Air. Treating that 35.243% as the weight on Boeing's upstream return response would reverse the economic object being estimated.

The company disclosures are consistent with the mechanism underlying that distinction. Boeing describes commercial-aircraft demand as heavily dependent on airlines and states that deterioration in the financial condition of major airline customers can reduce orders, revenues, profitability, cash flow, and backlog. Intel separately describes reliance on third-party foundries and component suppliers and states that supplier capacity constraints, delivery delays, and interruptions can prevent it from completing or supplying products. These filings do not identify the four Altsets percentages used here, but they establish why customer-side revenue dependence and supplier-side cost dependence have different cash-flow channels.

Daily market data cover 46 matched trading sessions from July 22 through September 29, 2026. Korean source-firm closes occur before the corresponding U.S. focal-firm close, giving the same-calendar-day regression a directional timing convention. Historical prices for SK hynix, Samsung Electronics, Hyundai Glovis, Korean Air, Intel, Boeing, and SPY were taken from daily series sourced by StockAnalysis from S&P Global Market Intelligence.

Evidence

The unconditional correlations are modest and do not sort the four relationships into a common transmission pattern. SK hynix and Samsung have raw same-day correlations with Intel of 0.190 and 0.275. Hyundai Glovis and Korean Air have correlations with Boeing of -0.092 and -0.122. After the focal U.S. return is residualized on SPY, ordinary all-day edge betas remain small: 0.137 for SK hynix -> Intel, 0.187 for Samsung -> Intel, -0.138 for Hyundai Glovis -> Boeing, and -0.097 for Korean Air -> Boeing. The tail regression changes the magnitude of every pair and preserves the cross-firm sign split.

The Intel estimates initially fit the local-transmission hypothesis. SK hynix's downside coefficient of 0.566 is roughly four times its all-day coefficient, while Samsung's 0.601 is roughly three times its ordinary coefficient. On source-tail days, Intel's average market-residual return is -2.74% for the SK hynix conditioning set and -3.42% for the Samsung conditioning set. The Samsung coefficient is estimated more precisely than the SK hynix coefficient, although neither 20th-percentile estimate warrants a broad population inference from ten tail observations. The result is economically narrower: within this matched return window, Intel reacts more positively to extreme negative Korean semiconductor returns than its unconditional source-return sensitivity suggests.

Boeing produces evidence against a simple same-direction propagation mechanism. Its tail coefficient is -0.772 when Hyundai Glovis is the source and -0.955 when Korean Air is the source. The corresponding average Boeing market residual on source-tail days is positive, approximately 0.31% for Hyundai Glovis and 0.59% for Korean Air. A commercial relationship therefore identifies economically linked observations without determining the sign of the short-horizon return coefficient. For Korean Air, an airline-specific loss can coexist with a positive Boeing residual for reasons that the edge itself cannot adjudicate. For Hyundai Glovis, the negative sign similarly contradicts a direct same-day supplier-loss transmission prediction. Assigning larger relationship weights to those coefficients would increase the magnitude of the wrong-signed statistic rather than rescue the hypothesis.

The aggregation makes the centrality comparison explicit. The table below reports weighted averages of the 20th-percentile market-residualized edge betas. Supplier Revenue weighting is deliberately applied mechanically in one column, while the direction-aware column switches to Customer Cost % whenever the focal firm is the customer. Relationship Size uses each edge's historical median.

Global degree barely distinguishes the focal firms, while their selected tail coefficients have opposite signs. That is evidence against treating centrality as a sufficient statistic for pair-level downside behavior. Economic weighting, however, adds much less than the contrast between firms might suggest. Intel's binary statistic is 0.583 and its three economically weighted versions lie between 0.573 and 0.584 because the two tail betas themselves are close. Boeing ranges from -0.849 to -0.918. Supplier Revenue %, direction-aware exposure, and Relationship Size alter which edge receives greater influence, but they do not overturn the basic pair-level pattern.

This result separates two claims that are easily conflated. Local commercial weights contain information absent from degree centrality because they identify which side of the contract bears the economic exposure and how large that exposure has been through time. Yet weighting cannot manufacture explanatory power when the underlying pair coefficients are similar, factor-driven, or opposite to the predicted transmission direction. In this sample, the greatest empirical gain comes from estimating conditional edge coefficients rather than from choosing among reasonable economic weighting schemes.

Stress

Industry residualization is the strongest challenge to the Intel result. The focal return model is expanded to include SOXX for Intel and XLI for Boeing alongside SPY. SOXX is an especially demanding control because Intel itself is a constituent; iShares reported Intel at 5.64% of SOXX on August 31, 2026 and above 10% in a later September snapshot. XLI likewise held Boeing at approximately 3.02% on September 9. The resulting residual therefore removes both sector-wide movement and some mechanically embedded focal-company movement.

The Intel result changes sharply. The target regression $R^2$ rises from 0.371 under SPY alone to 0.790 when SOXX is included. SK hynix's downside coefficient changes from 0.566 to -0.126, while Samsung's changes from 0.601 to 0.118. The direction-aware weighted aggregate moves from 0.584 to approximately zero at -0.0003. The equal-weight aggregate similarly moves from 0.583 to -0.004. Supplier Revenue weighting produces -0.075 because that scheme concentrates weight on SK hynix, whose sector-adjusted coefficient becomes negative. Relationship Size weighting leaves only 0.004. The apparent Intel edge-tail relation is therefore largely absorbed by the semiconductor factor in this short window.

That failure test changes the interpretation of the economic weights. SK hynix and Samsung are both meaningful commercial counterparties to Intel in the Altsets history, and Intel's 2025 filing separately describes exposure to third-party supplier interruptions and capacity constraints. Yet the positive same-day tail coefficients in the broad-market model cannot be assigned confidently to those contracts when a semiconductor-sector return removes almost all of the effect. The commercial edge helps locate a plausible transmission channel. Factor residualization determines whether the return evidence distinguishes that channel from a common industry state. This empirical distinction is consistent with Levi and Welch's warning that apparent downside-beta information can be subsumed by conventional factor exposure.

Boeing behaves differently under the same stress. Adding XLI moves the Hyundai Glovis tail coefficient only slightly, from -0.772 to -0.781, and the Korean Air coefficient from -0.955 to -1.026. The direction-aware Boeing aggregate becomes -0.964 rather than -0.908. Broad industrial exposure therefore does not account for the negative sign pattern in the same way that SOXX accounts for Intel's positive coefficients. The evidence still fails the direct positive-transmission hypothesis, and the model is intentionally agnostic about which omitted news variable generates the inverse relation.

The tail cutoff gives a second test of whether the estimates are artifacts of one arbitrary quantile. SK hynix's residual tail beta is 0.157 at the 15th percentile, 0.566 at the 20th, 0.522 at the 25th, and 0.442 at the 30th. Samsung remains positive across the same sequence at 0.516, 0.601, 0.589, and 0.661. Hyundai Glovis remains negative from -0.543 to -0.772 across the four thresholds. Korean Air likewise remains negative, ranging from -0.784 to -1.093. The broad sign structure therefore survives moderate changes in the definition of a severe source return, although SK hynix weakens in the most extreme seven-day subset.

Deleting the single worst source-return day supplies a more direct concentration test. SK hynix remains positive at 0.463 and Samsung at 0.683. Hyundai Glovis becomes more negative at -1.143. Korean Air is the exception: its coefficient collapses from -0.955 to -0.081 after its worst source day is removed. The Korean Air estimate therefore carries much less evidence of a persistent inverse relationship than the Hyundai Glovis estimate. A tail statistic that simply multiplied Korean Air's coefficient by its very large 35.243% customer-cost share would have magnified precisely the observation least appropriate for measuring Boeing's own economic dependence. Direction and stability are doing substantive work that raw relationship magnitude cannot replace.

Conclusion

The four-edge experiment is inconsistent with global network degree serving as a sufficient description of downside dependence. Intel and Boeing occupy similar positions in the Altsets network, with degree centralities of 0.003917 and 0.003624, yet the selected Korean-source tail coefficients differ in sign and magnitude. The distinction remains hidden if the network is reduced to node prominence. Pair-level conditioning therefore adds information about where tail comovement is occurring.

The stronger proposition that economically dominant edges explain that tail dependence receives less support. Supplier Revenue %, direction-aware dependence, and Relationship Size generate only modest changes relative to binary weighting within the selected pairs. Intel's initial positive edge-weighted tail beta is also mostly eliminated by a semiconductor-sector control. The local edge variables describe economic exposure correctly, but common industry states can still dominate the return covariance attached to those edges. Boeing supplies the complementary failure case: its negative coefficients persist after industrial-sector residualization, contradicting a simple positive propagation interpretation despite documented commercial links.

The quantitative object that survives these tests is therefore a factor-purged, direction-aware edge tail coefficient rather than centrality or relationship weight by itself. Centrality describes structural reach. Supplier Revenue % and Customer Cost % describe which side of a contract bears economic dependence. Relationship Size describes scale. The downside beta describes realized conditional market comovement. Those quantities answer different questions, and collapsing them into one undifferentiated network score loses the distinction the experiment exposes.

For empirical work on commercial-network tail risk, the useful sequence is to identify the directed edge, select the dependency metric from the focal firm's economic side, estimate the adverse-state return coefficient after conventional factor removal, and only then aggregate across counterparties. Under that construction, a large commercial edge with a near-zero factor-purged tail coefficient contributes little to measured return transmission. A globally central firm can still have a high local tail statistic if a few economically important edges carry positive residual coefficients. A negative or unstable coefficient remains negative or unstable regardless of the contractual weight assigned to it.

The small panel examined here produces a result narrower than a network-wide asset-pricing anomaly, but more discriminating than the proposition that connected companies become more correlated in bad markets. Global structure fails to characterize the selected pair behavior. Raw economic weighting fails to separate commercial transmission from common sector exposure. Direction-aware, factor-purged tail estimation distinguishes those cases and supplies a falsifiable object for broader cross-sectional testing.

References

Altsets supply chain dataset.

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