https://doi.org/10.71734/DP‑2026‑37

Fundamental economic linkages between firms or industries are empirically associated with time lags and predictive relations between the respective equity returns. New theoretical research suggests this does not have to be a sign of market failure, but can be a natural consequence of how risk is priced in network economies.

A pervasive pattern in financial markets

The return of one asset can predict the return of another, economically linked asset in the following period. This phenomenon, known as cross-predictability, is a very robust pattern in finance, documented across industries, countries, and asset classes over multiple decades. Most explanations attribute it to market frictions: slow information diffusion, investor inattention, or limits to arbitrage. This paper offers a complementary perspective grounded in equilibrium asset pricing theory. The authors show that cross-predictability can arise in a fully efficient, frictionless market as a natural consequence of directed cash flow linkages. The paper derives precise conditions under which this mechanism operates and points to directions for future empirical work.

The mechanism: directed linkages and equilibrium asset pricing

The key insight is that economic linkages are typically directed. A shock to one firm, sector, or country often raises the probability of subsequent shocks to connected firms, sectors or countries, but not necessarily the other way around. Think of a supplier whose difficulties raise the risk of production disruptions for its customers downstream.

Equilibrium asset pricing theory suggests that this directional structure should already be reflected in risk premia today, even if shocks never materialize in sample. The asset that can spread shocks to others earns a higher risk premium because its cash flows are more systematic. The asset on the receiving end earns an extra premium because it faces a higher risk of cash flow shocks overall. The paper shows that these two channels are tied to the same parameter: the strength of the cash flow linkage. As a result, in this example, the return differential between supplier assets today should predict the return differential between their linked customer assets in the future. The theory thus suggests that cross-predictability is not a puzzle to be explained away. It is the equilibrium signature of directed cash flow linkages in network economies.

Two conditions are sufficient

The theoretical result rests on two conditions. First, cash flow linkages must have a direction. Importantly, though, cross-predictability arises irrespective of whether shocks propagate from supplier to customer assets, the other way around, or in both directions. Second, there must be cross-sectional differences in the strengths of these linkages. As long as some linkages are stronger than others, return differentials today will be informative about future return differentials of linked assets. These are mild conditions, plausibly satisfied in most real-world networks.

The mechanism is general and applies widely

The mechanism identified in this paper is general, applying wherever directed cash flow linkages exist. In global production networks, shocks to commodity exporters raise disruption risks for manufacturing firms in importing countries. In energy markets, stress among producers propagates to energy-intensive industries. In banking systems, difficulties at interconnected institutions raise tail risk for other banks. In the context of climate transition, repricing of carbon-intensive firms creates downstream risks for sectors that rely on them as input suppliers. In fiscal networks within currency unions, sovereign stress can propagate across member states. In all these settings, directed linkages generate predictable patterns in relative risk premia which can be visible in return data even when no shocks ever materialize.

What this means for understanding cross-predictability

For central banks and institutions that monitor financial markets, the paper offers an analytical lens for interpreting return patterns in network economies. Cross-predictability strategies need not reflect informational inefficiencies: they may reflect equilibrium compensation for network risk.

A rich body of empirical work documents cross-predictability across many settings, also in recent samples: along customer-supplier relations, across industries linked by input-output relations, based on technological similarity, within peer groups, and in cross-stock momentum strategies. The equilibrium mechanism in this paper is supported by studies which show that fundamental linkages lead to delayed propagation of cash flow shocks.

Cross-predictability has been studied for decades, and many explanations exist. The theoretical argument put forward here does not seek to replace them, but to add one that has so far been missing: a risk-based equilibrium channel rooted in the directed network structure of the real economy. Even in a world of fully rational, fully informed investors in complete markets, directed cash flow linkages suffice to generate the return patterns empiricists have documented. The paper thereby offers guidance for empirical researchers working on cross-predictability. It proves that directed cash flow linkages leave a systematic imprint on risk premia, with their strength serving as a natural control variable in empirical work.

Konermann, P., C. Meinerding (2026), Cross-predictability of returns: An equilibrium perspective, Bundesbank Discussion Paper, No 37/2026.