Theory to Practice

Valuation of firms in a supply chain

The context

A cornerstone of macrofinance literature is the diversification argument advanced by Lucas, which holds that when a portfolio is properly diversified, the impact of firm-specific distress shocks is extremely limited. It follows, then, that rational investors generally consider firm-specific risk premia as negligible. This contention is a key component of the Consumption Capital Asset Pricing Model (CCAPM), and many macrodynamic stochastic general equilibrium models (macro-DSGE) that center on economies with a representative firm. 


In our article, we reconsider this argument in the context of an economy made up of a network of firms which share production and financial relationships. This means that financial distress, when it happens, propagates throughout the entire network, triggering a process of economic contagion. We go further to quantify the impact of this contagion on the prices of financial assets associated with the firms in question and relative risk premia. Specifically, we demonstrate that this impact is not negligible, when taken at an aggregate level, depending on the global properties of the network and how the effects deriving from firm-specific distress ripple through supply chains. 


Let’s take three specific streams in the literature. The first studies credit risk pricing when defaults generate contagion effects via reduced-form models. The second refers to macroeconomic studies on firm-specific and/or sector-specific shocks that can trigger aggregate fluctuations in production, trade, and banking networks. The third and final stream relates to the overall equilibrium in production sectors with multiple firms. 


In our article, we study the price dynamic by considering the impact of firm-specific financial distress on companies in a network; we use a model similar to one used to predict the spread of an epidemic. We show that there are two classes of dynamics. 


  • In the first, collaboration between firms is limited and the impact of firm-specific shocks on portfolios can be diversified, which means that valuations of the representative agent are not affected. In such cases, we can apply the standard form of the Lucas model.   
  • In the second, firms are so closely integrated that distress in one generates a cascade effect along the entire supply chain. This means that such shocks are not diversifiable. The chain reaction that is triggered (or financial pandemic) requires the introduction of a new risk premium component. This component, which we call network distress risk, cannot be explained by traditional systematic factors. 


In our study, we derive closed solutions for asset prices as a function of the properties of networks formed by firms, and discuss these properties. From an empirical standpoint, we find evidence of a network distress risk premium that is statistically and economically significant, following a structural break in the economy. This we mark at 1984 for the North American firms included in a CRSP-Compustat panel.

The research

In this study, we propose an innovative approach to reduce the dimensionality of the problem by capturing the salient characteristics of the network. This approach is based on a reduced-form representation of the network which we developed by building two characteristic measures of the role that a given firm plays within a supply chain: its vulnerability and its systemicness. 


We consider a firm vulnerable if its performance depends to a large extent on the performance of other firms in its network. A firm is systemic, instead, if its performance has a substantial impact on the performance of other firms. By introducing these two parameters, which we can easily determine by looking at the properties of the firm and the supply chain, we can derive closed-form solutions both for the “tipping point” (the threshold separating supercritical from subcritical dynamics due to the intensity of the contagion), and the long-term likelihood that the firm could be contaminated by the financial distress propagating throughout the network. 


To verify the validity of the theoretical conclusions, we empirically tested our model using data from a panel of CRSP-Compustat firms covering the period 1970-2019. We next matched this panel with input-output accounts data available at the sector level published by the US Bureau of Economic Analysis (BEA). We then used the sequence of input-output matrices to obtain a singular value decomposition, which allowed us to estimate firm-specific systemicness and vulnerability at a sectoral level, and to construct a temporal index of network distress. 


We find a structural break in distress propagation in June of 1984. This finding aligns with a transition from a subcritical to a supercritical state. Moreover, this change can be linked to a modification in corporate crisis management following a change in US bankruptcy law. As predicted by the model, the risk premium associated with systemic contagion before this transition is zero, and subsequently turns positive and significant. 


In a state of supercritical equilibrium, shocks related to the distress of apparently diversifiable firms generate cascade effects that reverberate through the chain, creating aggregate fluctuations. In such states, these effects are long-term, leading investors to demand compensation ex-ante. This in turn gives rise to a second distinct source of risk premia (i.e. network distress risk).  


The basis for our empirical tests were measures of vulnerability and systemicness which we estimated at a sector level. Our results confirm the model’s predictions and allow us to discern a connection between the valuation of securities corresponding to network firms, and economic variables that we can glean from the financial statements of firms in the CRSP-Compustat panel.  

Conclusions and takeaways

This analysis opens up a number of new directions for future research. First, our model offers valuable insight for a clearer understanding of the relationship that links idiosyncratic return volatility on individual securities to risk premia. Further, this model can potentially be useful in rationalizing the perplexing inverse relationship that we have demonstrated between idiosyncratic risk and risk premia.  


Finally, a research stream we are currently exploring consists in applying this model to analyze systemic risk for financial institutions. In this case, directly impacting market expectations are the price expectations of financial institutions and illiquidity. The result may be instability as well as feedback effects that engender multiple equilibria arising from self-fulling prophesies.