The notion of an economy as a network of more or less tightly linked units has recently become popular in the finance and economics literature, especially in the aftermath of the financial and economic crisis. In this project we analyze the implications of different network structures for equilibrium asset prices and returns. One special aspect that we focus on is the fact that links in a network can have a direction, i.e., that it can make a difference if the link is from node i to node j or the other way around.
A simple example for such a directed link is a customer-supplier relationship between two firms. Shocks to the profitability of a large customer will certainly have a negative impact on the small supplier and, among other things, increase its default risk, while a shock to the small supplier is much less likely to have significant consequences for the large customer. Another important aspect of this kind of shock propagation is that it has a time dimension and does not happen in one single instant. In the above example the riskiness of the supplier increases, implying a higher likelihood of negative shocks in the future, and this in turn might negatively affect other firms linked to the supplier.
These two features, i.e. the fact that shock propagation can have a direction and that the spreading of shocks through the system takes time, cannot be captured by a pure diffusion/correlation framework (due to its inherent symmetry) or by contemporaneous jumps. We therefore propose a model featuring multiple economic units ('firms') whose dividends are linked via self-exciting and mutually exciting jump processes. With such processes, a downward jump in the cash flow of one firm then increases the probability of subsequent negative shocks to its own cash flow as well as to those of other firms. The direction and magnitude of this shock propagation characterizes the network structure of our economy, which thus manifests itself only indirectly via the dynamics of jump risks as state variables, but not directly in the level of cash flows. Aggregate consumption, a key quantity in any equilibrium model, is driven by the sum of all the individual jumps, but a given jump always affects the cash flows of only one firm at a time. Our model is general and flexible in the sense that it can represent arbitrary network structures. Nevertheless, it still remains tractable with at least semi-closed form expressions for all equilibrium quantities, since it belongs to the exponentially affine class, for which there is a well-developed solution theory. The representative agent in our model has recursive preferences of the Epstein-Zin type. These preferences are a key ingredient, since they generate premia for the risk of higher future jump intensities of the dividends. The representative agent's preference for early resolution of uncertainty, i.e., the fact that she cares about the risk associated with future values of the state variables, implies that the price-dividend ratios of all assets will react to a jump in one individual dividend, and it is the structure of the network which determines the direction and the magnitude of this reaction.
Our results so far indicate that the directedness and the timing of shocks have first-order implications for key asset pricing quantities like valuation ratios, expected returns, and return volatilities. Taking these features into account can lead to a substantially different interpretation of empirical findings, e.g., concerning a flight-to-quality effect. The model generates the positive centrality premium documented empirically in Ahern (2013) and we show that this premium is distinctly different from a standard CAPM-like premium for market risk.
A first working paper draft was completed in November 2014 and is currently being revised. The results show that the model has very rich economic implications and can serve as a theoretical foundation for a number of papers dealing with the impact of network structures on asset prices. The next step will be to submit the paper to a top journal. Because the model involves an arbitrary number of assets, an empirical investigation of the cross-sectional predictions of the model also seems worthwhile in the future.
|Nicole Branger, Patrick Konermann, Christoph Meinerding, Christian Schlag||Equilibrium Asset Pricing in Directed Networks|
forthcoming in Review of Finance
|2020||Financial Markets||Dynamic Networks, Mutually Exciting Processes, Asset Pricing, General Equilibrium, Recursive Preferences|