Jose A. Scheinkman, Princeton University Proposal 0718407
Many fundamental questions concerning economic welfare require assessing how economic agents trade off risk and return. Examples of such questions are "What are the costs to society of the economic fluctuations observed in business cycles?", "how much do financial markets contribute to economic wellbeing?" and "what is the role of financial markets in economic development?".
A central function of financial markets is to provide risk-sharing. Economic theory predicts that asset prices reflect how individuals value macroeconomic risks. When individuals are risk-averse an asset with cash flows that exhibit a larger risk exposure to aggregate risk will have a lower price to guarantee a higher expected return - that is asset prices display a risk-return trade off that reflects agents' attitude toward risks. For this reason, and because they are easily available, asset prices are the single most important source of information on how agents value risks.
In financial economics risk-return tradeoffs typically show how expected rates of return over small intervals are altered as we change the exposure to the underlying shocks that impinge on the economy. An alternative notion of risk-return focuses on what happens as the length of time between valuation and cash flows becomes large. This project investigates the long run risk-return relationship in financial markets.
Usually, an equilibrium valuation model in continuous time gives the prices of the instantaneous exposure of payoffs to certain risks. Values over different horizons can, in principle, be inferred by integrating these local prices. However, these computations are difficult when there are nonlinearities in the evolution of state variables or in the cash flows that are being evaluated. For this reason the project adopts an alternative approach based on an operator formulation of asset prices in a Markov environment. This alternative approach associates to stochastic processes that satisfy a "multiplicative property" a positive eigenvalue, a martingale, and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long run approximation, and the eigenfunction gives the long run dependence on the Markov state. A long run risk-return tradeoff is obtained by mapping the long run risk characteristics of cash flows into the corresponding eigenvalues and eigenfunctions.
One reason to be interested in long-run implications of asset pricing is that frictions that are ignored in many traditional models, such as inertia in decision making for example, make it unlikely that the high frequency implications of frictionless and fully rational economic models will be confirmed by the data. One possibility is that the implications of these models are more plausible for longer horizons, when some of these frictions play a smaller role. Motivated by this hypothesis the project uses asset prices to estimate models that combine a reference "fundamental" model with a perturbation with an importance that diminishes at longer horizons.
