Long-Run Risk is the Worst-Case Scenario
2014-16 | With Dew-Becker | December 2014
We study an investor who is unsure of the dynamics of the economy. Not only are parameters unknown, but the investor does not even know what order model to estimate. She estimates her consumption process non-parametrically and prices assets using a pessimistic model that minimizes lifetime utility subject to a constraint on statistical plausibility. The equilibrium is exactly solvable and we show that the pricing model always includes long-run risks. With a single free parameter determining risk preferences, the model generates high and volatile risk premia, excess volatility in stock returns, return predictability, interest rates that are uncorrelated with expected consumption growth, and investor expectations that are consistent with survey evidence. Risk aversion is equal to 4.8, there is no stochastic volatility or disasters, and the pricing model is statistically nearly indistinguishable from the true data-generating process. The analysis yields a general characterization of behavior under a very broad form of model uncertainty.
2013-29 | September 2013
What determines the frequency domain properties of a stochastic process? How much risk comes from high frequencies, business cycle frequencies or low frequency swings? If these properties are under the influence of an agent, who is compensated by a principal according to the distribution of risk across frequencies, then the nature of this contracting problem will affect the spectral properties of the endogenous outcome. We imagine two thought experiments: in the first, the principal (or `regulator’) is myopic with regard to certain frequencies – he is characterized by a filter – and the agent (`bank’) chooses to hide risk by shifting power from frequencies to which the regulator is attuned to those to which he is not. Thus, the regulator is fooled into thinking there has been an overall reduction in risk when, in fact, there has simply been a frequency shift. In the second thought experiment, the regulator is not myopic, but simply cares more about risk from certain frequencies, perhaps due to the preferences of the constituents he represents or because certain types of market incompleteness make certain frequencies of risk more damaging. We model this intuition by positing a filter design problem for the agent and also by a particular type of portfolio selection problem, in which the agent chooses among investment projects with different spectral properties. We discuss implications of these models for macroprudential policy and regulatory arbitrage.
Doubts and Variability: A Robust Perspective on Exotic Consumption Series
2013-28 | With Smith | September 2013
In order for consumption based asset pricing models to reconcile data on returns with that on consumption, researchers have resorted to augmenting the consumption series in exotic ways. When an agent’s consumption series is subject to changes in volatility, we show that concerns for model misspecification can induce fears of both disasters and long run risk. We appeal to this pessimistic view to explain why introducing stochastic volatility in the presence of model uncertainty helps generate a more plausible unconditional market price of risk and time variation in the conditional market price of risk. Our analysis is based on a parameterization derived from Bayesian estimation of our stochastic volatility model using US consumption data.
Robust Stress Testing
| With McKenna | September 2013
In recent years, stress testing has become an important component of financial and macroprudential regulation. Despite the general consensus that such testing has been useful along certain dimensions, the techniques of stress testing are still being honed. This partly reflects certain concerns that have been raised over the nature of the stress test scenarios as currently applied. In response to these concerns we propose to use the methods of Robust Control analysis to identify and construct adverse scenarios that are naturally interpretable as stress tests. These scenarios emerge from a particular pessimistic twist to a benchmark forecasting model that posits (1) a law of motion for a state and (2) the dependence of bank `performance’ on this state. This pessimistic twist is often referred to as a `worst case distribution’. We will use this distribution to generate candidate scenarios and simulations for stress tests.
Manuscript | With Smith | May 2012
We examine the problem of an agent who faces income risk and who insures himself by accumulating holdings of a riskless bond, subject to a no-borrowing constraint. The problem is novel since the agent is concerned that his benchmark model is misspecified. We use robust control analysis to model this concern. We consider two benchmark models of income risk – a simple one-shock case and a two-shock case. We characterize the ‘worst case’ models entertained by the agent and examine how their properties inform his actions. We show that the agent’s fears can be represented by processes featuring an adverse shift in the distribution of his income. In the two shock case the worst case model exhibits positive correlations between the income components – even though no such correlation exists under the benchmark. Overall the agent fears a world in which he is driven to low levels of wealth more rapidly than in his benchmark model. This enhances his desire to accumulate wealth, from a precautionary motive. Importantly, the distortions to the conditional distributions of innovations are more pronounced when the agent’s wealth level is low. Thus the pessimism of the robust agent is state dependent. This opens an interesting avenue to feedbacks between the agent’s pessimism and the decisions that are, in turn, influenced by this pessimism. Although this paper currently only deals with the partial equilibrium process of an individual agent, it hints at a promising approach to endogenizing disagreement in heterogeneous agent models and raises issues regarding how econometricians should identify orthogonal latent risk factors based on the behavior of robust households.
Robust Animal Spirits
Journal of Monetary Economics 59(8), December 2012, 738-750 | With Smith
In a real business cycle model, an agent’s fear of model misspecification interacts with stochastic volatility to induce time varying worst case scenarios. These time varying worst case scenarios capture a notion of animal spirits where the probability distributions used to evaluate decision rules and price assets do not necessarily reflect the fundamental characteristics of the economy. Households entertain a pessimistic view of the world and their pessimism varies with the overall level of volatility in the economy, implying an amplification of the effects of volatility shocks. By using perturbation methods and Monte Carlo techniques we extend the class of models analyzed with robust control methods to include the sort of nonlinear production-based DSGE models that are popular in academic research and policymaking practice.