A Speculative Asset Pricing Model of Financial Instability∗

I develop a dynamic equilibrium model that incorporates incorrect beliefs about crash risk and use it to explain the available empirical evidence on financial booms and busts. In the model, if a long period of time goes by without a crash, some investors’ perceived crash risk falls below the true crash risk, inducing them to take on excessive leverage. Following a drop in fundamentals, these investors de-lever substantially, both because of their high pre-crash leverage and because they now believe future crashes to be more likely. Together, these two channels generate a crash in the risky asset price that is much larger than the drop in fundamentals. The lower perceived crash risk after years with no crashes also means that the average excess return on the risky asset is low at precisely the moment when any crash that occurs would be especially large in size; moreover, it means that, in the event of a crash, some investors may default and banks may sustain large unexpected losses. Finally, the model shows how pre-crash warning signs can generate financial fragility. By reducing investors’ optimism, warning signs also increase investors’ uncertainty about their beliefs and thereby make them more likely to overreact to future bad news. ∗I am indebted to Nicholas Barberis and Jonathan Ingersoll for guidance and encouragement. I also thank George Constantinides, Cary Frydman, Robin Greenwood, Gary Gorton, Peter Kelly, Alan Moreira, Tyler Muir, Gordon Phillips, Sergio Rebelo, Andrei Shleifer, Wei Xiong, and seminar participants at Caltech, Chicago Booth, MSU, Northwestern Kellogg, Notre Dame, OSU Fisher, Princeton, Texas A&M, USC Marshall, WUSTL Olin, and Yale University for their helpful comments. †Yale School of Management, [email protected]. A central topic of study in economics is financial instability—crashes in financial markets, bank losses and failures, as well as the economic downturns that often accompany these events. One of the most striking findings to emerge from recent research on these issues is the close link between debt accumulation and subsequent instability. In a comprehensive analysis of financial crises over the past eight centuries across 66 countries, Reinhart and Rogoff (2009) show that debt accumulation during an economic boom often induces greater systemic risks than is initially apparent, and can be followed by a severe financial crash. Similarly, Mian and Sufi (2010, 2011, 2014) document a sharp rise in household leverage during the years before the Great Recession; Glick and Lansing (2010) and Jorda, Schularick, and Taylor (2011) demonstrate a close relation between the build-up of credit expansion and the severity of subsequent recessions; and Baron and Xiong (2014) find that bank credit expansion predicts a higher probability of a subsequent equity crash. What is the origin of this debt-linked financial instability? A growing strand of empirical work highlights the importance of incorrect beliefs about crash risk: Coval, Jurek, and Stafford (2009) show that investors underestimated the probability and the correlations of mortgage defaults during the most recent credit boom; Foote, Gerardi, and Willen (2012) suggest that both investors and banks underestimate the likelihood of a potential crash event during economic booms; Coval, Pan, and Stafford (2014) find that suppliers of downside economic insurance products underestimate crash risk before a crash occurs; and Baron and Xiong (2014) discover that, although crash risk is significantly higher following bank credit expansions, the equity excess returns are nevertheless lower, even in the absence of crashes. Although these empirical findings all suggest that incorrect beliefs about crash risk may play a role in generating credit booms, asset bubbles, and price crashes, a formal dynamic theory that captures this narrative has yet to be developed. In this paper, I develop a continuous-time equilibrium model that studies the impact of incorrect beliefs about crash risk on asset prices, portfolio decisions, and bank losses. There are two assets in the infinite-horizon economy: a risk-free asset with a fixed return; and a risky asset which is a claim to a stream of dividends that are subject to occasional crashes in fundamentals governed by a Poisson process with a constant likelihood (I use “likelihood” and “intensity” interchangeably hereafter). There are three types of agents: speculators, long-term investors, and banks. Both speculators and long-term investors trade in the asset markets. Banks, on the other hand, provide collateralized funding to speculators when these speculators want to take a levered position in the risky asset. Long-term investors exhibit a downward-sloping demand for the risky asset; their presence allows speculators to sell their risky asset holdings when they become too pessimistic. Speculators—and their belief structure—are a primary focus of the paper. While the true crash intensity is constant, speculators have incorrect views about it—they believe that the crash intensity switches between a high-intensity state and a low-intensity state. This is the only difference between the speculators in my model and the agents in a model with full information; the speculators make proper Bayesian updates to their beliefs based on the observed crashes and are otherwise fully rational in their optimizations. Importantly, this one deviation drives many of the model implications.