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The Time-Varying Risk of Macroeconomic Disasters∗

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The Time-Varying Risk of Macroeconomic Disasters∗ The Time-Varying Risk of Macroeconomic Disasters∗ Roberto Marf`ey Julien P´enassez This draft: November 18, 2018 Abstract The rare disasters model relates the equity premium to the probability of a large decline in consumption. A critical prediction of the model is that future macroeconomic disasters are forecastable. This paper tests this prediction and estimates the probability of a disaster using a dataset of 42 countries over more than a century. We find that disasters are indeed forecastable by a wide array of variables. The most robust predictor of future disasters is the dividend-price ratio, in line with theory. Our probability estimate strongly correlates with the dividend-price ratio and forecasts stock returns. A variable disaster model, calibrated from macroeconomic data alone, further confirms the link between disaster risk and the equity premium. JEL: E44, G12, G17 Keywords: rare disasters, equity premium, return predictability ∗We thank Daniel Andrei, Patrick Augustin, Jules van Binsbergen, Pierre Collin-Dufresne, George Constan- tinides, Max Croce, Magnus Dahlquist, Leland Farmer, Xavier Gabaix, Anisha Ghosh, Eric Ghysels, Fran¸cois Gourio, Daniel Greenwald, Robin Greenwood, Benjamin Holcblat, Hendrik H¨ulsbusch, Christian Julliard, Leonid Kogan, Peter Kondor, Christos Koulovatianos, Hening Liu, Andr´eLucas, Sydney Ludvingson, Rajnish Mehra, Christoph Meinerding, Alan Moreira, Tyler Muir, Urszula Szczerbowicz, Adrien Verdelhan, Tan Wang, and Michael Weber for helpful comments. We also benefitted from helpful comments by conference and seminar participants at the Columbia University Macro Lunch, U. of Luxembourg, U. of Chile, Fundao Getlio Vargas (Rio), McGill University, and conference participants at the CEPR ESSFM Gerzensee 2017 meeting, SAFE Asset Pricing Workshop 2017, NFA 2017, Paris December 2017 Finance Meeting, and the MFA 2018. We thank Robert Barro, Jos´eUrs´ua,Asaf Manela, and Alan Moreira for making their data publicly available. yCollegio Carlo Alberto, Via Real Collegio, 30, 10024 Moncalieri (Torino), Italy; +39 (011) 670-5229; [email protected], http://robertomarfe.altervista.org zUniversity of Luxembourg, 4 rue Albert Borschette, 1246 Luxembourg, Luxembourg; +352 466644 5824; [email protected], http://jpenasse.wordpress.com Many puzzles in finance arise from the inability of models to reconcile, quantitatively, asset returns and macroeconomic risks. A classic example is the equity premium puzzle: average stock returns are far too high to be explained by the observed risk in consumption (Mehra and Prescott, 1985). Another well-known example is that stock returns can be predicted by valuation ratios such as the dividend-price ratio (Campbell and Shiller 1988b). Likewise, stock market volatility is too high to reflect forecasts of future dividends (Shiller, 1981). These puzzles might be resolved if one assumes that financial markets compensate for the risk of infrequent but severe macroeconomic disasters. Barro(2006) uses international data from the last 100 years to document several episodes of large declines in consumption growth. These macroeconomic disasters occur with an annual frequency of about 3% and are strong enough to generate a sizable equity premium, as hypothesized by Rietz(1988). A first generation of models assumes that disasters arise with a constant probability (see e.g., Barro 2009; Barro and Jin 2011; Nakamura et al. 2013). The next generation of papers shows that allowing the risk of disaster to vary over time generates excess volatility and predictability (Gabaix, 2012; Gourio, 2012; Wachter, 2013) and also solves puzzles related to the markets for bonds, options, and currencies (Gabaix, 2012; Gourio, 2013; Farhi and Gabaix, 2016; Hasler and Marfe, 2016).1 Variable disasters also offer the possibility of connecting macroeconomic aggregates with asset prices in production economies (Gabaix, 2011; Gourio, 2012; Kilic and Wachter, 2015; Isor´eand Szczerbowicz, 2016). This paper estimates the time-varying probability of a macroeconomic disaster. Our ap- proach follows closely the seminal work of Barro(2006), who finds that the average number of disasters across countries and across time in the past century|in other words, the uncondi- tional probability of a macroeconomic disaster|is high enough to rationalize the unconditional equity premium. We go one step further and propose a simple way to estimate the time-varying probability of a macroeconomic disaster. We document that the conditional probability of a disaster varies over time and is strongly correlated with the conditional equity premium. This step is critical for assessing how well disaster risk can rationalize why asset prices are volatile and why valuation ratios forecast future returns. Formally, we propose a regression-based approach to infer the probability of a macroeco- nomic disaster over the next year. A sufficient condition for disaster risk to vary over time is to find that rare disasters are forecastable. We thus set up a predictive panel in which the left-hand side variable is an indicator equal to one when a given country i experiences a disaster 1Another strand of research maintains a constant probability of disasters but assumes that the representative agent learns about the model parameters or states (Weitzman 2007, Koulovatianos and Wieland 2011, Du and Elkamhi 2012, Lu and Siemer 2016, Johannes et al. 2016). There is also a burgeoning literature on the implication of disagreements about the likelihood of rare disasters (see, e.g. Chen et al. 2012; Piatti 2015). 1 in t+1, and zero otherwise. In our baseline specification, a disaster is defined as a two standard deviation drop in consumption growth in a given year. On the right-hand side, we consider a wide range of time-t macroeconomic, political, and financial variables, such as consumption growth, various crisis indicators, and asset prices. The fitted values in this regression gives us π^i;t, the time-t probability of a disaster in country i at time t + 1. We find that macroeconomic crises are forecastable, which indicates that disaster risk varies over time. Among our range of right-hand side variables, dividend-price ratios on broad stock indices emerge as robust predictors of future disasters. This is particularly interesting because the DP ratio is a reasonable proxy for the conditional equity premium (Blanchard, 1993; van Binsbergen and Koijen, 2010). To get a sense of magnitudes, a 10% increase in the S&P 500 dividend-price ratio raises the likelihood of a crisis from an unconditional probability of 3.1 percent to 18.3 percent. This is precisely what one would expect if investors where shunning stocks when disaster risk is high. In other words, we find a strong relation between the global equity premium and the likelihood of a crisis, as predicted by rare-disaster models. Interestingly, variation in disaster risk mostly comes from its global component, which we noteπ ^t and define as the average of country-estimatesπ ^i;t. This global component captures 62% of the variation of individual country probabilities. Figure1 shows ^πt and the S&P 500 dividend-price ratio, our main proxy for the world equity premium. Disaster risk typically varies between 0% and 5%, with sharper increases during each of the two world wars, the Great Depression, and the Korean War. Consistently with the evidence that the dividend-price ratio forecasts individual disasters, we observe a tight connection betweenπ ^t and the DP ratio, our proxy for the global equity premium (correlation of 0:66). Both series spike during the Great Depression and the two world wars, yet also around less prominent events such as the 1907 Knickerbocker Crisis and the 1936{1939 Spanish Civil War. In the postwar period, both are relatively low during the sixties, then surge after the first oil crisis of 1973 and remain high thereafter, before declining again during the \Great Moderation" period. Finally, disaster risk and the equity premium rise during the 2008-2009 financial crisis, both in modest proportion in comparison to pre-WW2 crises. When constructingπ ^, we exploit the fact that the DP ratio forecasts future disasters, so that part of this correlation is of course mechanical. (One can actually achieve a 100% correlation betweenπ ^ and the DP ratio, by excluding all predicting variables except the DP ratio.) Yet, in fact, we obtain a quite similar π-estimate when we exclude the DP ratio from our panel regression (the correlation is then 0.44). Of course, forecasting power declines substantially when we do so, which is consistent with the idea that equity prices contain incremental information. 2 We next extend our methodology to calibrate a variable disaster model in the spirit of Wachter(2013). Namely, we consider a discrete-time economy, populated by a representative agent with recursive preferences, in which asset prices are derived from the dynamics of aggregate consumption. Consumption growth is subject to rare disasters, which occur with a time-varying probability. The model is of exponential affine type so it can be solved with standard techniques and yields simple, closed-form solutions. We use this model as a laboratory to assess both the qualitative and quantitative effects of our measure of time-varying disaster probability|that is, our only state variable. We emphasize that our calibration does not rely on asset price data. Consumption dynamics parameters can be estimated using our international panel of disasters. To do so, we treat the global disaster probability as a latent variable. The econometrician observes the number of disasters occurring over a given year t + 1, which is a noisy signal of the true time-t disaster probability. While assuming that this probability follows an exogenously specified time-series process, we infer the time-varying probability via a (non-Gaussian) Kalman filter. Although we only use macroeconomic data to calibrate our model, we find that it can gen- erate a large and volatile equity premium|along with a low risk-free rate|under conservative preferences. We find that time-varying disaster risk is crucial in generating a quantitatively large and volatile equity premium as well as volatile returns.
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