Rare Disasters Research Articles

Rare Disasters and Risk Sharing with Heterogeneous Beliefs

Risks of rare economic disasters can have a large impact on asset prices. At the same time, difficulties in inference regarding both the likelihood and severity of disasters, as well as agency problems, can lead to significant disagreements among investors about disaster risk. We show that such disagreements generate strong risk-sharing motives, such that just a small number of optimists in the economy will significantly reduce the disaster risk premium. Our model highlights the latent nature of disaster risk. The disaster risk premium will likely be low and smooth during normal times but increases dramatically when the risk-sharing capacity of the optimists is reduced, e.g., following a disaster. The model also helps reconcile the difference in the amount of disaster risk implied by financial markets and international macroeconomic data, and provides caution to the approach of extracting disaster probabilities from asset prices, which will disproportionately reflect the beliefs of a small group of optimists. Finally, our model predicts an inverse U-shaped relation between the equity premium and the size of the disaster insurance market. The Author 2012. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Rare Macro Disasters in Credit and Option Markets

We show that the slight possibility of a macroeconomic disaster of moderate magnitude can explain important features across credit, option, and equity markets. Our consumption-based equilibrium model captures the empirical level and volatility of credit spreads, generates a flexible credit term structure and provides a good fi t to a century of observed spreads. The model matches the widespread volatility smirk in index options as well as the first two moments of government bond and equity market returns. Our model reveals a dynamic relationship between credit and option markets that helps explain the inconclusive evidence found in the empirical literature when regressing credit spreads on the option smirk.

Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance *

This article incorporates a time-varying severity of disasters into the hypothesis proposed by Rietz (1988) and Barro (2006) that risk premia result from the possibility of rare large disasters. During a disaster an asset's fundamental value falls by a time-varying amount. This in turn generates time-varying risk premia and, thus, volatile asset prices and return predictability. Using the recent technique of linearity-generating processes, the model is tractable and all prices are exactly solved in closed form. In this article's framework, the following empirical regularities can be understood quantitatively: (i) equity premium puzzle; (ii) risk-free rate puzzle; (iii) excess volatility puzzle; (iv) predictability of aggregate stock market returns with price-dividend ratios; (v) often greater explanatory power of characteristics than covariances for asset returns; (vi) upward-sloping nominal yield curve; (vii) predictability of future bond excess returns and long-term rates via the slope of the yield curve; (viii) corporate bond spread puzzle; (ix) high price of deep out-of-the-money puts; and (x) high put prices being followed by high stock returns. The calibration passes a variance bound test, as normal-times market volatility is consistent with the wide dispersion of disaster outcomes in the historical record. The model extends to a setting with many factors and to Epstein-Zin preferences.

Variance bounds on the permanent and transitory components of stochastic discount factors

In this paper, we develop lower bounds on the variance of the permanent component and the transitory component, and on the variance of the ratio of the permanent to the transitory components of SDFs. Exactly solved eigenfunction problems are then used to study the empirical attributes of asset pricing models that incorporate long-run risk, external habit persistence, and rare disasters. Specific quantitative implications are developed for the variance of the permanent and the transitory components, the return behavior of the long-term bond, and the comovement between the transitory and the permanent components of SDFs.

Performance Evaluation with High Moments and Disaster Risk

Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (Journal of Political Economy, 2008) and Foster and Hart (Journal of Political Economy, 2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that “anomalous” investment strategies such as “momentum” or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.

Carry Trade and Momentum in Currency Markets

We examine the empirical properties of the payoffs to two popular currency speculation strategies: the carry trade and momentum. We review three possible explanations for the apparent profitability of these strategies. The first is that speculators are being compensated for bearing risk. The second is that these strategies are vulnerable to rare disasters or peso problems. The third is that there is price pressure in currency markets.

On the effects of rare disasters and uncertainty shocks for risk premia in non-linear DSGE models

This paper studies how rare disasters and uncertainty shocks affect risk premia in DSGE models approximated to second and third order. Based on an extension of the results in Schmitt-Grohé and Uribe (2004) to third order, we derive propositions for how rare disasters, stochastic volatility, and GARCH affect any type of risk premia in a wide class of DSGE models. To quantify the effects, we set up a standard New Keynesian DSGE model where total factor productivity includes rare disasters, stochastic volatility, and GARCH. We find that rare disasters increase the level of the 10-year nominal term premium, whereas a key effect of uncertainty shocks, i.e. stochastic volatility and GARCH, is an increase in the variability of this premium.

Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation methods, we examine a variety of alternatives, including least-squares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of which are numerically stable and can handle ill-conditioned problems. Second, instead of conventional Monte Carlo integration, we use accurate quadrature and monomial integration. We test our generalized stochastic simulation algorithm (GSSA) in three applications: the standard representative–agent neoclassical growth model, a model with rare disasters, and a multicountry model with hundreds of state variables. GSSA is simple to program, and MATLAB codes are provided.

Variance Bounds on the Permanent and Transitory Components of Stochastic Discount Factors

In this paper, we develop lower bounds on the variance of the permanent component and the transitory component, and on the variance of the ratio of the permanent to the transitory components of SDFs. Exactly solved eigenfunction problems are then used to study the empirical attributes of asset pricing models that incorporate long-run risk, external habit persistence, and rare disasters. Specific quantitative implications are developed for the variance of the permanent and the transitory components, the return behavior of the long-term bond, and the comovement between the transitory and the permanent components of SDFs.

Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.

Are Heuristics Better than Theory if Market Crashes are Possible?

Financial advisers often recommend that investors should place (100 − age) % of their wealth in a well-diversified equity portfolio. Another popular approach is based on the complete markets model with CRRA utility and i.i.d. returns which implies a constant portfolio share invested in stocks. I solve a calibrated life-cycle model with stochastic labor income and rare disasters to investigate the welfare costs of constraining portfolio allocations to mimic these heuristics. When there is a possibility of a stock-market crash accompanied by a macroeconomic contraction, the simple rules of thumb outperform the more sophisticated dynamic programming rule that ignores the risk of rare disasters. The annual utility loss of following the complete markets solution amounts to only 0.5% relative to the optimal allocation. The (100-age)% rule also generates reasonably small welfare losses. In contrast, ignoring disasters can impose a cost as high as 5%.

Life-Cycle Portfolio Allocation When Disasters are Possible

JEL classifications: D91, E21, G11 In contrast to the predictions of life-cycle models with homothetic utility and risky labor income, the majority of US households do not hold any wealth in the stock market. Even among stockholders, the equity share out of net worth is modest. I develop a life-cycle model in which there are rare disasters, calibrated to match the joint empirical distribution of stock market crashes and macroeconomic contractions. The model provides an explanation for the low portfolio share in equity. About half of the decrease in stock holdings can be attributed to the correlation between stock market crashes and depressions. Furthermore, a 6% perceived probability of disaster is sufficient to deter the median household from investing in stocks during its working life. Small differences in expectations lead to dramatically different portfolios, consistent with the heterogeneity of asset allocation in data.

The Redistribution of Macroeconomic Risks by Dutch Institutions

We study the effects of macroeconomic shocks on different cohorts in the Dutch economy. From a calibrated stochastic model of macroeconomic risks, we derive typical shocks to productivity, demography and asset returns. The effects of these shocks are then simulated using an overlapping-generations model that contains a detailed specification of taxes, premiums, and benefits under Dutch law. We look at both the direct impact of shocks on agents wealth and at the redistribution and insurance that are carried out by the government and the pension system. While both these entities generally act to insure shocks across cohorts, our results show that the insurance role of the government is much larger than that of the occupational pension funds. We further find that there is little cross-correlation between different risks, except in the case of rare disasters.

Time-varying rare disaster risk and stock returns

This study provides empirical support for theoretical models that allow for time-varying rare disaster risk. Using a database of 447 international political crises during the period 1918–2006, we create a crisis index that shows substantial variation over time. Changes in this crisis index, our proxy for changes in perceived disaster probability, have a large impact on both the mean and volatility of world stock market returns. Crisis risk is positively correlated with the earnings–price ratio and the dividend yield. Cross-sectional tests also show that crisis risk is priced: Industries that are more crisis risk sensitive yield higher returns.

How Non-Gaussian Shocks Affect Risk Premia in Non-Linear DSGE Models

This paper studies how non-Gaussian shocks aect risk premia in DSGE models approx- imated to second and third order. Based on an extension of the results in Schmitt-Grohe & Uribe (2004) to third order, we derive propositions for how rare disasters, stochastic volatility, and GARCH aect any risk premia in a wide class of DSGE models. To quantify these eects, we then set up a standard New Keynesian DSGE model where total factor productivity includes rare disasters, stochastic volatility, and GARCH. We …nd that rare disasters increase the mean level of the 10-year nominal term premium, whereas a key eect of stochastic volatility and GARCH is an increase in the variability of this premium.

Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Risk Premia in General Equilibrium

This paper shows that non-linearities imposed by a neoclassical production function alone can generate time-varying and asymmetric risk premia over the business cycle. These (empirical) key features become relevant, and asset market implications improve substantially when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to endowment economies, the curvature of the policy functions affects the risk premium through controlling the individual’s effective risk aversion.

On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models

This paper studies how rare disasters and uncertainty shocks affect risk premia in DSGE models approximated to second and third order. Based on an extension of the results in Schmitt-Grohe & Uribe (2004) to third order, we derive propositions for how rare disasters, stochastic volatility, and GARCH affect any type of risk premia in a wide class of DSGE models. To quantify the effects, we set up a standard New Keynesian DSGE model where total factor productivity includes rare disasters, stochastic volatility, and GARCH. We find that rare disasters increase the level of the 10-year nominal term premium, whereas a key effect of uncertainty shocks, i.e. stochastic volatility and GARCH, is an increase in the variability of this premium.

Affine Disagreement and Asset Pricing

Models of heterogeneous beliefs can generate rich implications for trading and asset pricing (see Suleyman Basak 2005 for a recent survey). When studying such models, aggregation often leads to difficulty in computing equilibrium outcomes. In this paper, we introduce a flexible framework to model heterogeneous beliefs in the economy, which we refer to as “affine’’ disagreement about fundamentals. Affine processes (see Darrel Duffie, Jun Pan, and Kenneth Singleton 2000) are appealing as they provide a large degree of flexibility in modeling the conditional means, volatilities, and jumps for various quantities of interest while remaining analytically tractable. Our affine heterogeneous beliefs framework allows further for stochastic disagreement among agents about growth rates, volatility dynamics, as well as the likelihood of jumps and the distribution of jump sizes. Disagreement about rare disasters provides an interesting case study for our framework. Research by Thomas A. Rietz (1988), Francis Longstaff and Monika Piazzesi (2004), Robert J. Barro (2006) and others show that the possible occurrence of rare disasters that result in severe losses in consumption can have large impact on asset prices. However, the relatively short sample period and lack of historical precedents of disaster events (at least in the United States) make it difficult to precisely measure the frequencies of disasters or the size of their Asset Pricing: new risk chAnnels †