Disastrous disappointments: asset-pricing with disaster risk and disappointment aversion

In this paper, I combine disappointment aversion, as employed by Routledge and Zin and Campanale, Castro and Clementi, with rare disasters in the spirit of Rietz, Barro, Gourio, Gabaix and others. I find that, when the model's representative agent is endowed with an empirically plausible degree of disappointment aversion, a rare disaster model can produce moments of asset returns that match the data reasonably well, using disaster probabilities and disaster sizes much smaller than have been employed previously in the literature. This is good news. Quantifying the disaster risk faced by any one country is inherently difficult with limited time series data. And, it is open to debate whether the disaster risk relevant to, say, US investors is well-approximated by the sizable risks found by Barro and co-authors in cross-country data. On the other hand, we have evidence that individuals tend to over-weight bad or disappointing outcomes, relative to the outcomes' weights under expected utility. Recognizing aversion to disappointment means that disaster risks need not be nearly as large as suggested by the cross-country evidence for a rare disaster model to produce average equity premia and risk-free rates that match the data. I illustrate the interaction between disaster risk and disappointment aversion both analytically and in the context of a simple Rietz-like model of asset-pricing with rare disasters. I then analyze a richer model, in the spirit of Barro, with a distribution of disaster sizes, Epstein-Zin preferences, and partial default (in the event of a disaster) on the economy's "risk-free" asset. For small elasticities of intertemporal substitution, the model is able to match almost exactly the means and standard deviations of the equity return and risk-free rate, for disaster risks one-half or one-fourth the estimated sizes from Barro. For larger elasticities of intertemporal substitution, the model's fit is less satisfactory, though it fails in a direction not often viewed as problematic--it under-predicts the volatility of the riskfree rate. Even so, apart from that failing, the results are broadly similar to those obtained by Gourio but with disaster risks one-half or onefourth as large.