A Tale of Two Tails: A Model-free Approach to Estimating Disaster Risk Premia and Testing Asset Pricing Models

Abstract: I introduce a model-free methodology to assess the impact of disaster risk on the market return. Using S&P500 returns and the risk-neutral quantile function derived from option prices, I employ quantile regression to estimate local differences between the conditional physical and risk-neutral distributions. The results indicate substantial disparities primarily in the left-tail, reflecting the influence of disaster risk on the equity premium. These differences vary over time and persist beyond crisis periods. On average, the bottom 5% of returns contribute to 17% of the equity premium, shedding light on the Peso problem. I also find that disaster risk increases the stochastic discount factor's volatility. Using a lower bound observed from option prices on the left-tail difference between the physical and risk-neutral quantile functions, I obtain similar results, reinforcing the robustness of my findings.