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

TL;DR

This paper presents a model-free method using option prices and quantile regression to measure disaster risk's impact on market returns, revealing significant tail disparities and their role in the equity premium.

Contribution

It introduces a novel, model-free approach combining option-derived risk-neutral distributions with quantile regression to assess disaster risk effects on asset returns.

Findings

Disaster risk significantly influences the left tail of return distributions.

The bottom 5% of returns account for 17% of the equity premium.

Disaster risk increases stochastic discount factor volatility.

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.