Recovering Risk Aversion from Option Prices and Realized Returns

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Abstract
A relationship exists between aggregate risk-neutral and subjective probability distributions and risk aversion functions. We empirically derive risk aversion functions implied by options prices and realized returns on the S&P500 index simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and largely consistent with standard assumptions made in economic theory. Postcrash, they are partially negative and partially increasing and irreconcilable with those assumptions. Mispricing in the option market is the most likely cause. Simulated trading strategies exploiting this mispricing show excess returns, even after accounting for the possibility of further crashes, transaction costs, and hedges against the downside risk.