An Anatomy of the Market Return

Abstract

This paper introduces a model-free decomposition of S&P 500 forward market index returns in terms of realized and implied dispersion, downside, and tail risk using option portfolios. The decomposition lends itself by construction to learn about the different sources of risk in the market return, and subsequently to visual and formal diagnosing of asset pricing models. It utilizes a novel conditional frequency analysis on the basis of available options rather than the times series of the S&P 500.

Empirically, downside risk accounts for most of the forward market return, while symmetric tail risk is not prominently featured. The predictable, persistent part of the realized return is small. Nevertheless, signals revealed by this risk anatomy provide predictive out-of-sample power for realized returns in particular for longer maturities. Furthermore, it indicates that models with identically and independently distributed state variables are generally misspecified in this market, and that care must be taken when calibrating disaster risk models. A formal test based on the risk anatomy rejects a model with time-varying disaster intensity.

Keywords: equity premium, model-free, risk aversion, skewness, signal processing

JEL Classification: C02, C23, C52, C61, G11, G12