A Decomposition of Conditional Risk Premia and Implications for Representative Agent Models

Abstract

We develop a methodology to decompose the conditional market risk premium and risk premia on higher moments of excess market returns into components related to contingent claims on down, up, and normal market returns. We call these components the downside, upside, and central risk premia. The decompositions do not depend on assumptions about investor preferences nor do they depend on assumptions about the market return distribution. They can be computed in real time using a cross-section of option prices. The components' contributions to total risk premia vary over time and across investment horizon, as do the total risk premia themselves. Our risk premium decompositions offer powerful tools for evaluating representative agent models in a conditional setting. We develop a related methodology to estimate analogous conditional decompositions implied by prominent representative agent models and compare these to the data-implied decompositions. Although many representative agent models are able to match the unconditional market risk premium thus “explaining” the risk premium puzzle, they generally do a poor job matching conditional risk premia and their components. Our results provide a host of new empirical facts regarding sources of conditional risk premia and identify a set of new challenges for representative agent models.