Minimum-Variance Kernels and Economic Risk Premia

This paper offers a novel way of testing whether prespecified risk variables command significant risk premia. Specifically, we construct portfolios of securities to mimick the variation in the chosen risk variables, and we estimate the conditional and unconditional expected returns on these portfolios in excess of the risk-free rate. We also test for the ability of these hedging portfolios to price the returns on a large collection of assets. Our approach has several advantages over more traditional approachs that model asset returns as linear functions of a given set of explicit factors. First, the risk premia that we estimate do not depend on the appropriate specification of either an asset-pricing model or a stochastic process for asset returns. Second, while we allow for time variation in the conditional risk premia associated with economic risks, our estimates of the unconditional premia do not require explicit modeling of such time variation. Third, we can introduce conditioning information effectively to expand the set of asset returns under scrutiny and improve the ability of the hedging portfolio returns to track the economic risks. Fourth, we are able to impose the no-arbitrage positivity restriction on the pricing kernel, a requirement missing from the standard formulation of multi-beta models.