We examine the prediction of Merton’s intertemporal CAPM that time varying risk premiums arise from the conditional covariances of returns on assets with the return on the market and other state variables. We find a positive and significant price of risk for the covariance with the market return that is driven by the time series variation in the conditional covariances, and the risk-premium on the market remains positive and significant after controlling for additional state variables. Our method estimates the risk-return tradeoff in the ICAPM using multiple portfolios as test assets.