Expected and realized returns in conditional asset pricing models: A new testing approach

We develop a new approach for testing conditional asset pricing models that avoids the issues in using realized returns as a proxy for expected returns. Testable restrictions are developed by asking what realized returns we would observe, given the pricing model under scrutiny. The new reverse testing approach is used to test the Merton ICAPM and a long-standing risk–return puzzle: the price of market risk has often turned out to be insignificant and at times even negative. The results from the new testing approach on US data give strong support for a positive relationship between conditional variance and the equity premium.