Multifactor models and their consistency with the ICAPM

Can any multifactor model be interpreted as a variant of the Intertemporal CAPM (ICAPM)? The ICAPM places restrictions on time-series and cross-sectional behavior of state variables and factors. If a state variable forecasts positive (negative) changes in investment opportunities in time-series regressions, its innovation should earn a positive (negative) risk price in the cross-sectional test of the respective multifactor model. Second, the market (covariance) price of risk must be economically plausible as an estimate of the coefficient of relative risk aversion (RRA). We apply our ICAPM criteria to eight popular multifactor models and the results show that most models do not satisfy the ICAPM restrictions. Specifically, the “hedging” risk prices have the wrong sign and the estimates of RRA are not economically plausible. Overall, the Fama and French (1993) and Carhart (1997) models perform the best in consistently meeting the ICAPM restrictions. The remaining models, which represent some of the most relevant examples presented in the empirical asset pricing literature, can still empirically explain the size, value, and momentum anomalies, but they are generally inconsistent with the ICAPM.