Since the development of consumption based asset pricing model in the 1980's numerous studies attempted to test the empirical performance of the model. The main feature of the model is its simplicity in explaining dynamic intertemporal asset pricing models. The model's intuition is based on the fundamental pricing equation. This equation relates the opportunity cost of postponing current consumption which is reflected in the loss of marginal utility to expected gains in marginal utility in the future, and therefore the assets are priced such that the losses incurred today should match the gains received later. Assets that payoff high in good times are less valuable than the ones that pay the same amount in bad times. In pricing assets insurance against higher volatility in consumption is the key to understand the model's predictions.
The predictions of this simple model are strong, however it performs empirically poor. Hansen and Singleton (1982) reject the model on pricing of US equities and conclude that the model is not capturing the time variation and cross sectional returns of equities and bonds simultaneously. Moreover, the model performs worse than The Capital Asset Pricing Model (CAPM) which is a special case of the consumption model itself. There are a significant number of portfolio based models which perform better than the consumption based models, yet most of them are the derivations of the consumption based model.
There are significant number of attempts to generalize the key features of the model to reconcile data with model predictions. Some address the issue of changing preferences to include habit formation which was initially proposed by Constantinides (1990) and later modified by Campbell and Cochrane (1999) to include recessions. These models are able to capture time variation in asset returns. The utility depends on current and past levels of consumption.
Therefore, bad shocks drive the consumption level to the habit level, increase the risk aversion and increase expected returns. One important implication is that even in the case of lower risk aversion parameters, small changes in consumption leads to significant volatility in marginal utilities. Therefore, risk aversion moves counter cyclically with the business cycle. However, this modification only allows for low risk free rate but does not explain a high premium on risky assets since both of these returns move with the business cycle.
