Long-Run Risk, the Wealth-Consumption Ratio, and the Temporal Pricing of Risk

Representative agent consumption based asset pricing models have made great strides in accounting for many important features of asset returns. The long run risk (LRR) models of Ravi Bansal and Amir Yaron (2004) are a prime example of this progress. Yet, several other representative agent models, such as the external habit model of John Y. Campbell and John H. Cochrane (1999) and the variable rare disasters model of Xavier Gabaix (2008), seem to be able to match a similar set of asset pricing moments. Additional moments would be useful to help distinguish between these models. Hanno Lustig, Stijn Van Nieuwerburgh, and Adrien Verdelhan (2009) argue that the wealth-consumption ratio is such a moment. A comparison of the wealth-consumption ratio in the LRR model and in the data is favorable to the LRR model. This is no small feat because the wealth-consumption ratio is not a target in the usual calibrations of the model, and the LRR is — so far — the sole model able to reproduce both the equity premium and the wealth-consumption ratio. The LRR model matches the properties of the wealth-consumption ratio despite the fact that it implies a negative real bond risk premium. This is because it generates quite a bit of consumption cash flow risk to offset the negative discount rate risk.