Abstract
The reliability of traditional asset pricing tests depends on: (1) correlations between asset returns and factors; (2) the time-series sample size T compared to the number of assets N. For macro-risk factors, like consumption growth, (1)-(2) are often such that traditional tests cannot be trusted. We extend the Gibbons-Ross-Shanken statistic to test identification of risk premia and construct their 95% confidence sets. These sets are wide or unbounded when T and N are close, yet they show that average returns are not fully spanned by betas when T exceeds N considerably. Our findings indicate when meaningful empirical inference is feasible.
Highlights
The reliability of traditional asset pricing tests depends on: (i) the correlations between asset returns and factors; (ii) the time series sample size T compared to the number of assets N
It has been well documented that the canonical consumption measure from the National Income and Product Accounts (NIPA) leads to small correlations between consumption growth and asset returns that could be improved by adopting alternative consumption measures, including the three-year consumption measure in Parker and Julliard (2005), the fourth-quarter to fourth-quarter consumption measure in Jagannathan and Wang (2007), the garbage measure in Savov (2011), and the unfiltered NIPA consumption measure in Kroencke (2017)
We propose two straightforward asset pricing tests that, unlike traditional tests, are valid for all possible strengths of identification of the risk premia and for scenarios in which the time series sample size exceeds the number of test assets
Summary
To further articulate the identification of the risk premia, we assume that the moment equation applies to the returns on any repackaged portfolio of assets, which can be characterized by an N-dimensional weight vector w whose elements add up to one, w ιN = 1, with ιN the N-dimensional vector of ones. Tβr)ehtuasrnas.loWwherenratnhke number value, a of risk similar factors exceeds one and the matrix argument can be made to show that there is not enough variation in the cross-section of asset returns to identify all risk premia.. A full rank value of the matrix (ιN β) implies that there is enough variation in the cross-section of asset returns to identify the risk premia. Examples of lower rank values of the matrix are settings in which the betas are zero or identical over the different assets. Irrespective of premia, a generic requirement wishtehtahtetrhrees(ιeNar... cβh)emrsautrsiex (1) or (9) to infer risk has full rank value
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