Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2016, Volume 84, Issue 3

Time-Varying Risk Premium in Large Cross-Sectional Equity Data Sets
p. 985-1046

Patrick Gagliardini, Elisa Ossola, Olivier Scaillet

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time‐varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset‐specific instruments. The estimator uses simple weighted two‐pass cross‐sectional regressions, and we show its consistency and asymptotic normality under increasing cross‐sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no‐arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi‐period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time‐invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four‐factor model capturing market, size, value, and momentum effects.

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Supplemental Material

Supplement to "Time-Varying Risk Premium in Large Cross-Sectional Equity Datasets"

These supplementary materials provide the derivation of Equations (9)-(12) (Appendix 3), the proofs of technical lemmas used in the paper (Appendix 4), the link of our no-arbitrage pricing restrictions with Chamberlain and Rothschild (1983) results (Appendix 5), the check that the high-level assumptions in the paper hold under block-dependence (Appendix 6), and the results of Monte-Carlo experiments that investigate the finite-sample properties of the estimators and test statistics (Appendix 7).  Finally, we investigate the effects of model misspecification on risk premia estimation and give estimates of the pseudo-true values (Appendix 8).

Supplement to "Time-Varying Risk Premium in Large Cross-Sectional Equity Datasets"

This zip file contains the replication files for the manuscript.