Econometrics and Finance Seminar: Paolo Zaffaroni

Estimating Risk Premia Using Large Cross-Sections

Paolo ZAFFARONI, Imperial College, London

Tens of thousands of stocks are traded every day in financial markets, providing an extremely rich information set to validate and estimate asset pricing models. At the same time, it is convenient to consider short time series, to avoid structural breaks and to mitigate the documented time- variation of the distribution of stock returns. Based on these considerations, this paper presents a limiting theory for estimating and testing linear asset-pricing models when a very large number of assets N is available together with a fixed, possibly very small, time-series dimension, applicable to both traded and non-traded factors. For this purpose, we focus on Shanken’s (1992) estimator, which we show to exhibit many desirable properties. We demonstrate that: first, it is an OLS-based estimator that, unlike others, does not require preliminary estimation of the bias-adjustment; second, it converges at the true ex-post risk premia at rate N; third, it has an asymptotically normal distribution; fourth, its limiting covariance matrix can be consistently estimated. Based on the pricing errors associated with the Shanken estimator, we propose a new test of the no-arbitrage asset pricing restriction, and establish its asymptotic distribution (assuming that the restriction holds) that only requires the number of assets N to diverge. Finally, we show how our results can be extended to deal with the more realistic case of unbalanced panels. The practical relevance of our findings is demonstrated using Monte Carlo simulations and an empirical application to asset- pricing models with traded risk factors. Our analysis suggests that the market, size, and value factors are often priced in the cross-section of NYSE-AMEX-NASDAQ individual stock returns. (with Valentina RAPONI and Cesare ROBOTTI)