• Email: lingxiao@wustl.edu.

  • Address: One Brookings Drive, Campus Box 1208, St. Louis, MO 63130, USA.


Abstract. Revisiting the framework of Barillas and Shanken (2018), BS henceforth, we show that the Bayesian marginal likelihood-based model comparison method in that paper is unsound: the priors on the nuisance parameters across models must satisfy a change of variable property for densities that is violated by the Jeffreys priors used in the BS method. Extensive simulation exercises confirm that the BS method performs unsatisfactorily. We derive a new class of improper priors on the nuisance parameters, starting from a single improper prior, which leads to valid marginal likelihoods and model comparisons. The performance of our marginal likelihoods is significantly better, allowing for reliable Bayesian work on which factors are risk factors in asset pricing models.

Internet Appendix. [pdf]

Working Papers

Abstract. Taking the union of the risk factors recently proposed by Fama and French (1993, 2015, 2018), Hou, Xue, and Zhang (2015), Stambaugh and Yuan (2017), and Daniel, Hirshleifer, and Sun (2019), a pool we refer to as the “winners”, we ask what collection of winners from winners emerge when each factor is allowed to play the role of a risk factor, or a non-risk factor. Our comparison of 4,095 models shows that a six factor model consisting of Mkt, SMB, MOM, ROE, MGMT, and PEAD as risk factors has the largest Bayesian posterior probability. Moreover, this collection displays superior out-of-sample predictive performance, higher Sharpe ratios, and greater ability in pricing anomalies, than the preceding models. These results suggest that both fundamental and behavioral factors play an important role in explaining the cross-section of expected equity returns.

Abstract. This paper derives an asymptotically optimal test for testing whether a jump occurs within a given period of time for high-frequency data. In this situation, the jump time, i.e. the nuisance parameter, only presents under the alternative but not under the null. Furthermore, those high frequency observations are contaminated with microstructure noise, hence a realized spot volatility estimator using the pre-averaging method is also proposed as a byproduct of the test.

Selected Work in Progress
  • Which Macro Factor is Risk Factor: A Bayesian Moment-based Analysis (Joint work with Siddhartha Chib, Kuntara Pukthuanthong, Minchul Shin, and Anna Simoni)
  • Selecting the Best Market Predictors: A Bayesian Approach (Joint with Guofu Zhou)
  • A Test for Jumps with Finite or Infinite Activity (Joint work with Junnan He)