Improvement in finite sample properties of the Hansen–Jagannathan distance test

Jagannathan and Wang [Jagannthan, R., and Wang, Z., “The conditional CAPM and the cross-section of expected returns.” Journal of Finance, 51 (1996), 3–53] derive the asymptotic distribution of the Hansen–Jagannathan distance (HJ-distance) proposed by Hansen and Jagannathan [Hansen, L.P., and Jagannathan, R., Assessing specific errors in stochastic discount factor models." Journal of Finance, 52 (1997), 557–590], and develop a specification test of asset pricing models based on the HJ-distance. While the HJ-distance has several desirable properties, Ahn and Gadarowski [Ahn, S.C., and Gadarowski, C., “Small sample properties of the GMM specification test based on the Hansen–Jagannathan distance.” Journal of Empirical Finance, 11 (2004), 109–132] find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This paper proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method [Ledoit, O., and Wolf, M., “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection.” Journal of Empirical Finance, 10 (2003), 603–621] to compute its weighting matrix. The proposed method improves the finite sample performance of the HJ-distance test significantly.