Testing Linear Factor Pricing Models with Individual Securities in Japan: Application of Shrinkage Estimation

Abstract

This study proposes a multivariate test for linear factor asset pricing models when the number of assets, N, is larger than the time dimension of returns, T. We extend the exact test proposed by Gibbons et al. (1989) to obtain a nonsingular covariance matrix with fewer estimation errors in the case of T < N. We apply the shrinkage estimation to the covariance matrix of the idiosyncratic error and obtain the sampling distribution of the proposed test statistics by using the fixed-design wild bootstrap to address the conditional heteroskedasticity and cross-sectional correlation. Our Monte-Carlo evidence shows that the proposed test statistics have a satisfying size and power. By using the proposed test statistics, we find that the Tokyo Stock Price Index is not mean-variance efficient most of the time from 1985 to 2015 compared with the tangency portfolio constructed from the individual securities of the Tokyo Stock Exchange first section, while efficiency hypothesis of the market portfolio in the second section is not rejected during periods of Asian financial crisis and the global financial crisis.