The Review of Financial Studies/v 13 n 1 2000 conflicting empirical results.We argue below that asymmetry is more likely to be found in conditional covariances and re-examine whether conditional betas display asymmetry for our sample. Third,since our model combines modeling volatility dynamics and risk premiums,we quantify the risk implications of the estimated volatility dynamics.Most applications of GARCH models,with a few exceptions,have not yet embraced asymmetric volatility models.For example,parameterizations of CAPM models that use GARCH [see, e.g.,Engel et al.(1995)1,models of volatility spillover across equity markets [see,e.g.,Hamao,Masulis,and Ng (1990)],and stochastic volatility models for options [Hull and White (1987)]have typically not used asymmetric volatility models.2 This is surprising since a number of sophisticated models have been developed to accommodate asymmetric volatility [see,e.g.,Nelson (1991),Glosten,Jagannathan,and Runkle (1993),and Hentschel (1995)],and the results in Pagan and Schwert (1990)and Engle and Ng (1993)indicate that these volatility models outperform standard GARCH models.If these models yield different conditional volatilities from symmetric GARCH models,their economic implications will be different too.With an asymmetric volatility model, risk and the cost of capital may increase more in response to negative market return shocks than in response to positive shocks.Whereas the economic importance of such effects is indisputable,it is not ex ante clear that statistically significant asymmetric volatility has economically important risk implications. Finally,whereas most of the empirical analysis so far (see Table 1) has focused on U.S.stock returns,our empirical application focuses on the market return and portfolio returns constructed from Japanese stocks in the Nikkei index.As Engle and Ng (1993)conclude for the Japanese Topix index,our results indicate that asymmetry is an impor- tant feature of stock market volatility in the Japanese market as well. The remainder of the article is organized as follows.Section 1 formulates our empirical model,the empirical hypotheses,and explains the role of leverage in generating asymmetric risk and volatility.A set of specification tests is also discussed.Section 2 discusses the data and the empirical results.Section 3 considers the economic implications of our model and Section 4 evaluates the robustness of the empirical results. The final section summarizes the results and outlines directions for further research. 2Exceptions are Koutmos and Booth(1995)and Ng(1996)in the volatility spillover literature and Amin and Ng (1993),Duan (1995),and Wu (1998)in the options literature. 4The Reiew of Financial Studies 13 n 1 2000 conflicting empirical results. We argue below that asymmetry is more likely to be found in conditional covariances and re-examine whether conditional betas display asymmetry for our sample. Third, since our model combines modeling volatility dynamics and risk premiums, we quantify the risk implications of the estimated volatility dynamics. Most applications of GARCH models, with a few exceptions, have not yet embraced asymmetric volatility models. For example, parameterizations of CAPM models that use GARCH see,
e.g., Engel et al. 1995 , models of volatility spillover across equity Ž . markets see, e.g., Hamao, Masulis, and Ng 1990 , and stochastic
Ž . volatility models for options Hull and White 1987 have typically not
Ž . used asymmetric volatility models.2 This is surprising since a number of sophisticated models have been developed to accommodate asymmetric volatility see, e.g., Nelson 1991 , Glosten, Jagannathan, and Runkle
Ž . Ž. Ž. 1993 , and Hentschel 1995 , and the results in Pagan and Schwert Ž. Ž. 1990 and Engle and Ng 1993 indicate that these volatility models outperform standard GARCH models. If these models yield different conditional volatilities from symmetric GARCH models, their economic implications will be different too. With an asymmetric volatility model, risk and the cost of capital may increase more in response to negative market return shocks than in response to positive shocks. Whereas the economic importance of such effects is indisputable, it is not ex ante clear that statistically significant asymmetric volatility has economically important risk implications. Finally, whereas most of the empirical analysis so far see Table 1 Ž . has focused on U.S. stock returns, our empirical application focuses on the market return and portfolio returns constructed from Japanese stocks in the Nikkei index. As Engle and Ng 1993 conclude for the Ž . Japanese Topix index, our results indicate that asymmetry is an impor￾tant feature of stock market volatility in the Japanese market as well. The remainder of the article is organized as follows. Section 1 formulates our empirical model, the empirical hypotheses, and explains the role of leverage in generating asymmetric risk and volatility. A set of specification tests is also discussed. Section 2 discusses the data and the empirical results. Section 3 considers the economic implications of our model and Section 4 evaluates the robustness of the empirical results. The final section summarizes the results and outlines directions for further research. 2 Exceptions are Koutmos and Booth 1995 and Ng 1996 in the volatility spillover literature and Ž. Ž. Amin and Ng 1993 , Duan 1995 , and Wu 1998 in the options literature. Ž. Ž. Ž. 4