Quantile relationships between standard, diffusion and jump betas across Japanese banks

Using high frequency financial data and associated risk decomposition and quantile regression techniques we characterise some stylised facts and relationship(s) between standard betas, diffusion betas and jump betas of individual stocks and portfolios in Japanese market. We then investigate whether the beta in the conventional CAPM is the weighted average of the jump beta and diffusion beta in the jump-diffusion model and how these different betas behave across different banks. Our empirical findings indicate that jump betas are cross-sectionally more dispersed than diffusion and standard betas. We find that the relationship(s) between the three betas are non-linear. We also find that standard betas are influenced more by diffusion betas than the jump betas, although the actual magnitude of the weights differ significantly across the quantile. This relationship holds for both individual stocks and portfolios. Empirical studies have shown that betas vary systematically across large and small firm equities. For large equity portfolios, the jump beta-diffusion beta ratios are lower that the jump beta diffusion beta ratios of the small equity portfolios. Empirically, we further find that the standard CAPM beta is composed of two-components, i.e. it is the weighted average of the diffusion component and the jump component.