Essays on asset pricing

Significant jumps have been found in stock prices and stock indexes, suggesting that jump risk is a part of systematic risks. Since jump risk is priced, adding jump risk into the traditional finance models has significant empirical and theoretical meanings. This dissertation focuses on testing and exploring the usage of the jump-diffusion two-beta asset pricing model. The dissertation consists of three essays: The three essays, investigate the dual beta (i.e. diffusion beta and jump beta) asset pricing model conditional on the state (i.e. up or down) of the market, the quantile relationships between standard beta, diffusion beta and jump beta and lastly, the quantile relationships between beta-changes and volume. The first essay of this dissertation concerns the capital asset pricing model (CAPM) beta (or standard beta), which is assumed to be the sole and constant measure of systematic risk in the CAPM model. However, it is now considered an empirical fact that the beta of a risky asset or portfolio is not the sole measure of systematic risk but is also time varying. Often, the market beta is not enough to explain the cross-sectional variations of average equity returns. For this reason researchers have proposed alternatives to the classical CAPM. More specifically, Todorov and Bollerslev (2010) showed that the CAPM beta can be further decomposed into a diffusion beta and a jump beta. Therefore, the first essay of this dissertation investigates whether assets with different decomposed betas are priced more efficiently. In particular, we investigate the systematic risk exposures of Japanese banks for both continuous and discontinuous market risks. Using high frequency data from 2001 to 2012, we decompose the standard betas of Japanese banking stocks into its diffusion and jump components. We find that jump betas on average are larger than diffusion betas, indicating that stocks respond differently to information associated with continuous and discontinuous market movements. We also find that larger stocks are more sensitive to discontinuities than their smaller counterparts; high leveraged stocks are more exposed to unexpected market-wide news and profitable firms are equally sensitive to both diffusion and jump market risks. By allowing for asymmetric market states we show that diffusion and jump betas both carry large and significant premiums in both up and down markets, but that these premiums differ substantially during periods of financial crises from those present during stable conditions. The second essay also applies the CAPM decomposition approach to compute the diffusion betas and jump betas. However, this essay takes a step further from the second essay and estimates the quantile-relationship(s) between standard betas, diffusion betas and jump betas of individual stocks and portfolios in the Japanese market. It also examines whether the beta in the standard CAPM is the weighted average of the jump beta and diffusion beta in the decomposed (jump-diffusion) CAPM model. A key insight of this essay is that even though the diffusion returns and jump returns are orthogonal according to the Todorov and Bollerslev (2010) decomposition, the two component betas (i.e. diffusion and jump betas) are neither restricted nor found to be orthogonal. Using quantile regression techniques, we find that jump betas have a higher variability than the diffusion and standard betas and the relationship(s) between the three betas are non-linear. Our findings also demonstrate that standard beta is more weighted by diffusion beta than jump beta, although the actual magnitudes of the weights differ significantly across the quantiles. We also show that the betas vary systematically across (large and small) firm sizes. Empirically, we also find support for the notion that the standard CAPM beta is a ‘summary proxy’ for the systematic risks in a jump-diffusion market process, i.e. a weighted average of the diffusion beta and the jump beta (at the median quantile). The third essay applies the same quantile-regression methodology, as used in the third essay, to examine the behaviour of time-vary beta-changes (or beta uncertainty) conditional on trading volume. By quantile-regressing the various betas (standard beta, diffusion and jump beta) on trading volume, our results depict a non-linear relationship. The volume-beta relationships at the tail quantiles are found to be quite different from those at high quantiles and at the mean. Since the systematic risk, beta, is a function of price-changes (price uncertainty) (according to the CAPM), we also examine whether the observed non-linear linkages between beta and volume is also analogously mirrored by price-changes and volume. The findings indicate a positive (negative) relationship between stock price changes and volume from top (bottom) quantiles. The relation is not entirely contemporaneous since lagged volume also found to contain predictive power for price-changes.