My dissertation addresses two main issues regarding asset returns: econometric modeling of asset returns in chapters 2 and 3 and puzzling features of the standard consumption-based asset pricing model (C-CAPM) in chapters 4 and 5. Chapter 2 develops a new theoretical derivation for the GARCH-skew-t model as a mixture distribution of normal and inverted-chi-square in order to represent the three important stylized facts of financial data: volatility clustering, skewness and thick-tails. The GARCH-skew-t is same as the GARCH-t model if the skewness parameter is shut-off. The GARCH-skew-t is applied to U.S. excess stock market returns, and the equity premium is computed based on the estimated model. It is shown that skewness and kurtosis can have significant effect on the equity premium and that with sufficiently negatively skewed distribution of the excess returns, a finite equity premium can be assured, contrary to the case of the Student t in which an infinite equity premium arises.
Chapter 3 provides a new empirical guidance for modeling a skewed and thick-tailed error distribution along with GARCH effects based on the theoretical derivation for the GARCH-skew-t model and empirical findings on the Realized Volatility (RV) measure, constructed from the summation of higher frequency squared (demeaned) returns. Based on an 80-year sample of U.S. daily stock market returns, it is found that the distribution of monthly RV conditional on past returns is approximately the inverted-chi-square while monthly market returns, conditional on RV and past returns are normally distributed with RV in both mean and variance. These empirical findings serve as the building blocks underlying the GARCH-skew-t model. Thus, the findings provide a new empirical justification for the GARCH-skew-t modeling of equity returns. Moreover, the implied GARCH-skew-t model accurately represents the three important stylized facts for equity returns.
Chapter 4 provides a possible solution to asset return puzzles such as high equity premium and low riskfree rate based on parameter uncertainty. It is shown that parameter uncertainty underlying the data generating process can lead to a negatively skewed and thick-tailed distribution that can explain most of the high equity premium and low riskfree rate even with the degree of risk aversion below 10 in the CRRA utility function.
Chapter 5 investigates a possible link between stock market volatility and macroeconomic risk. This chapter studies why U.S. stock market volatility has not changed much during the “great moderation” era of the 1980s in contrast to the prediction made by the standard C-CAPM. A new model is developed such that aggregate consumption is decomposed into stock and non-stock source of income so that stock dividends are a small part of consumption. This new model predicts that the great moderation of macroeconomic risk must have originated from declining volatility of shocks to the relatively large non-stock factor of production while shocks to the relatively small stock assets have been persistently volatile during the moderation era. Furthermore, the model shows that the systematic risk of holding equity is positively associated with the stock share of total wealth.