Three essays on asset pricing
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Date
2016
Authors
Zhou, Ji
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Abstract
This thesis consists of three essays. In the first essay, we derive a pricing kernel for a continuous-time long-run risks (LRR) economy with the Epstein-Zin utility function, non-i.i.d. consumption growth, and incomplete information about fundamentals. In equilibrium, agents learn about latent conditional mean of consumption growth and price equity simultaneously. Since the pricing kernel is endogenous and affected by learning, uncertainty about unobserved conditional mean of consumption growth affects risk prices corresponding to shocks in both consumption and dividend growth. We demonstrate our analytical results by applying the model to a profitability-based equity valuation model proposed by Pastor and Veronesi (2003). Calibration of the model demonstrates that the LRR model with learning has potential to fit levels of price-dividend ratios of the S&P 500 Composite Index, equity premium, and the short term interest rate simultaneously.
In essay two, we extend the LRR model with incomplete information proposed in essay one by incorporating inflation and applying the model to the valuation of nominal term structure of interest rate. We estimate the processes of state variables and latent variables using a Bayesian Markov-Chain Monte Carlo method. In the estimation, we rely only on the information in macro-economic data on aggregate consumption growth, inflation, and dividend growth on S&P 500 Composite Index. In this way, parameters and latent state variables are estimated outside the model. Estimation results suggest a mildly persistent LRR component. However, both real and nominal yield curves implied by the LRR model are downward-sloping. We show that the inverted yield curve is due to a negative risk premium, which is determined jointly by covariance between shocks in state variables and shocks in the nominal pricing kernel. Incorporating learning about the mean consumption growth flattens the yield curve but does not change the sign of the yield curve slope.
In essay three, we study the critique of the conditional affine factor asset pricing models proposed by Lewellen and Nagel (2006). They suggest that two important economic constraints are overlooked in cross-sectional regressions. First, the estimated unconditional slope associated with a risk factor should equal the average risk premium on that factor in a conditional model. Second, the estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We test both constraints on conditional models with time-varying betas and our results confirm the proposition. Also, from the functional relationship between conditional and unconditional betas, we identify an unconditional constraint on unconditional betas for time-varying beta models and develop a testing procedure subject to this constraint. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.
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Asset Pricing