Three Essays on Modeling Asset Returns: A Nonparametric Approach - Shamsi Zamenjani, Azam (My University, 2018)
This thesis examines three important topics in empirical finance: The nonparametric conditional beta, the propagation of risks between markets, and the predictability of the market return density using economics and financial variables. First, I introduce a model that links the conditional beta to the second order conditional moments of returns. A key insight of my approach is that if the joint distribution of stock returns and market returns are correctly specified, then it follows that their contemporaneous pricing relationship is completely determined by the associated conditional distribution. The model that I propose is able to study the effects of a big shock in the market on the beta of an individual stock or a portfolio. This approach allows the beta to be a flexible function of the sign and size of the market portfolio which is absent in the finance literature. My results demonstrate that beta does depend on the market portfolio in a nonlinear manner. This carries implications for systematic risk measurement significantly different than what we have in a fixed parametric model. My model nests the Gaussian and Student-t distribution as special cases but importantly allows for deviations from the elliptic family of distributions. This includes asymmetric distributions. I extend the model to include more assets and provide a test to see if other factors are priced. My empirical results illustrate that in the event of big shocks in the market the firm's beta coefficient can go down or shoot up, depending on the market conditions (volatility). Second, I extend the literature on the spillover effects or contagion effects that focus on the transmission of shocks through moments to spillover effects on the conditional density and seek to shed greater light on the contemporaneous information transmission between markets. The objective is to develop a joint model of returns on two different markets governed by an in infinite mixture model from which the conditional density of the first market given the returns of the other market can be derived. This enables us to study how a shock in one market influences the contemporaneous and future (one-day-ahead, one-week-ahead, and one-month ahead) conditional density of the other market. This makes it possible to explore the contemporaneous spillover effects of big shocks in one market on various features of the density of the other market such as conditional expected return, volatility, skewness and kurtosis, and value at risk. Third, I investigate the predictability of the market return density using financial and macroeconomic variables. The objective is to develop a Bayesian nonparametric model of the distribution of market returns where the weights of the mixture change over time. Available information on financial and macroeconomic variables is employed to predict the weights of the mixture components in the predictive density of market returns over time. This permits the density of market returns to be unknown and to change over time. Moreover, the proposed model examines whether certain financial and macroeconomic variables convey any useful information about the predictive density which extends the literature on an important question in empirical finance, the predictability of market return. Using the proposed stick-breaking model, instead of focusing only on the conditional mean or variance of market return, I investigate whether these variables are useful in predicting the entire density of stock returns through predicting the time-varying weights of the mixture density. I seek to predict features of the market return density in addition to what is captured by the first and second moments. This matters in empirical distributions in finance and economics where we might have heavy tails and asymmetry. I provide evidence that these features can be of great value in applications such as asset allocation and risk management. I evaluate the incremental improvement in the predicted density of market returns statistically by the log predictive likelihood criteria and economically by a portfolio selection application.