Semiparametric Characteristics-based Models of Asset Returns

This thesis, which includes three chapters, studies asset-specific characteristics such as capitalization, book-to-market ratio etc., and their implications on assets prices and portfolio management. This thesis selects characteristics that have prediction powers on assets excess returns and specifies a flexible regression model, including linear, non-linear and pairwise interactive parts. This thesis further analyses whether characteristics are relevant as mispricing components and factor loadings in an asset pricing factor model. Finally, this thesis develops an optimal portfolio selection method based on the constructed characteristics-based asset pricing model. Methodologies in this thesis are mainly proposed for two popular questions in financial econometrics, namely, high dimensional analysis and the approximation of uni-variate and multi-variate unknown functions. The tools extended by this thesis are B-splines and orthogonal series, and multi-variate unknown functions are approximated by tensor products. In terms of high dimensional problems, which are caused by both abundant financial data and diverging B-splines bases used to approximate unknown functions, they are solved by LASSO-style selection model and power enhanced hypothesis tests. The details of the three chapters are summarized below: Specification LASSO and an Application in Financial Markets This chapter proposes the method of Specification-LASSO in a flexible semi-parametric regression model that allows for the interactive effects between different covariates. Specification-LASSO extends LASSO and Adaptive Group LASSO to achieve both relevant variable selection and model specification. Specification-LASSO also gives preliminary estimates that facilitate the estimation of the regression model. Monte Carlo simulations show that the Specification-LASSO can accurately specify partially linear additive models with interactive effects. Finally, the proposed methods are applied in an empirical study, which examines the topic proposed by \cite{freyberger2020dissecting}, arguing that firms’ sizes may have interactive effects with other security-specific characteristics, which can explain the stocks excess returns together. Dynamic Peer Groups of Arbitrage Characteristics This chapter proposes an asset pricing factor model constructed with semi-parametric characteristics-based mispricing and factor loading functions. We approximate the unknown functions by B-splines sieve where the number of B-splines coefficients is diverging. We estimate this model and test the existence of the mispricing function by a power-enhanced hypothesis test. The enhanced test solves the low power problem caused by diverging B-splines coefficients, with the strengthened power approaches one asymptotically. We also investigate the structure of mispricing components through Hierarchical K-means Clusterings. We apply our methodology to CRSP (Center for Research in Security Prices) and Compustat data for the US stock market with one-year rolling windows during 1967-2017. This empirical study shows the presence of mispricing functions in certain time blocks. We also find that distinct clusters of the same characteristics lead to similar arbitrage returns, forming a “peer group” of arbitrage characteristics. A Dynamic Semiparametric Characteristics-based Model for Optimal Portfolio Selection This paper develops a two-step semiparametric methodology for portfolio weight selection for characteristics-based factor-tilt and factor-timing investment strategies. We build upon the expected utility maximization framework of \cite{brandt1999estimating} and \cite{ait2001variable}. We assume that assets returns obey a characteristics-based factor model with time-varying factor risk premia as in \cite{li2020dynamic}. We prove under our return-generating assumptions that an approximately optimal portfolio can be established using a two-step procedure in a market with a large number of assets. The first step finds optimal factor-mimicking sub-portfolios using a quadratic objective function over linear combinations of characteristics-based factor loadings. The second step dynamically combines these factor-mimicking sub-portfolios based on a time-varying signal, using the investor’s expected utility as the objective function. We develop and implement a two-stage semiparametric estimator. We apply it to CRSP (Center for Research in Security Prices) and FRED (Federal Reserve Economic Data) data and find excellent in-sample and out-sample performance consistent with investors’ risk aversion levels