A Dynamic Network of Arbitrage Characteristics

Abstract

We propose an asset pricing factor model constructed with semi-parametric characteristics based mispricing and factor loading functions. This model captures common movements of stock excess returns and includes a two-layer network of arbitrage returns interconnected by securityspecific characteristics. We approximate the unknown functions by B-splines 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-spline coefficients. Meanwhile, the strengthened power approaches to one asymptotically. And the dynamic networks are explored through Hierarchical K-Means Clusterings. We apply our methodology to CRSP monthly 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 and a dynamic network structure of arbitrage returns through groups of some characteristics.

A Dynamic Semiparametric Characteristics-based Model for Optimal Portfolio Selection

“…They all illustrated the validility of characteristics-based factor model and provided relevant empirical results. Li and Linton (2020) generalized the parametric part of Equation 2 as semiparametric functions to be consistent with earlier research. They also proposed power enhanced tests to verify their model, concluding that the semiparametric mispricing component h(X i ) was only significant in certain rolling windows.…”

“…This framework is an extension of Connor and Linton (2007) and Connor et al (2012), who assumed the factor beta function g(•) to be univariate. This model is a special case of Li and Linton (2020) except specifies the mean value of the factor premium φ jt .…”

“…The estimation of Equation 5 under Equation 6 is discussed in Li and Linton (2020), which is achieved mainly through "Projected Principal Component Analysis" (PPCA) by Fan et al (2016). The idea is to projected the 3 A TWO-STEP VERSION OF THE PORTFOLIO CHOICE PROBLEM 6 n × T asset excess returns onto the B-spline space spanned by X, where X = (X 1 , X 2 , .…”

“…Furthermore, we operate PCA on 1 nŶŶ ⊺ . Therefore, theĜ(X) is estimated as √ n times the largest J eigenvectors of 1 nŶŶ ⊺ under similar conditions as in Li and Linton (2020). Due to the property of the PCA, the assumption Equation 6 is satisfied.…”

“…Section two describes the econometric framework for our model. We assume the returns are generated by the asset pricing model in Li and Linton (2020) and that the factor risk premia are predictable based on a single-index function involving a set of both stationary and nonstationary predictors.…”