Risk, return and market condition: a new functional-beta capital asset pricing model

Abstract

In this research, we will focus on investigating the relationship between risk and return. We will propose a new model which leads to a more sensible approach to modelling the relationship between risk and return under different market conditions. It is an extension of the traditional single-index capital asset pricing model (CAPM) which reads as: The return R[subscript]i on individual Security i can be decomposed into the specific return α[subscript]I + ε[subscript]i (expected specific return α[subscript]i and random specific return ε[subscript]i) and the systematic return β[subscript]iR[subscript]m owing to the common market return R[subscript]m.In our new model, we suggest a functional-beta single-index CAPM, extending the work of three-beta CAPM (Galagedera and Faff, 2004) that takes into account the condition of market volatility. Differently from the three-beta CAPM, we allow β[subscript]i changing functionally with the market volatility σ[subscript]m, which is more flexible and adaptable to the changing structure of financial systems. The main contributions of this thesis are summarised as follows:• A new functional-beta CAPM, taking into account the conditions of market volatility, is proposed under the framework of widely applicable data generating processes of near epoch dependence (NED).• A semi-parametric estimation procedure based on least squares local linear modelling technique under NED is suggested with the large sample distributions of the estimators established.• Simulation study is fully made, illustrating that the suggested estimation procedure for the proposed functional-beta CAPM under near epoch dependence can work well. It provides reasonable estimates of the functional beta in the condition of moderate market volatility.• By using a set of stocks data sets collected from Australian stock market in the past ten years, empirical evidences of the functional-beta CAPM in Australia are carefully examined under both nonparametric and parametric model structures. Differently from the three- or multi-beta (constant) CAPM in Galagedera and Faff (2005), our new findings show that the functional beta can be reasonably parameterized as threshold (regime-switching) linear functions of market volatility with two or three regimes of market condition. In the condition of extreme market volatility, a threshold functional-beta CAPM is suggested.The CAPM provides a usable measure of risk that helps investors determine what return they deserve for putting their money at risk. Our new model is no doubt helpful to better understand the relationship between risk and return under different market conditions. It can be potentially applied widely, for example, it may be useful both for market investors and financial risk managers in their investment/management decision-making.