Non‐linear Equity Valuation: An Empirical Analysis

Abstract

Legacy COMPUSTAT Data pertaining to 226,165 firm‐year observations covering a 57 year period (1950–2006) across all industrial groups are used to empirically assess the likely form and magnitude of the biases that arise from linear equity valuation models. Linear equity valuation models dominate the empirical analysis of the literature but ignore a firm's growth and adaptation options, which, by default, are non‐linear in their determining variables. Given this, an orthogonal polynomial fitting procedure as summarized in Ataullah et al. (2009), which does take account of the growth and adaptation options available to firms, is used to obtain a power series expansion for the relationship between equity prices and their determining variables. Our purpose is to assess whether the inclusion of the non‐linear terms associated with the growth and adaptation options available to firms can provide a more complete description of the relationship between equity prices and their determining variables when compared to the simple linear models that characterize the empirical research of this area of the literature. Our empirical analysis classifies firms into negative efficiency, low efficiency, and high efficiency levels and then for each efficiency level, estimates the parameters implied by the Ataullah et al. (2009) orthogonal polynomial fitting procedure. Our results show that there is a very strong non‐linear relationship between equity value and its determining variables although the nature of the relationship varies according to the efficiency level considered.