Developing "Multifactor Asset Pricing Models" Using Threshold Regression Approach and Credit Risk Factor

Objective This study aims to develop threshold asset pricing models to enhance the performance of common multi-factor models. Over the past thirty years, asset pricing models have evolved by incorporating pricing anomalies as new factors that previous models could not explain, leading to the introduction of hundreds of such factors. This proliferation underscores the importance of the “parsimony” principle, which advocates for models with minimal factors and maximal explanatory power. Given the abundance of potential variables influencing asset returns, it is essential to seek models that balance simplicity and effectiveness. In line with this principle, this study proposes threshold asset pricing models where the proposed factors are applied selectively to certain companies rather than universally. Through cross-sectional tests and threshold cross-sectional regression analyses, the research examines the threshold effect of variables such as credit risk on expected returns, using the debt ratio as a threshold variable. It is anticipated that the impact of credit risk or financial distress on expected returns will differ across various levels of indebtedness. If the threshold effect of the debt ratio proves significant, credit risk factors can be applied selectively to specific groups of assets with particular characteristics in time-series tests. The ultimate goal is to develop a model that, instead of incorporating factors in a binary manner, considers their presence for certain assets based on threshold conditions. This approach aims to maximize explanatory power while adhering to the parsimony principle, ultimately improving the effectiveness of asset pricing models by using factors only where they are most relevant. Methods To evaluate the performance of threshold asset pricing models, data from companies in the Iranian capital market (2001-2023) were used after applying common filters. Threshold regression techniques investigated the threshold effect, and the GRS test along with A(|aᵢ|), A(|aᵢ|/|r̄ᵢ|), and AR², tested the research hypotheses. Results The results demonstrate that the distance-to-default variable, both individually and in conjunction with other characteristics, is influenced by the threshold effect of the debt ratio. Specifically, there is a significant negative relationship—where a lower distance-to-default corresponds to higher expected returns—for stocks with high debt ratios. This indicates that for companies with higher leverage, investors demand greater returns due to the increased risk of default. Utilizing the threshold effect of variables affecting asset returns in cross-sectional regressions allows for a more precise and detailed analysis of how these variables impact individual stock returns. Additionally, incorporating the default risk factor into the examined asset pricing models enhances their explanatory power and predictive ability, especially for test assets with high debt thresholds. This improvement highlights the effectiveness of considering threshold effects in the models, as it increases their ability to accurately predict returns for assets that are more susceptible to default risk due to higher levels of indebtedness. Conclusion The results suggest that to adhere to the parsimony principle, threshold asset pricing models can be used to develop pricing models and price a subset of test assets with specific characteristics, yielding appropriate results.