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

Document Type : Research Paper

Authors

1 Ph.D. Candidate, Department of Financial Engineering, Faculty of Administrative Sciences and Economics, University of Isfahan, Isfahan, Iran.

2 Assistant Prof., Department of Management, Faculty of Administrative Sciences and Economics, University of Isfahan, Isfahan, Iran.

Abstract

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.

Keywords

Main Subjects

References

 
Aalamifar, S., Khani, A. & Amiri, H. (2022). Developing Q-factor and Adjusted Q-factor Pricing Models by the Expected Investment Growth Factor using an Expected Return Factor. Financial Research Journal, 23(4), 593-624. (in Persian)
Anginer, D. & Yıldızhan, Ç. (2018). Is there a distress risk anomaly? Pricing of systematic default risk in the cross-section of equity returns. Review of Finance, 22(2), 633-660.
Aretz, K., Florackis, C. & Kostakis, A. (2018). Do stock returns really decrease with default risk? New international evidence. Management Science, 64(8), 3821-3842.
Asness, C. S., Frazzini, A. & Pedersen, L. H. (2014). Low-risk investing without industry bets. Financial Analysts Journal, 70(4), 24-41.
Avramov, D., Chordia, T., Jostova, G. & Philipov, A. (2009). Credit ratings and the cross-section of stock returns. Journal of Financial Markets, 12(3), 469-499.
Ball, R., Gerakos, J., Linnainmaa, J. T. & Nikolaev, V. (2016). Accruals, cash flows, and operating profitability in the cross section of stock returns. Journal of financial economics, 121(1), 28-45.
Bhandari, L. C. (1988). Debt/equity ratio and expected common stock returns: Empirical evidence. Journal of Finance, 43 (2), 507–528. Doi: 10.2307/2328473.
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
Campbell, J. Y., Hilscher, J. & Szilagyi, J. (2008). In search of distress risk. The Journal of finance, 63(6), 2899-2939.
Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of finance, 52(1), 57-82.
Chava, S. & Purnanandam, A. (2010). Is default risk negatively related to stock returns?. The Review of Financial Studies, 23(6), 2523-2559.
Cochrane, J. H. (2011). Presidential address: Discount rates. The Journal of finance, 66(4), 1047-1108.
Dichev, I. D. (1998). Is the risk of bankruptcy a systematic risk?. the Journal of Finance, 53(3), 1131-1147.
Eyvazlo, R., Hashemi, Y. & Qorbani, A. (2020). Multi-Factor asset pricing model in Iranian Capital Market. Financial Management Perspective, 10(32), 9-32. doi: 10.52547/JFMP.10.32.9 (in Persian)
Fama, E. F. & French, K. R. (1992). The cross‐section of expected stock returns. the Journal of Finance, 47(2), 427-465.
Fama, E. F. & French, K. R. (2015). A five-factor asset pricing model. Journal of financial economics, 116(1), 1-22.
Fama, E. F. & French, K. R. (2018). Choosing factors. Journal of financial economics, 128(2), 234- 252.
Fama, E. F. & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of political economy, 81(3), 607-636.
Filipe, S. F., Grammatikos, T. & Michala, D. (2016). Pricing default risk: The good, the bad, and the anomaly. Journal of Financial Stability, 26, 190-213.
Friewald, N., Wagner, C. & Zechner, J. (2014). The cross‐section of credit risk premia and equity returns. The Journal of Finance, 69(6), 2419-2469.
Gao, P., Parsons, C. A. & Shen, J. (2018). Global relation between financial distress and equity returns. The Review of Financial Studies, 31(1), 239-277.
Garlappi, L., & Yan, H. (2011). Financial distress and the cross‐section of equity returns. The journal of finance, 66(3), 789-822.
Garlappi, L., Shu, T., & Yan, H. (2008). Default risk, shareholder advantage, and stock returns. The Review of Financial Studies, 21(6), 2743-2778.
Ghazavi, Z. & Botshekan, M. (2019). Investigating the Effect of Default Risk on Individual Stocks Returns using Stocks listed in Tehran Stock Exchange. Financial Management Perspective, 9(27), 133-168. (in Persian)
Gomes, J. F. & Schmid, L. (2010). Levered returns. The Journal of Finance,65(2), 467- 494.
Gu, S., Kelly, B. & Xiu, D. (2020). Empirical asset pricing via machine learning. The Review of Financial Studies, 33(5), 2223-2273.
Guo, H. & Jiang, X. (2021). Aggregate Distress Risk and Equity Returns. Journal of Banking & Finance, 133, 106296.
Hansen, B. E. (2011). Threshold autoregression in economics. Statistics and its Interface, 4(2), 123-127.
Hou, K., Mo, H., Xue, C. & Zhang, L. (2018). Which Factors? Review of Finance, 23(1), 1-35.
Hou, K., Xue, C. & Zhang, L. (2015). Digesting anomalies: An investment approach. The Review of Financial Studies, 28(3), 650-705.
Jagannathan, R., Malakhov, A. & Novikov, D. (2010). Do hot hands exist among hedge fund managers? An empirical evaluation. The Journal of Finance, 65(1), 217- 255.
Khajavi, Sh. & Pourgoudarzi, A. (2020). Investigating the effect of default risk on explanatorypower of Fama-French five factor model (Evidence from Tehran Stock Exchange). Financial Knowledge of Security Analysis (Financial Studies), 13(46), 97-109. SID. https://sid.ir/paper/951394/en (in Persian)
Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47(1), 13–37.
McNeil, A. J., Frey, R. & Embrechts, P. (2015). Quantitative risk management: concepts, techniques and tools-revised edition: Princeton university press.
Mirzaie, M., Khani, A. & Botshekan, M. (2020). Developing Multifactor Asset Pricing Models Using Firm's Life Cycle. Financial Research Journal, 21(4), 545-569. (in Persian)
Modigliani, F. & Miller, M. H. (1963). Corporate income taxes and the cost of capital: a correction.The American economic review, 53(3), 433-443.
Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425–442.
Skočir, M. & Lončarski, I. (2018). Multi-factor asset pricing models: Factor construction choices and the revisit of pricing factors. Journal of International Financial Markets, Institutions and Money, 55, 65-80.
Vassalou, M. & Xing, Y. (2004). Default Risk in Equity Returns. The Journal of Finance, 59(2), 831-868.
Wahal, S. (2019). The profitability and investment premium: Pre-1963 evidence. Journal of Financial Economics, 131(2), 362-377.
Financial Research Journal
Volume 27, Issue 1
2025
Pages 140-166

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