A new approach to asset pricing models: the term structure of leverage and refinancing risk

The purpose of this study is not only to compare the Capital Asset Price Model, Arbitration Price Theory, Three Factor Price Model, Three Factor Price Model, and Five Factor Price Model to study the Capital Asset Price Model, Price Arbitration Price Theory, Three Factor Price Model, Four Factors Pricing Model and Five Factors Pricing Model for excess returns and for determining the best asset pricing model in terms of the ability to explain estimates of excess returns. This research includes explanatory research (explanatory research), namely looking at the relationship between research variables and testing hypotheses that have been formulated previously. This study examines the effect of variables in the asset pricing model and compares the asset pricing models in explaining excess returns. Based on the results of the research that has been carried out the best model that can be used in assessing the asset pricing model is the five Price Model Factors, this is evidenced by the value of R2 or R Square of 89.4%, the value is greater than the value of R2 or R Square Capital Asset Pricing Model, Arbitration Price Theory, Three Price Factor Models, and Four Price Factor Models, which were 34.7%, 55.2%, 77.2% and 79% respectively.

The purpose of this study is not only to compare the Capital Asset Price Model, Arbitration Price Theory, Three Factor Price Model, Three Factor Price Model, and Five Factor Price Model to study the Capital Asset Price Model, Price Arbitration Price Theory, Three Factor Price Model, Four Factors Pricing Model and Five Factors Pricing Model for excess returns and for determining the best asset pricing model in terms of the ability to explain estimates of excess returns. This research includes explanatory research (explanatory research), namely looking at the relationship between research variables and testing hypotheses that have been formulated previously. This study examines the effect of variables in the asset pricing model and compares the asset pricing models in explaining excess returns. Based on the results of the research that has been carried out the best model that can be used in assessing the asset pricing model is the five Price Model Factors, this is evidenced by the value of R2 or R Square of 89.4%, the value is greater than the value of R2 or R Square Capital Asset Pricing Model, Arbitration Price Theory, Three Price Factor Models, and Four Price Factor Models, which were 34.7%, 55.2%, 77.2% and 79% respectively.

Journal of Accounting Advances, (2020) 12(1): DOI: 10.22099/JAA.2021.39285.2077 Journal of Accounting Advances (JAA)Journal homepage: www.jaa.shirazu.ac.ir/?lang=en Developing Fama and French Multi-Factor Pricing Model Using a Fundamental Factor Based on Accounting CharacteristicsSanaz Aalamifar1, Abdollah Khani2*, Hadi Amir3 1. Ph.D. Candidate, Department of Accounting, Faculty of Administrative Science and Economics, University of Isfahan, Iran. sanazaalamifar@ase.ui.ac.irCorresponding author, Associate Prof., Department of Accounting, Faculty of Administrative Science and Economics, University of Isfahan, Isfahan, Iran. a.khani@ase.ui.ac.irAssistant Prof., Department of Economic, Faculty of Administrative Science and Economics, University of Isfahan, Isfahan, Iran. h.amiri@ase.ui.ac.ir ARTICLE INFABSTRACT Received: 2020-12-21Accepted: 2021-04-03 The purpose of the present research is to introduce a fundamental factor, based on related accounting characteristics (including earnings to price, book to price, sales growth rate, accruals, investment and growth in net operating assets), as a factor in the structure of Fama and French asset pricing model. The mentioned factor has been deducted from consumption theory and accounting principles and assumptions. In order to test the hypotheses, data of 345 companies listed in the Tehran Stock Exchange (TSE) and Iran Farabourse market, during the period 2006 to 2020, were used. To evaluate the performance of the multi-factor asset pricing model, test assets were ranked in two categories (once considering expected return characteristic, and once without considering the company’s expected return characteristic). In the following, using time series regression approach, the performance of augmented multifactor asset pricing models and corresponding conventional ones are compared. The results of this research showed that development of the research models with the fundamental factor based on mentioned accounting characteristics, can lead to improving the performance of these multi-factor models in explaining the variation in (expected) stock returns, and the test assets that considered the company’s expected return performed better compared to those that did not. The findings of this study indicate that the information in the financial statements has information content and can play an undeniable role in determining the expected return. * Corresponding author: Abdollah Khani Associate Prof., Department of Accounting, Faculty of Administrative Science and Economics, University of Isfahan, Isfahan, Iran. E-mail: a.khani@ase.ui.ac.ir 1-IntroductionIdentifying the correct asset pricing model has long been an important topic in the thematic literature of financial economics. Such a model not only explains stock returns, but also increases the ability to predict abnormal returns. The first models for estimating returns date back to the 1960s, when Markowitz’s (1952) new theory of securities attracted the attention of researchers. The first model for estimating returns was the capital asset pricing model (CAPM) which was presented by William Sharp (1964). In his research, William Sharp showed that return on asset was a function of line of market risk premium. But from 1975 to 1990, deviations and anomalies related to the CAPM model gradually became apparent. Following the recognition of these anomalies in accounting, in this study, based on the research of Penman and Zhou (2018), a fundamental factor based on accounting characteristics is introduced. For this purpose, consumption theory and accounting principles and assumptions will be used for initial identification; and empirical tests will be used for final identification of accounting characteristics that affect earnings growth and expected returns. Then these identified characteristics are summarized in a factor called the fundamental factor. Therefore, the purpose of this study is to evaluate the possibility of improving the performance of the asset pricing factor models in explaining the stock returns by adding a fundamental factor based on accounting characteristics. The hypothesis, methods, result and discussion and conclusion have been explained below. 2-HypothesisThe aim of this research is to introduce a fundamental factor based on accounting characteristics as a factor in the structure of the Fama and French asset pricing models. For this purpose, data of 345 companies, listed in the Tehran Stock Exchange, during the period 2006 to 2020 have been used. In order to achieve the objectives of this research, the following hypothesis are developed:H1: Adding a fundamental factor, based on accounting characteristics, to Fama and French three-factor model, improves its performance in explaining the stock returns.H2: Adding a fundamental factor, based on accounting characteristics, to Carhart four-factor model, improves its performance in explaining the stock returns.H3: Adding a fundamental factor, based on accounting characteristic, to Fama and French five-factor model, improves its performance in explaining the stock returns.H4: Adding a fundamental factor, based on accounting characteristics, to Fama and French six-factor model, improves its performance in explaining stock returns. 3- MethodsThis is an applied research in terms of purpose and an inferential and descriptive research, in terms of method. For data analysis and hypothesis testing, the data have been collected from 345 companies listed in the Tehran Stock Exchange for a period of 15 years (2006 to 2020). For initial calculations, the Excel and Ox Metrics software tools, and for the final analysis, Eviews and State software tools were used. 4- ResultsThe results of this research showed that a research model with fundamental factor, based on accounting characteristics, has a better performance in explaining the stock returns compared to the corresponding multifactor pricing models; and the tests that considered the company’s expected return, performed better compared to those that did not. 5- Discussion and Conclusion Findings of this research indicate that adding a fundamental factor based on accounting characteristics to Fama and French three-factor, Carhart four-factor, Fama and French five-factor, and Fame and French six-factor models, improves their performance in explaining the stock returns. In other words, developing a model with a fundamental factor, based on accounting characteristics, can lead to an improvement in the asset’s pricing model. This is a result of all the efforts that have been made since the time of Sharpe (1964). In addition, the research findings show that despite the research and efforts that have been made in the field of assets’ pricing, it is still possible to further develop this model from other angles in the financial field.

Traditional asset pricing theories and models are facing more and more challenges in empirical study. Machine learning provides a new tool for asset pricing research. Due to the low signal-to-noise ratio and concept drift of financial data, the theoretical constraints of economics are very important for the applicability of machine learning in asset pricing. Firstly, this paper introduces seven multi-factor asset pricing models based on ad hoc sparsity constraints, summarizes the characteristics and shortcomings of traditional asset pricing models. Then, we display the challenges of machine learning facing in empirical application of asset pricing, formulate the targeted economic constraints. Finally, we further discuss the possible future trends of machine learning algorithms in asset pricing.

In order to obtain a higher long-term average return from a portfolio, investors need to increase the level of risks that cannot be dispersed by diversification in the portfolio, and the asset pricing model can help investors to judge how much risk is reasonable to take. This paper will introduce the development process of several asset pricing models, and integrate and overview the applicability of the above several asset pricing models in Chinas capital market by combining the relevant research of domestic and foreign scholars over the years based on existing literature and data analysis results. Finally, it can be found that due to its strict prerequisites, Capital Asset Pricing Model (CAPM) has the lowest applicability in the Chinese stock market, while the Five-Factor Model and the pricing model based on beta decomposition both have good applicability, but it is hard to say which one is the best one to adapt to the Chinese stock market at present.

In portfolio management, a key input in portfolio construction is the expected return for an asset. In corporate financial management, computing a firm's cost of capital requires that the cost of equity be computed. The cost of equity is the expected return that investors require from investing in a corporation's common stock. Asset pricing models describe the relationship between the risks of a security and the expected return. The two most well-known equilibrium pricing models are the capital asset pricing model developed in the 1960s and the arbitrage pricing theory model developed in the mid 1970s. Other asset pricing models are based on empirical factors that affect expected returns. These multifactor pricing models are classified as statistical factor models, macroeconomic factor models, and fundamental factor models. Keywords: asset pricing model; risk factors; systematic risk factors; nondiversifiable risk factors; unsystematic risk factors; diversifiable risk factors; capital asset pricing model (CAPM); beta; capital market line (CML); market portfolio; security market line (SML); characteristic line; zero-beta portfolio; arbitrage pricing theory (APT) model; arbitrage principle; multifactor risk model; statistical factor model; macroeconomic factor model; fundamental factor model

INTRODUCTION Continuous-time stochastic processes arise in many applications in economics, but perhaps nowhere do they play as large a role as in finance. Following the pathbreaking work of Merton (1969, 1973) and Black and Scholes (1973), the use of continuous-time stochastic processes has become a common feature of many applications, especially asset pricing models. Even a casual comparison of the textbooks of the seventies (e.g., Fama and Miller (1972), Fama (1976)) with the current crop (e.g., Ingersoll (1987), Duffie (1988)) serves to demonstrate the remarkable speed with which the tools of stochastic process theory have been assimilated into mainstream finance. This survey will look at the specification and estimation of continuous-time stochastic processes. Although much of the discussion is relevant for other applications, I have chosen to write it from the perspective of someone interested in evaluating the empirical content of current continuous-time asset pricing models and in contributing to their future development. It is interesting to speculate on the reasons for the widespread adoption of continuous-time models in asset pricing. Although many come to mind, I would argue that they have been widely adopted not because of their empirical properties but in spite of them. The explosion and sophistication of theoretical research simply has not been matched by empirical work. Continuous-time asset pricing models typically involve restrictions linking the parameters of the price process to those of some underlying ‘forcing’ variables. In general equilibrium models, the forcing variables may be taste and technology. In option pricing models, they may be the term structure and/or the price of the underlying security. Tests of these models are invariably joint tests of ‘nuisance’ assumptions, including the specification of the forcing variable process.

My three essays contain three studies using multi-factor asset pricing models, where all the data are based on the US market. The first study extends intertemporal CAPMs with a few macro pricing factors: inflation or the cycle of industrial production (IP). I regard this specification of such models as a multi-factor pricing model, where this multi-factor linear pricing model can alternatively be derived from a consumption-based model from a theoretical perspective. I find significant evidence that the augmented multi-factor models outperform the original ICAPM. The results show that inflation is a key additional factor in the pricing models for the 25 size/book-to-market portfolios, while the cycle of IP is another vital additional factor in pricing models for the 25 size/momentum portfolios. Moreover, I find that most pricing information contained in the momentum factor is the inclusive information of the IP cycle, where the cycle of IP is generated by using the Hodrick–Prescott filter. The second study extends another two ICAPMs and Hou, Karolyi and Kho's three-factor model with inflation. The evidence shows that inflation significantly aids the original models in pricing 25 size/book-to-market portfolios in cross-sectional tests. Hence, I provide further robust evidence that inflation is the vital factor in the factor pricing models for the 25 size/book-to-market portfolios and a few other portfolios. Inflation provides additional explanatory power beyond Fama-French’s five factors in pricing the cross-sectional variation of 25 size/book-to-market portfolios. The third study investigates the performance of multi-factor asset pricing models in explaining the cross-section variation of the large number of expanding portfolios and a set of different portfolios, where the multi-factor models refer to the Fama-French three-factor model augmented by other pricing factors. I investigate the performance of several well-regarded multi-factor models by using Hansen’s general method of momentum (GMM), which is another alternative and very robust complement/guarantee to the only regression-based procedure in the previous literature. The results continuously support the superiority of the augmented multi-factor models. In general, augmented multi-factor models outperform the original models in a sound portion of different portfolios, where the original model refers to Fama-French’s three-factor model. In conclusion, my essays shed light on a fresh type of linear asset pricing model with sound theoretical background, and my research justifies the superiority of the multi-factor pricing model over Fama-French’s three-factor model in explaining the cross-sectional variation of equity returns with robust evidence.

We present a simple methodology that integrates commodity and asset pricing models. Given current evidence on the financialization of commodity markets, valuable information about commodity risk premiums can be extracted from asset pricing models and used to substantially improve the estimates of expected spot prices provided by current commodity price models. The methodology can be used with any pair of commodity and asset pricing models. An implementation of the methodology is presented using the Reasonable expected spot prices are obtained without negative consequences in the model's fit to futures prices.

This article examines three models for pricing risky assets, the capital asset pricing model (CAPM) from Sharpe and Lintner, the three factor model from Fama and French, and the four factor model from Carhart, in the Brazilian mark et for the period from 2002 to 2013. The data is composed of shares traded on the São Paulo Stock, Commodities, and Futures Exchange (BM&FBOVESPA) on a monthly basis, excluding financial sector shares, those with negative net equity, and those without consecutive monthly quotations. The proxy for market return is the Brazil Index (IBrX) and for riskless assets savings accounts are used. The 2008 crisis, an event of immense proportions and market losses, may have caused alterations in the relationship structure of risky assets, causing changes in pricing model results. Division of the total period into pre-crisis and post-crisis sub-periods is the strategy used in order to achieve the main objective: to analyze the effects of the crisis on asset pricing model results and their predictive power. It is verified that the factors considered are relevant in the Brazilian market in both periods, but between the periods, changes occur in the statistical relevance of sensitivities to the market premium and to the value factor. Moreover, the predictive ability of the pricing models is greater in the post-crisis period, especially for the multifactor models, with the four factor model able to improve predictions of portfolio returns in this period by up to 80%, when compared to the CAPM.

In recent years, scholars have explored hundreds of asset pricing factors built upon the foundation of the Fama five-factor model, sparking widespread discussion in the academic community. Simultaneously, the advancement of machine learning techniques has brought innovation to asset pricing factors. This article provides an overview of typical asset pricing factors and the application of machine learning in pricing models. It begins by discussing the construction of new asset pricing factors and then delves into the innovations brought about by machine learning in asset pricing models. The diversity of factors increases the fit of asset pricing models but also presents corresponding challenges. The application of machine learning techniques addresses issues such as overfitting in pricing models, further enhancing model effectiveness. The primary value of this article lies in summarizing various perspectives on asset pricing factors in recent years, exploring the significant applications of machine learning in asset pricing models, and providing a forward-looking view on the development of asset pricing models.

Bu çalışmanın amacı portföy aşırı getirilerinin varlık fiyatlandırma modellerinde yer alan bağımsız değişkenler ile açıklanıp açıklanamayacağını test etmektir. Varlık fiyatlandırma modeli olarak Finansal Varlık Fiyatlandırma Modeli ve Fama French Üç Faktörlü Fiyatlandırma Modeli kullanılmıştır. Zaman serisi ile regresyon analizinde Finansal Varlık Fiyatlandırma Modeli'nde piyasa risk primi ile portföy aşırı getirileri arasında pozitif ve anlamlı ilişkiler bulunmuştur. Fama French Üç Faktörlü Fiyatlandırma Modelin de ise piyasa risk primi ve firma büyüklüğü ile portföy aşırı getirileri arasında pozitif ve anlamlı bir ilişki bulunmuştur.

Explanation of Returns Changes in CAPM, TFPM, FFPM in Tehran Stock Exchange

This chapter starts with explaining the term “Asset Pricing”. It covers discussion on the different school of thoughts of asset pricing studies. The capital asset pricing model (CAPM) is discussed in the line of its goal, assumptions, validity, and significance. Thereafter detailed discussion was made on the different asset pricing models that evolved over a period of time namely from ICAPM to the various multifactor asset pricing models. Detailed discussion is also made on the (Fama and French, Journal of Financial Economics 33:3–56, Fama and French, 1993) portfolio construction methodology. Econometrics of the linear factor pricing models are covered in detail. Testing one model versus the other model is vital in asset pricing studies. Critical discussions are made on it taking suitable examples. This unit concluded with the actual implementation of the different asset pricing models using EViews. Furthermore, the panel regression is also covered in detail with suitable illustrations.

ACCORDING TO INTERTEMPORAL CAPITAL ASSET pricing models (ICAPM) in finance (Merton 1983), risk premia are the prices of risk built in assets priced according to their hedging capabilities against the uncertainties related to the relevant state variables in the economy. As the uncertainties of the state variables change over time, the prices of the risk related to the state variables, and consequently the risk premia on assets in general, vary over time, too. Following the growing evidence of the failure of the expectations hypothesis and the existence of time-varying risk premia in the term structure [see Shiller (1990) for a survey on the literature], these equilibrium asset pricing models have received economists' attention as an attractive theoretical framework for modeling risk premia in the term structure of interest rates (for example, Breeden 1986; Campbell 1986, 1987). Several empirical studies attempted to test the validity of these equilibrium asset pricing models of the term structure. However, due to the failure of the theoretical ICAPM in finance to identify the important state variables, most of the studies employed empirical models that do not require a complete, explicit representation of the state variables. Consequently, those studies do not reveal any information about the importance of different macroeconomic forcing variables in the determination of time-varying risk premia. This paper investigates explicitly the linkage between time-varying risk premia in the term structure and macroeconomic state variables. In that respect, the study is