Applying Multi-Factor Models of Stock Returns: Student Exercises and Applications

Multi-factor return models, along with the single-factor market model, occupy a pivotal place in the investments curriculum and are widely implemented in practice, both in stock selection and in portfolio manager evaluation. In this paper we show how to use student spreadsheet assignments and exercises to apply the single factor model and different multi-factor models to actual company returns data. The exercises include the computation and analysis of market model betas and applications of the Fama and French (1992) and the Chen and Zhang (2010) models. Extensions to other factor models are easy to incorporate. Students will gain a more integrated understanding of single and multi-factor models of expected stock returns and will be prepared to create their own models. The assignments are useful for a class using an actual portfolio (student managed investment fund) or in any class that includes portfolio management, or for cost of capital estimation methods in an advanced corporate finance class. (ProQuest: . denotes formulae omitted.)INTRODUCTIONThe Capital Asset Pricing Model (CAPM), developed by Sharpe (1964) and others, was a revolutionary development in the study and understanding of the relationship between risk and return for common stocks. Following Jensen (1967), the application of the CAPM in a multi-period situation is hereafter referred to as the Amarket model. @ In this model, the only systematic factor that influences the returns on equities is the sensitivity, or beta, of the stock as measured against a market index. The market model is used to estimate a linear relationship between the stock beta and the expected return on the stock. Any variation in stock returns that cannot be accounted for by stock betas is considered to be unsystematic, that is, unique to the firm and unpredictable. The single-index market model is a good starting point for students to study and implement because it is easy to visualize and demonstrate in two dimensions: the relationship between the security and the index (beta) is represented by the slope of the characteristic line; the relationship between risk and returns is represented by the slope of the security market line (RM - Rf). Multi-factor models such as those developed by Rosenberg (1974), Fama and French (1992), Haugen and Baker (1996), and Chen and Zhang (2010) are proven improvements on the CAPM-inspired single-index market model in explaining the cross-section of expected stock returns and are a subject of great importance in our investments curriculum. Factor models are also widely used in practice by investment management firms. The underlying premise of these multi-factor models is that certain common factors may be identified which capture the types of risk that are rewarded over long investment horizons. In most of these models, the market index developed in the context of the CAPM is one of the factors, representing Amarket risk. @Students with exposure to the CAPM and the market model are familiar with the idea that greater risk is compensated with higher expected long-term returns. However, they often have difficulty in the application of that knowledge to the analysis of risk as it relates to security returns, especially when there are multiple risk factors to consider. In addition, when using multiple factors in models we lose the simple, two-dimensional demonstrations possible with the market model. We find that by leading the students through actual applications of alternative factor models we can provide them with a greater understanding of these models and help them to correctly analyze the characteristics which explain the systematic differences in returns across securities. We can also help them develop an understanding of these models= strengths and weaknesses in explaining returns. This assists the students in developing a quantitative approach to the security selection process and the construction of portfolios. Because of the importance of these models both in theory and practice, we cover multi-factor models in both our regular investments classes and with the participants in our student managed investment fund (SMIF), and find these exercises are useful in both settings. …