Empirical Analysis of US Equity Portfolio Returns Using Econometric Modelling Assessment

Assessment

Objectives

• Select your portfolio and compute descriptive statistics for its monthly returns. 
• Estimate two regression models:
  • Model 1: Capital Asset Pricing Model (CAPM) 
  • Model 2: Fama-French 3-Factor Model.
• Discuss the empirical results in terms of intuition, statistical significance, and goodness-of-fit. 
• Run full diagnostic tests for each regression model and interpret results. 
• Compare the two models and identify which provides a more meaningful fit to your dataset.

Task

You are required to work individually on an empirical project. Although you should feel free to discuss aspects of your project with your fellow students if you wish, each student must be responsible for their own individual work. The project's main objective is to perform an econometric analysis on the returns of a US equity portfolio, with the aim of identifying which of two candidate models best fits the data.

This empirical project is based on actual market data of US equity returns. All the data that will be required for the empirical analysis is available on Moodle in the spreadsheet “Assignment 1 [DATA].xlsx.” This file contains the time-series of monthly returns for 100 US equity portfolios, plus the time-series of 3 market factors. As a first step, each student will need to select ONE portfolio, and this portfolio will constitute that student's dependent variable of interest. The spreadsheet contains the monthly returns of 100 portfolios formed based on size and book-to-market.

The sample spans over 55 years, from January 1970 to December 2024. The stocks included in each portfolio vary from relatively small (Size 1) to very large (Size 10), and from high growth (BM 1) to high value (BM 10). For example, the portfolio [Size 10 - BM 1] includes large, growth companies. The spreadsheet also contains a set of exogenous variables that might explain the returns of your portfolio:

• MKT: excess return of the market 
• SMB: return of small minus large stocks 
• HML: return of high-BM minus low-BM stocks

Brief Summary of Assessment Requirements

The assessment required students to conduct an empirical econometric analysis on US equity portfolio returns to determine which of two modelsthe Capital Asset Pricing Model (CAPM) or the Fama-French 3-Factor Modelprovides a better fit for the data. Students were instructed to:

• Select one portfolio from the provided dataset of 100 US equity portfolios (spanning January 1970 – December 2024).
• Compute descriptive statistics for the chosen portfolio’s monthly returns to understand its distribution, variability, and performance behavior.

• Estimate two regression models:

  • Model 1: CAPM to assess the relationship between the portfolio’s excess return and the market’s excess return.
  • Model 2: Fama-French 3-Factor Model to include additional risk factors such as size (SMB) and value (HML).
• Interpret and discuss the regression outputs based on statistical significance, economic intuition, and the overall goodness-of-fit.
• Run diagnostic tests for both models (to check for heteroscedasticity, autocorrelation, normality, and model specification).
• Compare results and justify which model best explains the variation in portfolio returns.

The assessment aimed to enhance analytical proficiency, econometric modeling skills, and understanding of asset pricing theories.

Mentor-Guided Approach and Step-by-Step Process

The academic mentor guided the student through a structured, evidence-based process to ensure conceptual clarity and methodological rigor throughout the analysis:

1. Portfolio Selection and Data Familiarization

   The mentor began by explaining the dataset structure100 portfolios categorized by size and book-to-market ratioand helped the student select a representative portfolio that reflects a realistic investment case. Guidance was given on understanding variables like MKT, SMB, and HML, along with their theoretical relevance.

2. Descriptive Statistical Analysis

   The mentor demonstrated how to compute and interpret key descriptive statistics (mean, standard deviation, skewness, kurtosis) using Excel and statistical software. This step helped the student understand the portfolio’s risk-return profile before applying econometric models.

3. Model Estimation (CAPM and Fama-French 3-Factor)

   The mentor guided the student in formulating both regression equations:

   • CAPM: Ri−Rf=α+β(Rm−Rf)+ϵR_i - R_f = \alpha + \beta (R_m - R_f) + \epsilonRi−Rf=α+β(Rm−Rf)+ϵ

   • Fama-French: Ri−Rf=α+β1(Rm−Rf)+β2SMB+β3HML+ϵR_i - R_f = \alpha + \beta_1 (R_m - R_f) + \beta_2 SMB + \beta_3 HML + \epsilonRi−Rf=α+β1(Rm−Rf)+β2SMB+β3HML+ϵ
     Detailed discussions were held on interpreting coefficientsparticularly how beta captures systematic risk and how additional factors (SMB, HML) refine model accuracy.

4. Interpretation of Results and Model Diagnostics

   The mentor emphasized the importance of economic reasoning along with statistical interpretation. The student learned to analyze the R⊃2; value, p-values, and t-statistics, and to perform diagnostic checks for assumptions such as linearity, homoscedasticity, and normality. This ensured model validity and robustness.

5. Model Comparison and Discussion

   Under mentor supervision, the student compared both models’ explanatory power and diagnostic outcomes. The discussion focused on how the inclusion of SMB and HML improved model fit, thus supporting the Fama-French model as a better explanatory framework for portfolio returns.

6. Conclusion and Learning Reflection

   The mentor guided the student in synthesizing findings into a cohesive conclusion, linking theoretical knowledge with empirical evidence. The student reflected on how econometric modeling deepens understanding of financial risk factors and enhances practical research competence.

Outcome and Learning Objectives Achieved

Through mentor-led guidance, the student successfully:

• Applied quantitative and econometric techniques to real-world financial data.
• Demonstrated understanding of asset pricing models and their implications.
• Developed skills in data analysis, interpretation, and statistical validation.
• Enhanced ability to communicate complex financial concepts to both technical and non-technical audiences.

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