Asset Pricing Models

Asset Pricing Models Based on Stock Return Analysis : CAPM and Fama-French Three-Factor Model

This project explores stock return behavior by applying the Fama-French Three-Factor Model, an extension of the Capital Asset Pricing Model (CAPM). The model decomposes stock returns into exposures to three key risk factors:

• Market Risk Premium (MKT-RF): Excess return of the market over the risk-free rate
• SMB (Small Minus Big): Size premium, capturing the excess returns of small-cap stocks over large-cap stocks
• HML (High Minus Low): Value premium, capturing excess returns of value stocks over growth stocks

Using monthly stock return data and corresponding Fama-French factor data, the project fits an Ordinary Least Squares (OLS) regression to estimate factor sensitivities (betas) of the stock returns. The model's explanatory power and the factor loadings provide insights into the stock’s investment style, such as size and value tilt, and its market exposure.

Additionally, the CAPM is derived as a restricted form of the Fama-French model by zeroing out the SMB and HML factors, allowing for a direct comparison of model performance.

✅ Key Highlights and Outcomes

• 📌 Objective: Analyze stock return behavior and investment style by estimating factor sensitivities using the Fama-French Three-Factor Model and comparing its performance to the CAPM.

• 📊 Data Preparation:

  • Loaded and processed monthly Fama-French factor data spanning over four decades.
  • Loaded daily stock return data, then resampled it to monthly returns to match factor data frequency.
  • Merged stock returns with factor data for regression analysis.

• 🧠 Model Fitting and Results:

  • Applied OLS regression to estimate factor loadings (betas) for the three Fama-French factors.

  • All factor coefficients were statistically significant with:

    • Market beta ~ 0.76: suggesting positive market sensitivity
    • SMB beta ~ -0.49: suggesting large-cap tilt
    • HML beta ~ 0.40: suggesting value tilt

  • Alpha (intercept) was positive and statistically significant (~0.59% monthly), suggesting potential abnormal returns not explained by the factors.

• ⚖️ Comparison with CAPM:

  • CAPM modeled by setting SMB and HML coefficients to zero, simplifying the Fama-French model.
  • Mean squared error (MSE) comparison showed the Fama-French model predicted returns better than CAPM.
  • Both models had limitations in capturing all the variability, as visible from predicted vs actual return plots.

• 📈 Visualization:

  • Plots comparing predicted cumulative returns from both models against actual returns were generated, illustrating that the Fama-French model better captures return dynamics.
  • Residual analysis and partial regression plots were used to assess model assumptions and factor contributions.

• 🎯 Insights:

  • The stock analyzed demonstrates strong value and large-cap characteristics.
  • While the Fama-French model improves over CAPM, additional factors or models may be necessary to fully capture the return drivers.