🎮 Finance Factor Model Game - Learn Stock Returns!

Follow the steps to calculate expected returns for different stock types! Click a stock to proceed.

📉 Market & Risk-Free Rate

📚 Learn About Factor Models

In finance, we use models to estimate stock returns. The simplest model is the **Capital Asset Pricing Model (CAPM)**, which uses the risk-free rate, market return, and beta to estimate expected returns. However, research shows that other factors impact stock returns. This led to the **Fama-French Three-Factor (FF3) Model** and later the **Fama-French Five-Factor (FF5) Model**.

🔢 CAPM Formula

E(R) = R_f + beta * (R_m - R_f)
Where:

• R_f = Risk-Free Rate
• R_m = Market Return
• beta = Stock’s sensitivity to the market (obtained from historical regression analysis)

📊 Fama-French Three-Factor (FF3) Model

FF3 improves on CAPM by adding two factors:

• **SMB (Small Minus Big)**: Small-cap stocks tend to outperform large-cap stocks.
• **HML (High Minus Low)**: Value stocks (high book-to-market ratio) tend to outperform growth stocks.

📈 Fama-French Five-Factor (FF5) Model

FF5 further refines FF3 by adding two more factors:

• **RMW (Robust Minus Weak)**: Companies with high profitability tend to perform better.
• **CMA (Conservative Minus Aggressive)**: Companies that invest conservatively outperform those with aggressive investment.

📊 How to Get beta_2, beta_3, beta_4, beta_5 (Factor Loadings)

The additional factor loadings beta_2, beta_3, beta_4, beta_5 are obtained using **multiple regression analysis**. This is done by regressing a stock’s **historical excess returns** on the Fama-French factor returns. Here’s how:

1. Get **historical stock returns** (monthly or annual).
2. Get **risk-free rate** and **factor return data** (SMB, HML, RMW, CMA) from Kenneth French’s Data Library.
3. Calculate **excess returns**: Excess Return = Stock Return - R_f
4. Run a **multiple regression**: Excess Return = beta_1 * (R_m - R_f) + beta_2 * SMB + beta_3 * HML + beta_4 * RMW + beta_5 * CMA + epsilon
5. From the regression output, **beta_1, beta_2, beta_3, beta_4, beta_5** are estimated coefficients, representing the sensitivity of the stock to each factor.

📌 What These Betas Mean

• ** beta_1 (Market Beta)**: Stock’s sensitivity to overall market movements.
• ** beta_2 (SMB Beta)**: Higher means stock behaves like a small-cap stock.
• ** beta_3 (HML Beta)**: Higher means stock behaves like a value stock.
• **beta_4 (RMW Beta)**: Higher means stock benefits from high profitability.
• **beta_5 (CMA Beta)**: Higher means stock performs well when companies invest conservatively.

If a stock has a high beta_2 (SMB), it behaves like a **small-cap** stock. If it has a high beta_3 (HML), it behaves like a **value** stock. Combining these betas helps estimate a stock’s expected return more accurately than CAPM alone.

To apply these models, enter the SMB, HML, RMW, and CMA values from Kenneth French’s Data Library and calculate expected returns!