TASK: Use the Fama-French Three Factors model to estimate the cost of equity for Walmart.
An example lesson to refer to is below (for Costco). To use the CAPM approach for Costco, let's assume that the risk-free rate is about 2% (based on the 10-year Treasury yield in May 2013) and a Value Line β for Costco of 0.75 (as of May 2013). With a market risk premium of 5%, the cost of equity kE for Costco is: 2% + 0.75 • 5% = 5.75%.
The FF Three Factors model: this model was developed by Fama and French (1995) and uses a time series regression of monthly returns on 3 independent variables. Specifically, the regression model is as follows:
Equation: Ru - Rft = βi • (Rmt - Rft) + (si • SMBt) + (hi • HMLt) + εit
In Equation 3.13., the left hand side (dependent variable) is the monthly excess returns of stock i over risk-free rate of return. The first independent variable on the right hand side of Equation 3.13., (Rmt - Rft), is the monthly excess returns on the market index. The second independent variable, SMBt, is the difference between monthly returns of small-cap stocks and large-cap stocks. The third independent variable, HML t, is the difference in monthly returns between high book-to-market stocks and low book-to-market stocks. The coefficients βi, si, and hi measure the sensitivity of stock i's returns on these three factors.
1. Estimating the cost of equity using this model uses the following equation:
Equation 3.14: kE = Rf +(βi • MRP) + (si • SMBP) + (hi • HMLP)
MRP is the market risk premium. SMBP is the expected size premium estimated using historical average annual returns on the small-cap and large-cap stocks. HMLP is the expected value premium estimated using historical average annual returns on the high book-to-market and low book-to-market stock portfolios. The coefficientsβi, s i, and h i are estimated from the time series regression Equation 3.13.
2. The Ibbotson Beta Book (now published by Morningstar) contains an estimate of the FF β coefficient, the SMB premium, and the HML premium for each company. So, to compute kE using Equation 3.14., we only need to get Rfand market risk premium (MRP). Rf is the yield on the Treasury bond and is available from the Federal Reserve's website. The MRP is assumed to be between 4.5% and 5.5% based on the earlier recommendation by Koller, Goedhart, and Wessels.
3. If you have no access to the Ibbotson Beta Book, then you need to run the time series regression Equation 3.13. yourself. Five data series need to be collected: the monthly returns of stock i, market index, and risk-free rate, as well as the monthly SMB and HML factor returns. You may get the historical price data for stock i from Yahoo! Finance. Data on the other four series is available from Professor French's website. From his website, click the U.S. Research Returns on the left panel (the first bullet point under Data Library). You will be directed to the section that contains downloadable data files. Choose the Fama/French Factors, as shown by Figure 3.17., to download a zip file that contains monthly data for four series needed to run time series regression Equation 3.13.
4. Before running the time series regression, make sure that you have converted the historical price series that you downloaded from finance.yahoo.com into a monthly returns series. Then, combining this monthly return series with the monthly data for four series from Professor French's website into a single Excel file. Figure 3.18 displays the combined file for Costco:
5. Run the time series regression Equation 3.13. with monthly series in column H as the dependent variable, and the series in columns D, E, and F as the three independent variables.