FAMA-FRENCH MODEL Concept and Application

Learning Objectives Concept of Fama and French model Concept of three risk factors in the model The interpretation of the model The pros and cons of the model 8 steps to use the Fama and French model An empirical study in UK market

Fama and French Literature on Factor Models An alternative asset pricing model to CAPM Three risk factors affecting asset expected return (Fama and French, 1993) Market risk premium Size effect or size premium Book-to-Market value effect or value premium

Model/ Formula (Fama-French, 1993) Rit – Rft = αit + βiM (RMt - Rft) + βisSMBt + βihHMLt + εit Rit is the total return of individual stock/portfolio i Rft is the risk free asset return RMt is the total market portfolio return Rit – Rft is expected excess return RMt - Rft is the excess return on a market portfolio index SMBt is the size premium HMLt is the value premium

Steps for Fama-French, 1993 Step 1: Collecting data Step 2: Construct portfolios formed on Size and value Step 3: Calculate average returns of each portfolio Step 4: calculate SMB Step 5: Calculate HML Step 6: Calculate Rit – Rft Step 7: Calculate RMt - Rft Step 8: Running multiple regression

STEP 1: Collecting data Book-to-market ratio (BE/ME) Market Capitalization (Market Cap) Monthly stock price including dividend Risk free rate of return (Rf): short-date Treasury Bills Market Return (Rm): monthly market index return

STEP 2: Construction of six Portfolio S/L Represented the group of portfolio that have a small size and low book-to-market value S/M Represented the group of portfolio that have a small size and medium book-to-market value S/H Represented the group of portfolio that have a small size and high book-to-market value B/L Represented the group of portfolio that have a big size and low book-to-market value B/M Represented the group of portfolio that have a big size and medium book-to-market value B/H Represented the group of portfolio that have a big size and high book-to-market value

Step 3: Calculate average returns of each portfolio Calculate the average return of each observed stock Calculate the average return of six constructed portfolios

Step 4: Calculate SMB Based on the formula: SMB= 1/3(Small Low + Small Medium + Small High) – 1/3(Big Low + Big Medium + Big High)

HML= ½(Small High + Big High) – ½ (Small Low + Big Low) Step 5: Calculate HML Based on the formula: HML= ½(Small High + Big High) – ½ (Small Low + Big Low)

Step 6: Calculate Rit – Rft Calculating stock return (Rit) Subtracting risk free rate of return from average return of each portfolio Rit= 𝑃 𝑖 − 𝑃 𝑖−1 𝑃 𝑖−1 (Rit x 100 – Rft x 100)

Step 7: Calculating Rmt – Rft Calculating Market return (Rmt) Subtracting risk free rate of return from market return Rmt= 𝑃 𝑖 − 𝑃 𝑖−1 𝑃 𝑖−1 (Rmt x 100 – Rft x 100)

Step 8: Running multiple regression Diagnostic tests (Nonstationary, Autocorrelation, Heteroscedasticity and Multicollinearity) Running multiple regression for one dependent (Rit – Rft) and three independent variables (Rmt – Rft), SMB and HML). Could use Excel or SPSS or Eviews software.

An Application using UK FTSE100 Data London Stock Exchange FTSE100 Period: 2009-2013 Monthly data Times series multiple regression test Sample: 94 stocks SEE EXCEL FILE

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