Fama-French 3-Factor Model: Regression and Stock Style Analysis

This assignment involves a financial analysis project focused on the Fama-French 3-factor model. The project utilizes real financial data for twenty stocks, employing multiple regression analysis to estimate the model. The solution details the construction of Small Minus Big (SMB) and High Minus Low (HML) factors, and the calculation of market risk premium. The student performs regression analysis to determine the significance of each factor, interpreting t-statistics and analyzing the impact of SMB and HML on individual stock returns. The assignment also classifies stocks based on their style (e.g., Small Value, Medium Neutral) according to the betas of HML and SMB. The process includes data preparation, regression execution, and the interpretation of results to discern whether a stock return significantly loads on one or more of the three factors and to discuss the empirical findings.

Assignment on Fama and French Model
Answer 1
Refer Excel
Answer 2 part a
For Small Minus Big and High minus Low factors, Fama and French model is constructed in
the following manner:
The stocks in a region are sorted in two market cap and three book to market equity groups at
the end of a particular period. Big stocks are generally in the top 90% of the end period
market cap for the region, small caps are generally in the bottom 10% of the market cap for
the region. The Book to Market Equity breakpoint generally for a region lies between the 30th
percentile and 70th percentile for the large cap stocks.
The developed portfolios use different type of size breaks instead of book to market equity.
The small minus big portfolio is the equal weighted average of the returns on the three small
stocks portfolios for the region chosen as reduced by the equal weighed average return of the
three big stock portfolios.
SMB = 1/3 (Small Value + Small Neutral + Small Growth) – 1/3 (Big Value + Big Neutral +
Big Growth).
On the other hand High Minus Low, represents the equal weighted average return for the two
high Book to Market portfolios for the chosen region as reduced by the average of the returns
for the two low Book to Market portfolios.
HML = 1/2 (Small Value + Big Value)– 1/2 (Small Growth + Big Growth).
Answer 3 part A
Market Risk Premium Small Minus Big High Minus low
Beta Beta Beta
Firm Alpha t (Alpha) MRP t (MRP) SMB t (SMB) HML t (HML)
RE 0.009033698 0.914985 0.152972437 0.602661 -0.18966 -0.46727 0.285132 0.372815
EVRG 0.006210114 0.886734 0.04347452 0.241457 0.048794 0.169478 0.049636 0.187693
ES 0.010128823 1.497477 0.372486266 2.142017 -0.57878 -2.08143 0.127129 0.497742
EXC 0.007253017 1.027057 0.236518076 1.302722 0.140933 0.485443 0.029617 0.111064
EXPE -0.00634392 -0.43502 0.863803199 2.303983 0.04634 0.077296 0.438418 0.796159
EXPD 0.009152672 1.067901 0.981737049 4.455432 0.716859 2.034545 0.592716 1.831421
EXR 0.011473233 1.224612 0.019066346 0.079157 0.152598 0.396198 -0.04933 -0.13945
XOM -0.00831563 0.007163 1.021963945 5.549196 0.563958 1.915049 0.513569 1.89863
FFIV -0.00669813 -0.60899 1.007462561 3.56284 0.304748 0.673979 0.385867 0.929078
FB 0.00009 0.007659 1.327126606 4.211093 0.222955 0.442424 -0.45848 -0.99048
FAST 0.006226647 0.53696 1.387813764 4.655117 0.089445 0.187626 0.491719 1.122957
FRT -0.00061313 -0.07324 0.449415792 2.088078 0.458543 1.332348 0.367127 1.161345
FDX -0.01953432 -1.98774 1.695313916 6.709994 0.04428 0.109601 0.182985 0.493099
FIS 0.006369312 1.102694 0.505134786 3.401586 -0.1595 -0.67171 -0.58672 -2.68998
FITB 0.003765901 0.501388 1.357284639 7.0289 -0.20909 -0.67714 1.412078 4.978769

Market Risk Premium Small Minus Big High Minus low
Beta Beta Beta
Firm Alpha t (Alpha) MRP t (MRP) SMB t (SMB) HML t (HML)
FE 0.011320354 1.50863 0.325405133 1.686781 -0.28271 -0.91647 -0.00454 -0.01602
FRC 0.013619582 1.474643 0.768284725 3.235615 1.204179 3.171498 0.602045 1.726277
FISV 0.008142891 1.200203 0.794543591 4.555177 -0.1406 -0.50409 -0.48999 -1.91261
FLT 0.003561751 0.33658 1.077230934 3.959546 -0.49278 -1.13273 -0.44621 -1.11665
FLIR -0.00317452 -0.27075 1.499840478 4.975663 -0.04645 -0.09637 0.013757 0.031073
The above computation has been done in the following manner:
Step 1:
The above computation has been done by taking difference between the return earned by the
stock as reduced by risk free rate of return for that particular month.
Step 2:
The resultant outcome of the above step has been considered as the Y factor/ variable for the
purpose of regression analysis.
Step 3
Consideration of Market Risk Premium, Small minus Big and High Minus Low as the
independent variable in the regression analysis.
Step 4
Usage of Data tab and data analysis tool
Step 5
Usage of Regression and run of software.
Step 6
Obtaining Analysis of Variance table.
Analysis of T statistic
Degree of importance of t statistic depends on the level of significance chosen for the purpose
of analysis. If the analysis is made at 95% confidence interval and two tails has been
considered then the value of t stat shall range between -1.96 to + 1.96 and any variable
between it shall be considered statistically significant. Further, if the confidence interval is set
at 99% then the value of t stat shall be in the range of + 2.33 to -2.33 and any variable
between it shall be considered statistically significant.
Answer 3 part B
Firm Style Remark
RE Small Value Beta of HML is low and Beta of SMB is negative
EVRG Small Value Beta of HML is low and Beta of SMB is low
ES Small Value Beta of HML is low and Beta of SMB is negative

EXC Medium Value Beta of HML is low and Beta of SMB is medium
EXPE Small Neutral Beta of HML is Medium and Beta of SMB is low
EXPD Medium Neutral Beta of HML is medium and Beta of SMB is medium
EXR Small Value Beta of HML is negative and Beta of SMB is low
XOM Medium Neutral Beta of HML is medium and Beta of SMB is medium
FFIV Small Value Beta of HML is low and Beta of SMB is low
FB Small Value Beta of HML is negative and Beta of SMB is low
FAST Small Neutral Beta of HML is Medium and Beta of SMB is low
FRT Small Neutral Beta of HML is Medium and Beta of SMB is low
FDX Small Value Beta of HML is low and Beta of SMB is low
FIS Small Value Beta of HML is negative and Beta of SMB is negative
FITB Small Growth Beta of HML is high and Beta of SMB is negative
FE Small Value Beta of HML is negative and Beta of SMB is negative
FRC Large Medium Beta of HML is medium and Beta of SMB is high
FISV Small Value Beta of HML is negative and Beta of SMB is negative
FLT Small Value Beta of HML is negative and Beta of SMB is negative
FLIR Small Value Beta of HML is low and Beta of SMB is negative
For the purpose of analysis, Beta of HML and beta of SMB has been considered. If beta of
SMB is low and HML is low, then the style shall be considered as Small Value stock.
Similarly, if the Beta of HML and beta of SMB is high, then the style shall be considered as
High Growth Stock. Similarly, for medium beta of HML and SMB, the style of investing has
been classified as Medium Neutal.