**Unformatted text preview: **Fama-French ThreeFactor Analysis Learning Objectives • Describe the Fama-French three-factor model
• Build a regression model in Excel
• Analyze how well an asset’s returns are explained by
the Fama-French three-factor model From a Single to MultiFactor ModelR = asset return
i • The traditional regression
model for analyzing excess
returns is the Capital Asset
Pricing Model (CAPM), a
single-factor model:
(� �−� �) = � � + � � (� ��� −� �) + ei
• The model stipulates
there is only one risk
factor: the return on
the market portfolio. Rf = risk-free rate of return
�i = difference between the asset’s
return and the expected return
βi = measure of the asset’s
systematic risk in relation to the
market
RMKT = the market return
ei = random error/non-systematic risk From a Single to MultiFactor Model (cont.)
• According to the CAPM theory, in the previous slide’s
equation, � (alpha) should equal 0. However, that is not
always the case.
• Researchers began investigating models where additional
factors (e.g. interest rates) could be added to the market
factor in order to better explain excess returns.
• Analyzing historical data, Eugene Fama and Kenneth French
noticed that small-cap stocks and value stocks tended to
outperform large-cap stocks and growth stocks. Fama-French ThreeFactor Model
• Fama and French added a size factor and a value factor to
the market factor:
(� �−� �) = � � + � � (� ���−� �)+ si(SMB) + hi(HML) + ei
• Empirically, their three-factor model explained historical
returns better than the single-factor market model,
explaining over 90% of excess returns as opposed to
approximately 70%. Size: (SMB) Small Minus
Big
(� �−� �) = � � + � � (� ���−� �)+ si(SMB) + hi(HML) + ei
• The size premium (SMB) is the average monthly return
on the smallest 30% of stocks (in terms of market
capitalization) minus the average monthly return on the
largest 30%.
• When small stocks do well relative to large stocks, this
will be positive; when they do worse than large stocks,
this will be negative. Value: (HML) High Minus
Low
(� −� ) = � + � (� −� )+ s (SMB) + h (HML) + e
� � � � ��� � i i i • The value premium (HML) is the average monthly return
for the 50% of stocks with the highest book-to-market ratio
minus the average return for the 50% of stocks with the
lowest book-to-market ratio.
• When high value stocks do well relative to low value stocks,
this will be positive; when they do worse than low value
stocks, this will be negative.
• High book-to-market stocks are considered “value” stocks;
low book-to-market stocks are considered “growth” stocks. Factor Betas
• Extending the single factor CAPM model, the Fama-French
model uses three factor betas: (� �−� �) = � � + � � (� ���−� �)+ si(SMB) + hi(HML) + ei
• A factor beta (sometimes called a “factor loading”) is the
sensitivity of security’s returns to a particular systematic
factor.
• With this model, market returns can roughly be
explained by three factors: (1) exposure to the overall
market (RMKT - Rf); (2) exposure to small cap stocks (SMB);
and (3) exposure to value stocks (HML). The Fama-French
Factors
• Ken French publishes datasets of the Fama-French factors
for distribution from his web site at Dartmouth University.
• For more detailed information on how these factors were
calculated, visit his web site at:
a_library.html
• As research continues, additional factors continue to be
added to the original three-factor model. Assignment
•Use a WRDS query to select and download
historical monthly returns for two exchange-traded
funds (ETFs).
•The Fama-French three-factor data will be
provided in this query’s output. Conclusion
•In the Capital Asset Pricing Model, the market portfolio return is the sole
source of risk.
•The Fama-French three-factor model suggests that portfolio returns can
roughly be explained by three factors:
(1) exposure to the broad market (RMKT - Rf)
(2) exposure to small stocks (SMB)
(3) exposure to value stocks (HML) •A factor beta represents the sensitivity of a portfolio’s returns to changes in a
systematic factor. Notes (cont.)
For Fama-French data:
• Monthly returns on the market portfolio are value-weighted
returns for all firms listed on the NYSE, AMEX, and NASDAQ.
• The risk-free rate is the return on 1-month T-bills.
• Additional information is available on Ken French’s web site:
ndex.html ...

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- Spring '14
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- Capital Asset Pricing Model, Kenneth French