Fama-French 3F Model

Fama &French (1992) The Cross Section of Expected Stock Return

Research Question

The relation between beta and cross sectional return is flat; can the variation in average

return be explained by variables such as size, market value, leverage, earning-price ratio

etc?

• Banz (1981) discovers that size can be used in explaining average stock return because it appears that average return on small stock is too high despite their low β and it is usually too low on large stock. This may be used as an explanatory variable.

• Bhandari (1988) finds that leverage has explanatory power on average stock return and it is not captured by stock beta as it theoretically should be.

• Statman (1980) shows that average return is positively related to the ratio of a firm’s book value to common equity.

• Basu (1983) shows that earning per share ratio can also be used in explaining average return.

Main Results of the Study!

• Beta does not seem to help explain cross section of average return,

• Although leverage and E/P may have explanatory power when tested alone their effect is dominated by size and book-to-market variables.

• This leads to the conclusion that risk might be captured by these two variables.

Data & Methodology

• All the nonfinancial firms that are listed in NYSE, AMEX and NASDAQ whose data is available in CRSP from 1963 to 1990.

• NYSE is as used as the market portfolio proxy.• Cross sectional regressions

Methodology Con’t• Form 10 size based portfolio and rank them,• Due to -0,98% correlation between size and β

subdivide each group into 10 subgroups based on their β, unrelated to the size,

• Calculate 12 month return using monthly returns on each portfolio and find the average return for full period,

• Calculate betas via time series regression over the whole period (330 months),

• Run a cross sectional regression.

Apperantly β has no significant explanatory power!

• Size related 10 portfolios show strong relation to beta but when 10 beta based sub portfolios are formed there is no significant relation observed.

• Maybe it is because other explanatory variables are correlated with β and this obscures the true relationship.

• Due to noise in beta calculation.

Jagadeesh & Titman (1993) Return to Buying Winner and Selling Losers

Research Question

• Is momentum strategy, which involves buying past winners selling the past losers a valid strategy?

• Can profitable trading strategies be constructed using momentum stocks??

Data & Methodology

• Relative strength trading strategy is analyzed based on price movement of last 3 to 12 month period.

• The data, which covers from 1965 to 1989 is from NYSE and AMEX.

Methodology Con’t

• If the stock prices over/underreact to info then profitable trading strategies based on past returns can be constructed.

• Accordingly, based on stock returns over the last 1, 2, 3, and 4 quarters portfolios are formed.

• These portfolios are held from 1 to 4 quarters in length, in total 16 different strategies examined.

• The same 16 strategies are conducted with a week lag between formation period and holding period.

Main Results of the Study

• All of the strategies generate positive return, • The stocks that generate significant abnormal

return start losing value around 12 months after the portfolio formation, and this trend continues up to 30 months, which indicates mean reverting behavior,

• The same behavior is observed around earning announcement.

Main Results of the Study

• The most profitable strategy is 12 months observation and 3 months holding, generates 1.31% monthly return. The same strategy w/ a week lag provides 1.49% per month.

• In each five year period from 1965 to 1989 just once the average return is not significant in 1975-79 due to heavy January effect.

• After the formation date first 12 month significant positive return which completely disappears after the 36th month.

• Beta (change in the riskiness of stock) cannot explain this phenomenon bc although beta changes- it went up during this period.

• Prior period 1941 to 1964 display similar pattern though not as significant.

• From 1980 to 1989 the strategy is tested around earning announcement, and on average winners generate 0,7% more than losers almost every month.

Average Size and Beta of the Portfolios

• Is it possible that winner Ps include high risk stocks systematically, or maybe size effect in place??

• It turns out that on average β of past losers is greater than β of past winners.

• Highest and lowest past return Ps are smaller than average Ps in market capitalization.

• Evidently, abnormal return is not due to risk or size!

Consider Serial Covariance of 6-month Return

• Is the source of abnormal return serial correlation between 6-month return?

• If yes we should observe positive correlation but in reality it is only -0,0028 which disproves the idea that serial correlation may be causing the abnormal return.

Profitability of Relative Strength Strategies Within Size- and Beta-based subsamples

• Stocks in 6 month/6month strategy are separated into 3 groups based on their beta and their size (Size: small-medium-big) and (beta: low-medium-high). This way the effect of size and beta will be observed if it exists.

• To further test the sub groups CAPM model is applied for portfolio return, winners minus losers, α comes out to be significant (t=3,84) for both winners and losers.

• It turns out that return on subsamples formed based on beta and size is similar to that of other strategies.

Seasonal Effect??

• It appears that only in the month of January momentum strategy losses its magnitude (almost 7% decreases in average return) but generates positive abnormal return in the rest of the year.

• Results indicate that every year in April maybe due to the fact that companies transfer money to pension funds the strategy consistently generates around 3% average monthly return.

Thank you!