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Chicago Booth BUSF 35150 - Fama-French and the cross section of stock returns — detailed notes

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Week 3 Fama French and the cross section of stock returns detailed notes 1 Big questions di erent from 2004 2005 a Last week does expected return vary over time Is 1999 2000 If so why Something about higher risk premium in recessions but we didn t really answer that one coming soon b This week does expected return vary across assets Is di erent from If so why c As we will see they are really not so distinct questions but for now the separation is conceptually useful 2 Background a CAPM b are defined from time series regressions c What we do look to see if high average returns are matched by high 3 The CAPM worked for many years a The CAPM on size portfolios frrom Discount Rates 1980 2010 1926 1979 20 14 12 15 Average Return 6 10 10 8 5 6 4 0 2 5 0 5 0 0 5 Betas 1 1 5 0 0 5 0 0 5 Betas 1 1 5 CAPM on Fama French size portfolios and 10 and 30 year government bonds montlhy data 1926 2009 The diagonal line is the fit of a cross sectional regression See also Asset Pricing plots Points i What this is each year sort all stocks by size total market equity Form 10 portfolios of small large stocks Look at the average returns and betas of the portfolios 117 ii The small firm portfolio has much higher than large firm portfolio Thus yes does seem to vary across assets Does this mean you should buy small stocks Not necessarily The small firm beta is much larger than large firm beta iii The size anomaly is the small amount by which the smallest firm portfolio lies too far above the line This is a glass that s 90 full iv Interestingly the anomaly in pre 79 data disappeared when CRSP cleaned up data b Thus the explanation given by the CAPM where are defined from time series regressions subtracts T bill rate i Note is a cross sectional relation The issue is that some assets have higher average returns than others It s not about predicting returns ii Portfolios have large because they have large is the thing to be explained is the right hand variable and is the slope coe cient or often iii are the errors the amount by which the CAPM is wrong the expected return earned above and beyond compensation for risk iv If we say it represents a premium for risk Not small stocks are good they pay higher but Small stocks are so risky they must pay a high to get people to hold them This is like our time series investigation in bad times is high You might think the opposite high means it s a good time to invest But if we all invested we d drive the price up and expected return down Di erentiate when you re asking about equilibrium vs your own portfolios v The slope should be the mean market return 1 so 1 That s why we usually write I like to emphasize this is the slope in the graph of vs but it s the same thing vi The size portfolios were a a rejection of the CAPM the smallest firm was statistically significant No longer in these data but an open debate vii Fama and French like tables of numbers You have to understand the idea equation or plot to know what they re talking about viii Why does the CAPM Explain the simplest version is suppose a security gets an average return twice the market but also has a beta of two Well I can get that same average return and same or less risk by just leveraging up the market or buying index futures etc 118 ix A bit more carefully if you hold the market portfolio and if a security has zero alpha if an expected return higher than the market return is matched by a beta higher than market beta then adding a bit of the security to your portfolio will not improve your portfolio s Sharpe ratio It will be just like levering up your market index 4 CAPM Example 2 industry portfolios 14 12 Durbl 10 Oil NoDur E R 8 Manuf Rm Telcm Utils Cross sectional regression e Chems MoneyShops Other 6 4 Cross section no Time series regression through Rm Rf 2 0 Rf 0 0 5 1 1 5 It s not perfect but the spread in average returns is related to betas a This is an example of how the CAPM worked ok in application after application for 20 years It s still a bit of a puzzle as the SML is too flat But we can make excuses for that betas are badly measured etc It doesn t scream that the model is wrong b However there is always a telescope a way to make small looking errors big and profitable If the too flat SML is real it invites beta arbitrage buy low beta stocks and short high beta stocks Frazzini s paper in the readings explores this fact and AQR is trading on it 5 The Value Puzzle a FF The CAPM works OK for size industry beta sorted portfolios and many others all the ones anyone tried from 1970 to about 1990 What about book market sorted portfolios b Inspiration like but across assets X 1 1 Thus if there are stocks with higher for whatever reason high they will have lower D P reveals to us which assets times have high low expected returns by investors FF use B M not D P because B is better across firms than dividends or earnings Many firms have 0 0 119 c Thus we should see low price High B M stocks have high average returns It s not surprising that value stocks have higher expected returns AND we should see them have high Expected return alone is not a puzzle All puzzles are joint puzzles of expected return and beta either high expected returns not matched by high betas or high low betas not matched by expected returns d Facts There is a big spread in average returns But market beta is a disaster From Discount rates The line rises as you go to value but the and lines do not comes from a single regression comes from the multiple regression with FF factors too Average returns and betas 0 8 E r Average return 0 6 b x E rmrf 0 4 x E rmrf 0 2 h x E hml 0 0 2 Growth Value Average returns and betas for Fama French 10 B M sorted portfolios Monthly data 1963 2010 e Note also in Discount rates the di erence pre and post 1963 Value portfolios gave higher average returns in the earlier period as they do now But the CAPM worked pretty well The betas were right The big puzzle post 63 is that the betas changed not the pattern of average returns Again all puzzles are joint puzzles of average returns and betas 120 1963 2009 1926 1963 1 V Average …


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Chicago Booth BUSF 35150 - Fama-French and the cross section of stock returns — detailed notes

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