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

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5 Week 3. Fama-French and the cross section of stock returns —overheads5.1 Fama and French ”Multifactor Anomalies”1. Big Questions2. CAPM,()= (+)(a) are defined from time series regressions= + + ;(= − )(b) What we do: see if attractive opportunities ()havehigher.3. Evidence: The CAPM worked great and still does on many assets.(a) From “Discount Rates” The CAPM works great on size portfolios.−0.5 0 0.5 1 1.5−505101520BetasAverage Return1926−1979−0.5 0 0.5 1 1.502468101214Betas1980−20104. CAPM Example 2: industry portfolios1030 0.5 1 1.502468101214NoDurDurblOilChemsManufTelcmUtilsShopsMoneyOtherRfRmβE(Re)Time series regression (through Rm, Rf) Cross sectional regression Cross section, no γ 5. The Value Puzzle(a) FF. Ok for size, industry, beta portfolios. What about book/market? Do low pricesmean high returns across stocks?(b) Facts: There is a big spread in average returns. But market beta is a disaster. Puzzledependsonaveragereturnsandbetas!From “Discount rates” Growth Value −0.200.20.40.60.8E(r)β x E(rmrf)b x E(rmrf)h x E(hml)Average returnAverage returns and betasAverage returns and betas for Fama - Frenc h 10 B/M sorted portfolios. Monthly data 1963-2010.104(c) Also in “Discount Rates”0 0.2 0.4 0.6 0.8 100.20.40.60.81G23456789VRfBetasAverage return1963−20090 0.5 1 1.500.20.40.60.811.2Betas1926−1963G23456789VRfVa lu e e ffect before and after 1963.105(d) Value From Asset Pricing1061071086. Fama-French solution:(a) Run time series regressions that include additional factors (portfolios of stocks) SMB,HML= + + + + ;  =1 2 for each  =1 2(b) Look across stocks()=+ ()+()+()(c) Result from “Discount rates.” Growth Value −0.200.20.40.60.8E(r)β x E(rmrf)b x E(rmrf)h x E(hml)Average returnAverage returns and betas109(d) 25 portfolios from Asset Pricing1101117. Fama-French paper:Book/market (NYSE breaks)Size (NYSE breaks)30%30%40%S/L S/M S/HB/LB/MB/HHML = (S/H + B/H)/2 – (S/L+B/L)/2SMB = (S/L +S/M+S/H)/3 – (B/L+B/M+B/H)/3SMBHML(a) Run time series regressions that include additional factors (portfolios of stocks) SMB,HML= + + + + ;  =1 2 for each  =1 2(b) Look across stocks at the cross-sectional implication of this time-series regression (Take of both sides again):()=+ ()+()+()This w orks pretty well ( notbig)exceptforsmallgrowth.(c) “Discount Rates” one stop summary again. Now look at the sum of red solid and reddashed lines. ()= × ()+ × ().112Growth Value −0.200.20.40.60.8E(r)β x E(rmrf)b x E(rmrf)h x E(hml)Average returnAverage returns and betasAverage returns and betas for Fama - Frenc h 10 B/M sorted portfolios. Monthly data 1963-2010.8. FF(a) See FF Table 1. In depth!(b) What’s wrong with ()=()+()? “Ho w you behav e ” vs. “who youare”(c) Understand the difference between “explaining returns” (time-series regression) and “ex-plaining average returns” (cross-sectional relation between average return and beta)!(d) The main point is to produce a robust model that explains other anomalies. That iswhat the CAPM did for many years. See Sales, long term reversal. Not momentum9. Do we really need the smb portfolio? Smb makes it a better model of returns, doesn’t helpmuch on average returns, and improves precision.(a) Example: Suppose the CAPM works add a beta-hedged industry portfolio.= + + ∗= − No w run= + + ∗+ i.  0, 2improves,  statistics improve, () decreases. The model of varianceimpro vesii.³´=  ()+³∗´=  ()+0The model of mean is unchanged.113(b) This is roughly true. FF keep SMB because it is so useful to explain the variance ofsize-sorted portfolios.10. Is it a tautology to “explain” 25 B/M, size portfolios by 2 B/M, size portfolios? (No, why?) → Other sorts.11. Where does FF come from?(a) ICAPM: “State variables of concern to investors” Suppose people don’t want stocks thatfall especially (more than others) in recessions.(b) APT: “Minimalist in terpretation.” Suppose 2=1,= + + +0→³´=  ()+ ()+ ()(c) Practice: like the CAPM for digesting anomalies.12. A big picture for “dissecting anomalies” and the whole question of multivariate forecasts:≈ ∞X=1+− ∞X=1∆+ reveals to us market expectations.(a) How can help?(b) can predict both  and ∆. can predict +1and +in opposite directions.(c) Fama and French “Dissecting anomalies:” This is why additional “cashflow forecast”anomaly variables help to forecast returns.(d) “Discount rates” the cay experiment turns out to forecast the time path of returns.11413. Regressions summary.(a) Forecasting+1=  + + +1;  =1 2 (b) The “market model” of returns (return variance)= + + ;  =1 2 for eac h (c) FF’s three-factor model of returns (return variance)= + + + + ;  =1 2 for each (d) The CAPM model of mean returns. (We implicitly run this when we look at expectedreturn vs. beta. We will run this “cross-sectional regression” explicitly soon.)³´= + ;  =1 2(e) The slope coefficient in d should equal the mean market return (since its beta is one) should = (), so we sometimes force


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

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