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## Discussion of Koijen, Lustig and Van Nieuwerburgh

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**Discussion of Koijen, Lustig and Van Nieuwerburgh**For the 2011 UBC Winter Finance Conference March, 2011 By Wayne Ferson University of Southern California**"The Cross-section and Time Series of Stock and Bond**Returns:" ● The Main Empirical Nuggets: (1) Δd more Cyclical for Value than Growth (2) Loadings on Bond yield factors (CP) monotonic across B/M quintile sorts ● Model Challenge: Connect (1) and (2)! ● The Lewellen, Nagel, Shanken (2010) Critique ● Smaller Things..**Model Challenge:**● Connect the Empirical Nuggets: (1) Δd More cyclical for Value than Growth (2) Bond yield factor (CP) loadings monotonic in B/M quintile sorts ● Main Empirical Design: 5 + 5: B/M + Bond Mats ------------------------------------------------------------------ => "Value riskier than Growth.“ ● Bond yield loadings capture bonds. ● The Market Prices the market. Should be lots of "3-factor models" that can articulate these dimensions! ------------------------------------------------------------------- Table I: its Var(1) shocks to {CP,yields, Rm}**Model Challenge:**"Standard Affine Model" -mt+1 = yt + (1/2)Λt'Λt + Λt'εt+1 εt+1=(εdt+1, εxt+1, εst+1)~ NID(0,.) εdt+1 = dividend growth shock εxt+1 = expected inflation shock εst+1 = latent state variable shock**Model Challenge:**εt+1=(εdt+1, εxt+1, εst+1)~ NID(0,.) εdt+1 = dividend growth shock εxt+1 = expected inflation shock εst+1 = latent state variable shock st+1 = ρsst + σsεst+1 Assert: st = CP! The Big Assumption: Δdt+1 = γ0 + γ1st + σdiεdt+1 + εit+1 (6)**Model Challenge:**εdt+1 = dividend growth shock εxt+1 = expected inflation shock εst+1 = latent state variable shock The Big Assumption: Δdit+1 = γ0i + γ1ist + σdiεdt+1 + εit+1 (6) Bond yields = An + Bn st + Cn xt, => CP shocks = f(εs,εx), not εd ! Stock Et(rit+1) = A γ1i + σdi [Affine in st]**Model Challenge:**Δdit+1 = γ0i + γ1ist + σdiεdt+1 + εit+1 (6) Stock Et(rit+1) = A γ1i + σdi [Affine in st] It’s the γ1i that (somehow) drives Value-Growth through st = CP * γ1i = Loading on lagged yield predictor (cf. Ferson and Harvey (JF 99) * Need to check specification of (6) VERY seriously in the data !**Calibration Issue:**Δdit+1 = γ0i + γ1ist + σdiεdt+1 + εit+1 (6) Calibration overstates: γ1VALUE - γ1GROWTH * Div growth differences from peak to last month of recession: Sample Max - Min is like an order statistic! * Model says γ1i = ∂Et(Δdt+1)/∂st => Exante is smoother than expost!**LNS (2010) Critique:**"The heart of our critique is that the literature has inadvertently adopted a low hurdle …because the size-B/M portfolios are well known to have a strong factor structure, in particular, FF’s factors explain more than 90% of the time variation in the (FF) portfolios’ realized returns and more than 80% of the cross-sectional variation in their average returns…. We show that …. almost any proposed factor(s) are likely to line up with expected returns—basically all that is required is for a factor to be (weakly) correlated with SMB or HML but not with the tiny, idiosyncratic three-factor residuals of the size-B/M portfolios."**LNS (2010) Critique:**Suppose exist 3 Factors, F, for the 5 + 5 + Rm design: r = Fβ + u. Suppose exist 3 variables, X with: Cov(X,F)≠0 and Cov(X,u)≈0 ("Strong factor structure") Write X = F V(F)-1Cov(F,X) + v, v┴r, So Cov(r,X)= Cov(r,F) V(F)-1Cov(F,X) And E(r) = Cov(r,F)V(F)-1λ = Cov(r,X) [V(F)-1Cov(F,X)]-1λ = Cov(r,X) λ***Implications of the LNS Critique:**How High is the Bar in your Designs? 1. Show us the factor structure of your BM + Bond + Rm design: Regress the 11 returns on Rm, HML, Long-Short Bond. If R2 is high, take the critique seriously! 2. Corporate Bond Alt. Sample: But is C.Bond ≈ w Stox + (1-w) Tbond? Regress C.Bond on the previous portfolios. Is R2 high? Intercepts? Test for mean variance spanning?**Implications of the LNS Critique:**How High is the Bar in your Designs? Individual Stocks - Now We Are Talking! * Don't wait until Page 42! * Rolling βi,CP sorts quintiles with a spread on returns and CAPM ά (2.6-3.1%), also work in 2-way sorts with BM. => Suggestive, but not a full blown test! => Do the tests!**Final Shots (Suggestions):*** Include D/P (or ∆d) Sorted Portfolios! * Check the Total Payout Definition of Dividends. * Refine your nulls and alternatives: We have ά's and λ's and standard errors: Ho: Model is perfect (ά=0), Ha: Its not. Ho: Factor not priced (λ=0), Ha: Its priced The story seems much richer than this … !