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Discussion of Koijen, Lustig and Van Nieuwerburgh

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:

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Discussion of Koijen, Lustig and Van Nieuwerburgh

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  1. Discussion of Koijen, Lustig and Van Nieuwerburgh For the 2011 UBC Winter Finance Conference March, 2011 By Wayne Ferson University of Southern California

  2. "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..

  3. 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}

  4. 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

  5. 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)

  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]

  7. 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 !

  8. 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!

  9. 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."

  10. 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*

  11. 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?

  12. 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!

  13. 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 … !

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