Discussion of Koijen, Lustig and Van Nieuwerburgh
For the 2011 UBC Winter Finance ConferenceMarch, 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
------------------------------------------------------------------(1)=> "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, εx
t+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=(εd
t+1, εxt+1, εs
t+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 + εi
t+1 (6)
Model Challenge: εd
t+1 = dividend growth shock εx
t+1 = expected inflation shock εs
t+1 = latent state variable shock
The Big Assumption:Δdit+1 = γ0i + γ1ist + σdiεd
t+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 + σdiεd
t+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 + σdiεd
t+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 … !
