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 … !