A Comparison of New Factor Models

Transcription

1 A Comparison of New Factor Models by Kewei Hou, Chen Xue, Lu Zhang Discussion by Christian Opp The Wharton School March 20, 2015

2 Overview Comparison of the q-factor model and the FF 5-factor model both on conceptual and empirical grounds My focus: HXZ s conceptual critique of FF14 Conceptual differences are largely about different assumptions about dynamics in investment, expected returns, etc... Check internal consistency of arguments Overall: q-theory framework is a useful way to motivate characteristics that measure variation in expected returns Note: q-theory cannot rationalize expected returns

3 Q-Theory Review Standard q-theory optimality condition: MC t = MBt+1 E t[r t+1]

4 Q-Theory Review Standard q-theory optimality condition: MC t = MBt+1 E t[r t+1] E t [R t+1 ] = E t [ F CFt+1 MC t ] + Pt+1

5 Q-Theory Review Standard q-theory optimality condition: MC t = MBt+1 E t[r t+1] E t [R t+1 ] = [ ] E F CFt+1 t + Pt+1 = MC t }{{} * One-period [ ] E P rofitt+1 t K t a Invt K t *... quadratic adj. cost, constant returns to scale, no depreciation...

6 Q-Theory Review Standard q-theory optimality condition: MC t = MBt+1 E t[r t+1] E t [R t+1 ] = [ ] E F CFt+1 t + Pt+1 = MC t }{{} * One-period [ ] E P rofitt+1 t K t a Invt K t *... quadratic adj. cost, constant returns to scale, no depreciation... Predictions given one-period model: Low current investment, fixing future profitability high E t[r t+1] High future profitability, fixing current investment high E t[r t+1] Additional assumption on dynamics (to motivate factors):

7 Q-Theory Review Standard q-theory optimality condition: MC t = MBt+1 E t[r t+1] E t [R t+1 ] = [ ] E F CFt+1 t + Pt+1 = MC t }{{} * One-period [ ] E P rofitt+1 t K t a Invt K t *... quadratic adj. cost, constant returns to scale, no depreciation... Predictions given one-period model: Low current investment, fixing future profitability high E t[r t+1] High future profitability, fixing current investment high E t[r t+1] Additional assumption on dynamics (to motivate factors): Future profitability = current profitability

8 Comparing to Valuation Theory Reconciling with standard present value identity used by FF14... E t [R t+1 ] = E t [F CF t+1 + P t+1 ] P t

9 Comparing to Valuation Theory Reconciling with standard present value identity used by FF14... E t [R t+1 ] = E t [F CF t+1 + P t+1 ] P t E t [F CF t+1 + MC t+1 K t+1 ] }{{} = MC t K t ** ** use previous assumptions so that q = MC = P K Observations: Naturally, both models discount future dividends / FCFs Disagreement with FF stems from different beliefs about dynamics of various variables (not from q-theory vs. PV eqn.): 1. FF use constant E t[r t+1] = R to motivate factors 2. FF use persistence in investment to motivate factors What does q-theory say about those two?...

10 Critique 1: The Momentum Critique HXZ: FF s constant R assumption is flawed...the internal rate of return can correlate negatively with the one-period-ahead expected return If so, what does q-theory predict for investment in long-term project?

11 Critique 1: The Momentum Critique HXZ: FF s constant R assumption is flawed...the internal rate of return can correlate negatively with the one-period-ahead expected return If so, what does q-theory predict for investment in long-term project? E t [R t+1 ] = E t[ F CF t+1 + encodes all E[R t+τ ] {}}{ P t+1 ] MC t

12 Critique 1: The Momentum Critique HXZ: FF s constant R assumption is flawed...the internal rate of return can correlate negatively with the one-period-ahead expected return If so, what does q-theory predict for investment in long-term project? E t [R t+1 ] = E t[ F CF t+1 + encodes all E[R t+τ ] {}}{ P t+1 ] MC t Main thought experiment: Fixing future profitability, how reconcile low investment (= low MC t)? Ambiguous q-theory prediction for E t [R t+1 ] due to Pt+1! 1. High E t[r t+1] but low future E t[r t+τ ] for τ > Low E t[r t+1] but future high E t[r t+τ ] for τ > 1.

13 Critique 1: The Momentum Critique HXZ: FF s constant R assumption is flawed...the internal rate of return can correlate negatively with the one-period-ahead expected return If so, what does q-theory predict for investment in long-term project? E t [R t+1 ] = E t[ F CF t+1 + encodes all E[R t+τ ] {}}{ P t+1 ] MC t Main thought experiment: Fixing future profitability, how reconcile low investment (= low MC t)? Ambiguous q-theory prediction for E t [R t+1 ] due to Pt+1! 1. High E t[r t+1] but low future E t[r t+τ ] for τ > Low E t[r t+1] but future high E t[r t+τ ] for τ > 1. Cannot separately identify E t [R t+1 ], only average future E[R t+τ ]!

14 Internal Consistency of Critiques Requirement for identification of one-period-ahead expected return: roughly constant E[R] until investment pays off... which brings us back to FF assumption

15 Internal Consistency of Critiques Requirement for identification of one-period-ahead expected return: roughly constant E[R] until investment pays off... which brings us back to FF assumption with momentum in E[R], one-period-ahead return only identified if the project life is less that a year! (after that reversal in E[R])!...

16 Internal Consistency of Critiques Requirement for identification of one-period-ahead expected return: roughly constant E[R] until investment pays off... which brings us back to FF assumption with momentum in E[R], one-period-ahead return only identified if the project life is less that a year! (after that reversal in E[R])!... Related to this: other critiques of FF s motivation...

17 Internal Consistency of Critiques Requirement for identification of one-period-ahead expected return: roughly constant E[R] until investment pays off... which brings us back to FF assumption with momentum in E[R], one-period-ahead return only identified if the project life is less that a year! (after that reversal in E[R])!... Related to this: other critiques of FF s motivation... HXZ: FF see a negative relation between expected investment and expected returns, whereas the relation between expected investment and the expected return is... positive in q theory.

18 Internal Consistency of Critiques Requirement for identification of one-period-ahead expected return: roughly constant E[R] until investment pays off... which brings us back to FF assumption with momentum in E[R], one-period-ahead return only identified if the project life is less that a year! (after that reversal in E[R])!... Related to this: other critiques of FF s motivation... HXZ: FF see a negative relation between expected investment and expected returns, whereas the relation between expected investment and the expected return is... positive in q theory. Not true if expected returns are persistent: High E[R t+1 ] high future E[R t+τ ] q-theory predicts low future investment as well (that is, also a negative relation)

19 Summary & Conclusion I enjoyed reading the paper. q-theory useful to motivate empirical measures that capture variation in expected returns Key differences between FF and HXZ: different assumptions about dynamics... not differences between q-theory and valuation theory. Some suggestions/notes: Internal consistency of arguments & identification of E t[r t+1]: problematic to criticize FF for a constant E[R] assumption when q-theory cannot identify E t[r t+1] either unless E[R] roughly constant Maybe focus on measuring investment in short-term projects.

20 Summary & Conclusion I enjoyed reading the paper. q-theory useful to motivate empirical measures that capture variation in expected returns Key differences between FF and HXZ: different assumptions about dynamics... not differences between q-theory and valuation theory. Some suggestions/notes: Internal consistency of arguments & identification of E t[r t+1]: problematic to criticize FF for a constant E[R] assumption when q-theory cannot identify E t[r t+1] either unless E[R] roughly constant Maybe focus on measuring investment in short-term projects. If E[R] persistent, q-theory can also predict positive correlation between E t[r t+1] and future investment. Further, it generally predicts smooth investment (also due to adjustment cost).