Testing the q-theory of Anomalies

Transcription

1 Testing the q-theory of Anomalies Toni M. Whited 1 Lu Zhang 2 1 University of Wisconsin at Madison 2 University of Rochester, University of Michigan, and NBER Carnegie Mellon University, May 2006 Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 1 / 41

2 Theme The q-theory explanations of the value, investment, and earnings anomalies are quantitatively important Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 2 / 41

3 Outline 1 Stylized Facts 2 The Model 3 Structural Tests 4 Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 3 / 41

4 Stylized Facts The value anomaly Stylized Facts Value stocks earn higher average returns than growth stocks, especially in small firms (Fama and French 1992, 1993) Average returns of the Fama-French 25 portfolios: Small Big Low High Sample: January 1972 to December 2003 Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 5 / 41

5 Stylized Facts Stylized Facts The value anomaly: abnormal returns (alphas) from factor models Small Big Small Big α CAPM (% per month) t-statistics for α CAPM Low High α FF (% per month) t-statistics for α FF Low High Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 6 / 41

6 Stylized Facts The investment anomaly Stylized Facts High investment-to-capital stocks earn lower average returns than low investment-to-capital stocks (Titman, Wei, and Xie 2004) Average returns and alphas of ten investment-to-capital portfolios: Low High means α CAPM α FF Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 7 / 41

7 Stylized Facts Stylized Facts The post-earnings-announcement drift Firms with positive earnings surprises earn higher average returns than firms with negative earnings surprises (Ball and Brown 1968; Bernard and Thomas 1989, 1990) Ten Standardized Unexpected Earnings (SUE) portfolios: Low High means α CAPM α FF Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 8 / 41

8 Stylized Facts Stylized Facts The post-earnings-announcement drift The post-earnings-announcement drift is stronger in small firms (Bernard and Thomas 1989, 1990) Average returns and alphas of the nine size-sue portfolios: SL SM SH ML MM MH BL BM BH means α CAPM α FF Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 9 / 41

9 The Model Objective The Model Construct a structural expected-return model to capture empirically the alphas of the value, investment, and earnings strategies A direct, pragmatic approach to the joint-hypothesis problem Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 11 / 41

10 The Model The neoclassical setup The Model The basic idea: link expected returns to firm characteristics directly without consumption (Cochrane 1991; Berk, Green, and Naik 1999) Firms use capital and costlessly adjustable inputs to produce a homogeneous output The operating-profit function Π(K jt, X jt ) Flow operating costs proportional to capital stock ck jt Capital accumulation: K jt+1 = I jt + (1 δ jt )K jt where δ jt is the rate of capital depreciation Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 12 / 41

11 The Model The Model The neoclassical setup Costs of investment (purchase-sales costs plus convex adjustment costs): Φ(I jt, K jt ) with Φ 1 0, Φ 2 0, Φ 11 > 0 At the beginning of period t, firms choose the level of one-period debt, B jt+1, to be repaid at the beginning of t +1 with the interest rate R(X jt+1 ) Firm j chooses {I jt+τ, K jt+τ+1, B jt+τ+1 } τ=0 to maximize V (K jt, B jt, X jt ): E t τ=0 M t+τ Π(K jt+τ, X jt+τ ) ck jt+τ Φ(I jt+τ, K jt+τ ) + B jt+τ+1 R ( X jt+τ ) Bjt+τ q jt+τ [ Kjt+τ+1 (1 δ jt+τ )K jt+τ I jt+τ ] Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 13 / 41

12 The Model Optimality conditions The Model q jt = Φ 1 (I jt, K jt ) }{{} Marginal cost of investment at period t [ ] q jt = E t M t+1 Π1 (K jt+1, X jt+1 ) c Φ 2 (I jt+1, K jt+1 ) + (1 δ jt+1 )q jt+1 }{{} Marginal benefit of investment at period t+1 Equivalently, 1 = E t [M t+1 rjt+1 I ], where the investment return r I jt+1 Π 1(K jt+1, X jt+1 ) c Φ 2 (I jt+1, K jt+1 ) + (1 δ jt+1 )Φ 1 (I jt+1, K jt+1 ) Φ 1 (I jt, K jt ) Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 14 / 41

13 The Model Testable implication The Model Dividend D jt Π(K jt, X jt ) ck jt Φ(I jt, K jt ) + B jt+1 R(X jt )B jt Ex-div equity P(K jt, B jt, X jt ) V (K jt, B jt, X jt ) D jt Stock return rjt+1 S jt+1 + D jt+1 )/P jt Leverage ν jt B jt+1 /(P(K jt, B jt, X jt ) + B jt+1 ) Under constant return to scale, rjt+1 I jtr(x jt+1 ) + (1 ν jt )rjt+1 S rjt+1 S r jt+1 I jtr(x jt+1 ) 1 ν jt }{{} Levered investment return Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 15 / 41

14 Structural Tests Test design Structural Tests Testable implication: the expected stock return equals the expected levered investment return (a function of characteristics only) Moment conditions in the GMM structural estimation: [( E rjt+1 S r jt+1 I ν ) jtr(x jt+1 ) Zjt] = 0 1 ν jt where Z jt is a vector of instrumental variables known at time t Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 17 / 41

15 Structural Tests Structural Tests Testing portfolios 55 testing portfolios: The Fama-French 25 size and book-to-market portfolios Ten investment-to-capital portfolios Ten Standardized Unexpected Earnings portfolios Nine size-sue portfolios The aggregate market portfolio Separate and joint estimation Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 18 / 41

16 Structural Tests Structural Tests Instrumental variables 8 instrumental variables A vector of ones 3 portfolio-specific variables: investment-to-capital, sales-to-capital, and book-to-market 4 aggregate variables: the dividend yield, the default premium, the term premium, and the Treasury bill rate Unconditional and conditional estimation Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 19 / 41

17 Structural Tests Functional forms Structural Tests Follow the empirical investment literature to parameterize the marginal product of capital and the augmented adjustment-cost function: Love (2003): Π 1 (K jt, X jt ) = κy jt K jt where Y jt : sales, κ: the capital share Whited (1998): Φ(I jt, K jt ) = I jt + [ ( ) a Ijt ( ) ] 3 K jt 3 a Ijt 3 K jt K jt Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 20 / 41

18 Sample construction Data source: the CRSP/COMPUSTAT merged dataset ( ) Data definitions: Variable Item # Explanation 1. Capital stock Item 7 Property, plant, and equipment (PPE) 2. Investment Items Capital expenditures of PPE Sales of PPE 3. Profits Items Income before extraordinary items plus depreciation and amortization 4. Output Item 12 Sales 5. Total debt Items 9+34 Long-term debt plus debt in current liabilities 6. Net equity Items Sale minus purchase of issuance common and prefer stocks 7. Depreciation Item 103 Depreciation expense 8. Market value Item Price per share times of equity common shares outstanding Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 22 / 41

19 GMM estimation and tests, unconditional estimation Separate Estimation Fama- Size- Investment- French 25 SUE SUE to-capital Joint Estimation a (0.831) (2.177) (2.084) (0.922) (1.239) a (1.621) (4.002) (5.775) (0.634) (0.992) c (0.135) (0.141) (0.077) (0.097) (0.082) κ (0.066) (0.136) (0.081) (0.083) (0.051) a.a.p.e J T d.f p-value (0.301) (0.009) (0.210) (0.209) (0.000) Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 23 / 41

20 Alphas from the q-model of expected returns, unconditional estimation Fama-French 25 portfolios, separate estimation: Small Big Small Big Average r S Average levered r I Low High Alphas from the q-model, α q t-statistics for α q Low High Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 24 / 41

21 Alphas from the q-model of expected returns, unconditional estimation Fama-French 25 portfolios, separate estimation: 2.5 Investment Returns Stock Returns Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 25 / 41

22 Intuition Recall: r I jt+1 = Π 1(K jt+1, X jt+1 ) c Φ 2 (I jt+1, K jt+1 ) + (1 δ jt+1 )Φ 1 (I jt+1, K jt+1 ) Φ 1 (I jt, K jt ) In a two-period model with quadratic adjustment costs: E t [r I jt+1 ] = κe t[y jt+1 /K jt+1 ] c + (1 E t [δ jt+1 ]) 1 + a(i jt /K jt ) Cash-flow channel: E t [Y jt+1 /K jt+1 ], E t [δ jt+1 ] Discount-rate channel: 1 + a(i jt /K jt ) = q jt = P jt /K jt+1 Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 26 / 41

23 Characteristic-based determinants of expected returns, Fama-French 25 portfolios Small Big Small Big Investment-to-capital Low High Sales-to-capital Average depreciation rates Low High Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 27 / 41

24 Ten investment-to-capital portfolios, separate and unconditional estimation Alphas: Low High Average r S Average levered r I Characteristics: α q Low High Average I/K Average Y /K Average δ Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 28 / 41

25 Alphas from the q-model of expected returns, unconditional estimation Ten investment-to-capital portfolios, separate estimation: 2 Investment Returns Stock Returns Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 29 / 41

26 Ten SUE portfolios, separate and unconditional estimation Alphas: Low High Average r S Average levered r I Characteristics: α q Low High Average I/K Average Y /K Average δ Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 30 / 41

27 Ten SUE portfolios, separate and unconditional estimation 2.5 Investment Returns Stock Returns Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 31 / 41

28 Nine size-sue portfolios, separate and unconditional estimation Alphas: SL SM SH ML MM MH BL BM BH Average r S Average levered r I Characteristics: α q SL SM SH ML MM MH BL BM BH Average I/K Average Y /K Average δ Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 32 / 41

29 Nine size-sue portfolios, separate and unconditional estimation Investment Returns Stock Returns Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 33 / 41

30 GMM estimation and tests, conditional estimation Separate Estimation Fama- Size- Investment- French 25 SUE SUE to-capital Joint Estimation a (1.527) (1.855) (1.633) (0.864) (1.037) a (0.835) (3.874) (6.227) (0.525) (1.119) c (0.125) (0.183) (0.093) (0.121) (0.085) κ (0.058) (0.132) (0.071) (0.085) (0.049) a.a.p.e J T d.f p-value (0.031) (0.001) (0.000) (0.000) (0.000) Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 34 / 41

31 Alphas of Fama-French 25 portfolios; separate, conditional estimation Small Big Small Big Average r S Average levered r I Low High Alphas from the q-model, α q t-statistics for α q Low High Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 35 / 41

32 Ten investment-to-capital portfolios; separate, conditional estimation Low High Average r S Average levered r I α q Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 36 / 41

33 Ten SUE and nine size-sue portfolios; separate, conditional estimation Low High Average r S Average levered r I α q SL SM SH ML MM MH BL BM BH Average r S Average levered r I α q Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 37 / 41

34 Alphas of Fama-French 25 portfolios; joint, conditional estimation Small Big Small Big Average r S Average levered r I Low High Alphas from the q-model, α q t-statistics for α q Low High Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 38 / 41

35 Ten investment-to-capital portfolios; joint, conditional estimation Low High Average r S Average levered r I α q Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 39 / 41

36 Ten SUE and nine size-sue portfolios; joint, conditional estimation Low High Average r S Average levered r I α q SL SM SH ML MM MH BL BM BH Average r S Average levered r I α q Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 40 / 41

37 Conclusion The q-theory mechanisms of anomalies are quantitatively important 1 Estimating the q-model of expected returns by minimizing the average differences between stock and levered investment returns 2 Reasonable empirical succuss in pricing Fama-French 25 and ten investment portfolios, including the small-growth portfolios 3 Limited performance in capturing the earnings anomalies Whited and Zhang (2006) Testing the q-theory of Anomalies Carnegie Mellon U. 41 / 41