Aggregation, Capital Heterogeneity, and the Investment CAPM

Transcription

1 Aggregation, Capital Heterogeneity, and the Investment CAPM Andrei S. Gonçalves 1 Chen Xue 2 Lu Zhang 3 1 UNC 2 University of Cincinnati 3 Ohio State and NBER BUSFIN 82 Ohio State, Autumn 218

2 Introduction Theme Aggregation and capital heterogeneity in the investment CAPM go a long way in explaining value and momentum simultaneously

3 Introduction Traditional asset pricing based on the demand of risky assets Markowitz (192) Treynor (1962), Sharpe (1964), Lintner (196), Mossin (1966) Merton (1973), Ross (1976) Rubinstein (1976), Lucas (1978), Breeden (1979) Hansen and Singleton (1982, 1983), Breeden, Gibbons, and Litzenberger (1989) Cochrane (2), Back (21), Campbell (217) Berk and DeMarzo (213), Bodie, Kane, and Marcus (214)

4 Introduction An emerging framework based on the supply of risky assets Böhm-Bawert (1891) Fisher (193), Hirshleifer (198, 196, 197) Modigliani and Miller (198) Cochrane (1991) Zhang (2, 217) Liu, Whited, and Zhang (29), Liu and Zhang (214) Hou, Xue, and Zhang (21, 217)

5 Introduction Marshall's scissors: Marshall 189 [1961, 9th edition, p. 348] Ricardo and Mill: Costs of production determine value Jevons, Menger, and Walras: Marginal utility determines value The water versus diamond debate We might as reasonably dispute whether it is the upper or under blade of a pair of scissors that cuts a piece of paper, as whether value is governed by utility or costs of production. It is true that when one blade is held still, and the cutting is aected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only so long as it claims to be merely a popular and not a strictly scientic account of what happens (our emphasis).

6 Introduction Campbell (217): An entire chapter on the investment model An empirical challenge facing the structural investment model: This problem, that dierent parameters are needed to t each anomaly, is a pervasive one in the q-theoretic asset pricing literature (p. 27).

7 Introduction The empirical challenge facing the structural investment model 29 JPE: 214 JME: journal of political economy TABLE 2 Parameter Estimates and Tests of Overidentification SUE B/M CI A. Matching Expected Returns a [1.7] [2.] [.3] a.3..2 [.] [.3] [.] x d.f p m.a.e B. Matching Expected Returns and Variances a [16.3] [4.8] [.] a Average predicted returns L 2L 1M 3L 2M 3M 1W 2W 3W Average realized returns

8 Introduction Average predicted versus realized stock returns, value- and equal-weighted value and momentum 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

9 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

10 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

11 The Model Setup Operating prots: Π(K it, C it, X it ) K it : Physical capital; C it : Current assets X it : A vector of exogenous shocks Constant returns to scale, Cobb-Douglas Capital accumulation: K it+1 = I it + (1 δ it )K it C it+1 = J it + C it Adjustment costs on physical capital: ( Iit ) 2 K it Φ(I it, K it ) = a 2 K it

12 The Model Optimal investments Optimal physical capital investment: E t [M t+1 r I ] = 1, in which it+1 the physical investment return: [ r I it+1 = (1 τ t+1 ) +(1 δ it+1 ) Y γ it+1 K K it+1 + a 2 ( Iit+1 K it+1 ) 2 ] + τ t+1 δ it+1 [ 1 + (1 τ t+1 )a ( Iit+1 K it+1 )] 1 + (1 τ t )a ( Iit K it ) Optimal current assets investment: E t [M t+1 r J ] = 1, in which the it+1 current investment return: r J it (1 τ t+1 )γ C Y it+1 C it+1

13 The Model A supply theory of asset pricing The weighted average of the investment returns equals the weighted average of the cost of equity and after-tax cost of debt: w K it r I it+1 + (1 w K it )r J it+1 = w B it r Ba it+1 + (1 w B it ) r S it+1 w K it = q it K it+1 /(q it K it+1 + C it+1 ) and w B it = B it+1/(p it + B it+1 ) Modigliani and Miller (198, Proposition II) The investment model of asset pricing: r S it+1 = w it K r I + (1 w K it+1 it )r J w B it+1 it r Ba it+1 1 wit B }{{} The fundamental return, rit+1 F

14 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

15 Econometric Methods Generalized Method of Moments, GMM Test the expected return implications of the investment model: E[r S pt+1 r F pt+1] =, r S : Portfolio p's stock return, r F : The fundamental return pt+1 pt+1 The pricing error: e p = E T [r S pt+1 r F pt+1 ], with E T [ ] the sample mean The investment model counterpart of Hansen and Singleton (1982)

16 Econometric Methods A technical point γ K and γ C enter the moment condition only in the form of γ = γ K + γ C : w K it r I it+1 + (1 w K it )r J it+1 = (1 τ t+1 )(γ K + γ C )Y it+1 /(K it+1 + C it+1 ) q it K it+1 /(K it+1 + C it+1 ) + C it+1 /(K it+1 + C it+1 ) + w K it (1 τ t+1 )(a/2) (I it+1 /K it+1 ) 2 + τ t+1 δ it+1 + (1 δ it+1 )q it+1 q it +(1 w K it ) The 2-capital model as parsimonious as the physical capital model

17 Econometric Methods GMM methodology, based on Hansen (1982) Let c (γ, a), g T the sample moments, D = g T / c The GMM objective function: g T Wg T, in which W = I Var(^c) = (D WD) 1 D WSWD(D WD) 1 /T Var(g T ) = [ I D(D WD) 1 D W ] S [ I D(D WD) 1 D W ] /T The overidentication test: g T [var(g T )] + g T χ 2 (# moments # parameters)

18 Econometric Methods Aggregation in prior studies Portfolio-level fundamental returns are constructed from portfolio-level accounting variables aggregated from the rm level: [ Npt i=1 E w iptr S ] ( ipt+1 ) r F γ pt+1 K, a; Y pt+1, K pt+1, I pt+1, δ pt+1, I pt, K pt, r Ba, w B = pt+1 pt N pt : The number of rms in portfolio p at the start of t, w ipt : Stock i's weight in portfolio p, r S : The return of stock i in ipt+1 p over time t, r F : The fundamental return of p pt+1 Aggregating rm-level characteristics to the portfolio level: I pt+1 = N pt I i=1 ipt+1, wpt B = N pt B i=1 ipt+1/ N pt (P i=1 ipt + B ipt+1 ), etc

19 Econometric Methods Exact aggregation Construct rm-level fundamental returns from rm-level accounting variables, then aggregate to portfolio-level fundamental returns: [ Npt i=1 E w iptr S N pt ( ipt+1 r F ipt+1 i=1 w ipt γ, a; Y ipt+1, K ipt+1, I ipt+1, δ ipt+1, I ipt, K ipt, r Ba ipt+1, w B ipt ) ] = Why? r F ipt+1 : Firm i's fundamental return, r F pt+1 varies with w ipt Economics: Firms can make dierent investment choices Econometrics: The substantial rm-level heterogeneity helps identify structural parameters

20 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

21 Data 4 testing deciles, January 1967December 21 Two sets of deciles: NYSE breakpoints and value-weighted returns All-but-micro breakpoints and equal-weighted returns Deciles formed on: Book-to-market: Bm Momentum (prior 11-month returns, 1-month horizon): R 11 Asset growth: I/A Return on equity: Roe

22 Data Average returns of the 4 testing deciles, value-weights L H H L The Bm deciles m t m The R 11 deciles m t m The I/A deciles m t m The Roe deciles m t m

23 Data Average returns of the 4 testing deciles, equal-weights L H H L The Bm deciles m t m The R 11 deciles m t m The I/A deciles m t m The Roe deciles m t m

24 Data Variable measurement Y it : Sales K it : Net property, plant, and equipment C it : Current assets B it+1 : Long-term debt plus short-term debt (zero if missing) P it : Market equity, from CRSP τ t : The statutory corporate income tax rate from the Commerce Cleaning House δ it : The amount of depreciation and amortization minus amortization, scaled by net PPE I it : K it+1 (1 δ it )K it rit B : Total interest and related expenses, scaled by total debt

25 Data Timing alignment Construct monthly fundamental returns from annual accounting variables to match with monthly stock returns For each month t, take rm-level accounting variables from the scal year end closest to month t to measure time-t variables in the model, and to take accounting variables from the subsequent scal year end to measure time-t + 1 variables Compound the portfolio stock returns within a 12-month rolling window with month t in the middle of the window to match with the portfolio fundamental return for month t

26 Data Descriptive statistics, rm-level variables, the full sample m σ % 2% % 7% 9% I it K it J it C it Y it+1 K it+1 Y it+1 C it Y it+1 K it+1 +C it K it+1 K it+1 +C it wit B δ it r B it

27 Data Correlation matrix, rm-level variables, the full sample I it+1 K it+1 J it C it J it+1 Y it+1 C it+1 K it+1 Y it+1 C it+1 Y it+1 K it+1 +C it+1 K it+1 K it+1 +C it+1 w B it δ it+1 r B it+1 I it K it I it+1 K it+1 J it C it J it+1 C it+1 Y it+1 K it+1 Y it+1 C it+1 Y it+1 K it+1 +C it+1 K it+1 K it+1 +C it+1 wit B.32.7 δ it+1.12

28 Data Histograms, rm versus portfolio I it /K it

29 Data Histograms, rm versus portfolio K it+1 /(K it+1 + C it+1 )

30 Data Histograms, rm versus portfolio Y it+1 /(K it+1 + C it+1 )

31 Data Histograms, rm versus portfolio Y it+1 /K it

32 Data Histograms, rm versus portfolio r B it

33 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

34 GMM Estimation and Tests The physical capital model estimated at the portfolio level, NYSE breakpoints and value-weights d.f. γ K [γ K ] a [a] m.a.e. e H L p Bm [2.41] 6.33 [1.93] R [1.14] 1.27 [.3] I/A [1.8] 1.13 [.4] Roe [.98]. [.] Bm-R [1.18] 2.3 [.48] I/A-Roe [1.2].8 [.3] Bm-R 11 -I/A-Roe [1.9] 1.73 [.3]

35 GMM Estimation and Tests The physical capital model estimated at the portfolio level, all-but-micro breakpoints and equal-weighteds d.f. γ K [γ K ] a [a] m.a.e. e H L p Bm [12.7] 63.4 [.1] R [1.29] 1.34 [.8] I/A [1.46] 2.24 [.2] Roe [1.11]. [.4] Bm-R [1.39] 2.8 [.2] I/A-Roe [1.33] 1.7 [.4] Bm-R 11 -I/A-Roe [1.34] 2. [.37]

36 GMM Estimation and Tests Average predicted versus realized stock returns, Bm-R 11, value- and equal-weights, the 1-capital model at the portfolio level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

37 GMM Estimation and Tests Bm-R 11 -I/A-Roe, value- and equal-weights, the 1-capital model at the portfolio level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

38 GMM Estimation and Tests The 2-capital model estimated at the rm level, NYSE breakpoints and value-weighted deciles d.f. γ K [γ K ] a [a] m.a.e. e H L p Bm [2.].37 [.] R [2.6] 3.74 [.] I/A [1.8] 1.6 [.69] Roe [2.76] 6.7 [.1] Bm-R [2.9] 3.6 [.1] I/A-Roe [1.84] 1.6 [.7] Bm-R 11 -I/A-Roe [2.] 3. [.]

39 GMM Estimation and Tests The 2-capital model estimated at the rm level, all-but-micro breakpoints and equal-weighted deciles d.f. γ K [γ K ] a [a] m.a.e. e H L p Bm [1.99] 3.6 [.1] R [1.97] 2.6 [.97] I/A [1.79] 1.99 [.47] Roe [1.98] 3.74 [.1] Bm-R [2.9] 3.28 [.26] I/A-Roe [1.84] 2. [.43] Bm-R 11 -I/A-Roe [1.96] 2.78 [.27]

40 GMM Estimation and Tests Average predicted versus realized stock returns, Bm-R 11, value- and equal-weights, the 2-capital model at the rm level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

41 GMM Estimation and Tests Bm-R 11 -I/A-Roe, value- and equal-weights, the 2-capital model at the rm level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

42 GMM Estimation and Tests Intuition The physical investment return: [ (1 τ t+1 ) r I it+1 = +(1 δ it+1 ) Y γ it+1 K K it+1 + a 2 ( Iit+1 K it+1 ) 2 ] + τ t+1 δ it+1 [ 1 + (1 τ t+1 )a ( Iit+1 K it+1 )] 1 + (1 τ t )a ( Iit K it )

43 GMM Estimation and Tests Comparative statics on the high-minus-low errors VW EW VW EW Bm I/A Benchmark I it /K it I it+1 /K it Y it+1 /(K it+1 + C it+1 ) R 11 Roe Benchmark I it /K it I it+1 /K it Y it+1 /(K it+1 + C it+1 )

44 GMM Estimation and Tests The impact of aggregation, Bm-R 11, value- and equal-weights, the 2-capital model at the portfolio level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

45 GMM Estimation and Tests The impact of aggregation, Bm-R 11 -I/A-Roe, value- and equal-weights, the 2-capital model at the portfolio level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

46 GMM Estimation and Tests The impact of capital heterogeneity, Bm-R 11, value- and equal-weights, the 1-capital model at the rm level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

47 GMM Estimation and Tests The impact of capital heterogeneity, Bm-R 11 -I/A-Roe, value- and equal-weights, the 1-capital model at the rm level 2 2 Average predicted returns L H Average predicted returns L H Average realized returns Average realized returns

48 Outline 1 The Model of the Firms 2 Econometric Methods 3 Data 4 GMM Estimation and Tests Diagnostics: Dynamics of Factor Premiums

49 Diagnostics Correlations between the stock returns of various leads and lags and the contemporaneous fundamental return, r F it r S it 24 r S it 12 r S it 3 r S it r S it+3 r S it+12 r S it+24 All rms vw-portfolios No microcaps ew-portfolios

50 Diagnostics Contemporaneous stock-fundamental return correlations L H H L Value-weighted deciles Bm R I/A Roe Equal-weighted deciles Bm R I/A Roe

51 Diagnostics The long-term dynamics of the (value-weighted) value premium, the stock and fundamental returns in event-time

52 Diagnostics The short-term dynamics of the (value-weighted) momentum premium, the stock and fundamental returns in event-time

53 Diagnostics The long-term dynamics of the (value-weighted) investment premium, the stock and fundamental returns in event-time

54 Diagnostics The short-term dynamics of the (value-weighted) Roe premium, the stock and fundamental returns in event-time

55 Diagnostics Time series of stock and fundamental returns, the (value-weighted) value premium, correlation =

56 Diagnostics Time series of stock and fundamental returns, the (value-weighted) momentum premium, correlation =

57 Diagnostics Time series of stock and fundamental returns, the (value-weighted) investment premium, correlation =

58 Diagnostics Time series of stock and fundamental returns, the (value-weighted) Roe premium, correlation =

59 Diagnostics Higher moments, the (value-weighted) Bm deciles L H H L σ r S r F S k r S r F K u r S r F

60 Diagnostics Higher moments, the (value-weighted) R 11 deciles L H H L σ r S r F S k r S r F K u r S r F

61 Diagnostics Higher moments, the (value-weighted) I/A deciles L H H L σ r S r F S k r S r F K u r S r F

62 Diagnostics Higher moments, the (value-weighted) Roe deciles L H H L σ r S r F S k r S r F K u r S r F

63 Conclusion Gonçalves, Xue, and Zhang (217) Aggregation and capital heterogeneity in the investment CAPM Future work: Toward the fundamental cost of capital