On the Persistence of Abnormal Returns: an Analysis Using Structural Equation Models

1. On the Persistence of Abnormal Returns: an Analysis Using Structural Equation Models Albert Satorra Universitat Pompeu Fabra. Barcelona & Juan Carlos Bou Universitat Jaume I. Castelló Bou and Satorra (2007), SMJ

2. This talk • Introduction: permanent and transitory components of profits (ROA) • Data & model • Substantive hypotheses • SEM: one- and two-level analyses • Variance decomposition of profits: • temporary vs permanent • Industry vs firm levels

3. actual profit rates differ widely across firms, both between and within industries. • Some firms show what can be regarded as ``abnormal returns'', i.e. returns that deviate substantially from the mean return level of all the firms. • According to economic theory, in a ``competitive market'' these differences should disappear as the time passes. • How much evidence exists of the persistence of abnormal returns, or how much variation of the returns can be attributed to permanent and time-vanishing components Introduction

4. Data • Initial sample: 5000 Spanish firms (excluding finance and public companies) • Screened database: 4931 firms • Financial Profit data were collected for each firm (Return On Assets, ROA) • 6 Time Period: 1995 – 2000 • Firms were classified by 4-digit SIC code • Number of Industries: 342(quasi average number of firms: 14.28)

5. ROA across time

6. Scatterplots and correlations

7. Summary statistics

8. Intraclass Correlations (within industry) Variable Correlation Y1 0.070 Y2 0.082 Y3 0.085 Y4 0.107 Y5 0.121 Y6 0.088

9. Seminario Modelos de Ecuaciones Estructurales. Universitat Jaume I, Castelló, 12 y 13 de Julio de 2004 Albert Satorra & Juan Carlos Bou Anderson and Hsiao's State-Dependence model (1982) Using SEM, this is Kenny and Zautra's (1985) Trait-State-Error model.Here we extend these models to two-level data

10. one-level SEM

13. Test statistics See Satorra (1982) for asymptotic robustness of these normal-theory test statistics, and Satorra and Bentler (1994) for robust versions of these statistics.

14. Estimates for one-level model Chi2 goodness-of-fit test = 17.45, df = 10, p-value = 0.095 All the variances of the D’s are equal except for D of 1998 (that has greater variance, 28.14) . The variances of the E’s are unrestricted. Variance of A1 subject to a non-linear restriction.

15. Roughly: 65 25 10 %

16. Permanent component

17. IP TWO-LEVEL SEM: * INDUSTRY level: * FIRM level: 1 1 1 1 1 1 ROA95 ROA96 ROA97 ROA98 ROA99 ROA00 E1 E2 E3 E4 E5 E6 1 1 1 1 1 1 b b b b b AI AI AI AI AI AI 0 0 0 0 0 1 2 3 4 5 6 DI DI DI DI DI DI 1 2 3 4 5 6 FP 1 1 1 1 1 1 ROA95 ROA96 ROA97 ROA98 ROA99 ROA00 E1 E2 E3 E4 E5 E6 1 1 1 1 1 1 b b b b b AF AF AF AF AF AF 1 1 1 1 1 1 2 3 4 5 6 DF DF DF DF DF DF 1 2 3 4 5 6

18. Two-level variation zgi := (Yig1, Yig2, ...., YigT)’ Firm: i=1,2, ..., ng; Industry: g=1, 2, ..., G Time: t=1,2, ..., T zgi = m + ug + vig level 1: vig~ S1 = S1 (q) level 2: ug~S2 = S2 (q)

19. See Muthén and Satorra, 1995

20. ... in the balanced case See Muthén and Satorra, 1995

21. TESTS OF MODEL FIT Chi-Square Test of Model Fit Value 32.727* Degrees of Freedom 31 P-Value 0.3821 Scaling Correction Factor 2.411 for MLM

22. Firm level Industry level

23. Conclusions: two-level model Var(A) Var(P) • There exist significant permanent and temporary profit differences at industry and firm level INSERT TABLE 5 • Industry effects < Firm effects • Industry permanent differences < firm permanent differences • Industry temporary differences < firm temporary differences • The same “memory” parameter, common b = .72 , of the transitory component of firm and industry levels (noise, Var(D), is not included in this variance decomposition)