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

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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
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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

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Introduction

• 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

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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)

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ROA across time
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Scatterplots and correlations
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Summary statistics
   
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Intraclass Correlations (within industry)
Variable Correlation Y1
0.070 Y2 0.082 Y3
0.085 Y4 0.107
Y5 0.121 Y6 0.088
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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
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one-level SEM
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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.
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Estimates for one-level model
Chi2 goodness-of-fit test 17.45, df 10,
p-value 0.095 All the variances of the
Ds are equal except for D of 1998 (that has
greater variance, 28.14) . The variances of the
Es are unrestricted. Variance of A1 subject to
a non-linear restriction.
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Roughly 65 25 10
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Permanent component
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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
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Two-level variation
zgi (Yig1, Yig2, ...., YigT) Firm
i1,2, ..., ng Industry g1, 2, ..., G Time
t1,2, ..., T zgi m ug vig
level 1 vig S1 S1
(q) level 2 ug S2 S2 (q)
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See Muthén and Satorra, 1995
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... in the balanced case
See Muthén and Satorra, 1995
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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

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Firm level Industry level
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Conclusions two-level model

• There exist significant permanent and temporary
  profit differences at industry and firm level
• INSERT TABLE 5
• Industry effects lt Firm effects
• Industry permanent differences lt firm permanent
  differences
• Industry temporary differences lt firm temporary
  differences
• The same memory parameter, common b .72 ,
  of the transitory component of firm and industry
  levels

Var(A)
Var(P)
(noise, Var(D), is not included in this variance
decomposition)