Testarea empirica a modelelor CAPM şi APT la Bursa de
Download
Report
Transcript Testarea empirica a modelelor CAPM şi APT la Bursa de
THE EMPIRICAL TESTING OF
CAPITAL ASSET PRICING
MODEL AND OF THE
ARBITRAGE PRICING
THEORY
ADRIAN
COJOCARU
Market Data
Period
Selection
October 1998 – September 2002
I have selected 20 shares: All from the BET market index and
the rest from the Composite BET index, to insure
diversification among different sectors of the economy
End of the month returns, a total of 48 observations
Normality Test
Skewness
Kurtosis
JarqueBera
0.1107
0.8692
3.8976
7.6554
0.0218
0.0191
0.0945
0.3119
3.7449
1.8883
0.3890
ALR
0.0251
0.1712
-0.2547
4.0971
2.9264
0.2315
2
ARC
0.009
0.1776
-0.1521
5.3607
11.331
0.0035
3
ASP
0.0141
0.1247
0.0855
4.0461
2.2472
0.3251
4
ATB
0.0155
0.2293
-1.1123
8.9318
80.2692
0.0001
5
AZO
0.0377
0.1545
0.751
4.636
9.8647
0.0072
6
DAC
0.0318
0.1748
1.669
6.5821
47.9463
0.0001
7
ELJ
0.0151
0.2568
-1.7667
12.654
211.3693
0.0001
8
EPT
0.0249
0.3091
-0.3762
11.318
139.5097
0.0001
9
EXC
0.0384
0.1821
1.395
4.8518
22.4263
0.0001
10
IMP
-0.0007
0.271
-0.5791
4.0104
4.725
0.0942
Stock
Average Std Dev
BET
0.0355
BETC
1
P-value
11
IMS
-0.0019
0.1695
-1.0061
5.1037
16.9494
0.0002
12
INX
0.0681
0.1828
0.5331
3.5886
2.9662
0.2269
13
OIL
0.0357
0.2037
1.267
5.7379
27.8344
0.0001
14
OLT
0.0098
0.1427
1.4231
5.7343
31.1547
0.0001
15
PCL
0.0111
0.1498
0.6309
5.0639
11.7037
0.0029
16
RAF
0.015
0.2255
-0.6243
4.0265
5.2252
0.0733
17
RLS
0.0072
0.1792
-2.7394
16.741
437.661
0.0001
18
SCD
0.024
0.151
-1.6381
9.7324
112.1171
0.0001
19
TER
-0.0025
0.2235
-1.7595
7.2558
60.9913
0.0001
20
TLV
0.0069
0.1941
-0.6758
4.5343
8.3615
0.0153
2.4
2.0
1.6
1.2
0.8
0.4
0.0
-.4
-.3
-.2
-.1
.0
.1
.2
.3
.4
.5
.6
.7
IN X
4
3
2
1
0
-1.2
-0.8
-0.4
0.0
ELJ
0.4
0.8
CAPM
Sharpe (1964)
Rit i im Rmt it
APT
Ross (1976)
Ri 0 1bi1 i2bi2 k bik i
APT
CAPM
APT
CAPM
APT
CAPM
R2
R2
adj R2
adj R2
Prob.
Prob.
ALR
0.4155 0.2814
0.3611
0.2658 0.0001 0.0001
ARC
0.3084 0.2470
0.2441
0.2307 0.0027 0.0003
ASP
0.2251 0.0611
0.1530
0.0407 0.0243 0.0903
ATB
0.1040 0.0316
0.0206
0.0105 0.3054 0.2270
AZO
0.2965 0.1145
0.2311
0.0953 0.0038 0.0186
DAC
0.4660 0.3636
0.4164
0.3498 0.0000 0.0000
ELJ
0.1032 0.0865
0.0198
0.0666 0.3094 0.0425
EPT
0.2519 0.0109
0.1823
-0.0106 0.0125 0.4803
EXC
0.0900 0.0189
0.0053
-0.0024 0.3865 0.3509
IMP
0.1429 0.1165
0.0632
0.0973 0.1479 0.0176
IMS
0.1686 0.0062
0.0913
-0.0154 0.0873 0.5951
APT
CAPM
APT
CAPM
APT
CAPM
R2
R2
adj R2
adj R2
Prob.
Prob.
IMS
0.1686
0.0062
0.0913
-0.0154
0.0873
0.5951
INX
0.1249
0.0579
0.0435
0.0374
0.2092
0.0995
OIL
0.1785
0.0892
0.1021
0.0694
0.0706
0.0393
OLT
0.1600
0.1445
0.0819
0.1259
0.1045
0.0077
PCL
0.3470
0.2939
0.2863
0.2786
0.0009
0.0001
RAF
0.0626
0.0190
-0.0246
-0.0023
0.5847
0.3498
RLS
0.0503
0.0345
-0.0381
0.0135
0.6863
0.2060
SCD
0.3470
0.2759
0.2862
0.2602
0.0009
0.0001
TER
0.1657
0.1581
0.0881
0.1398
0.0927
0.0051
TLV
0.0645
0.0526
-0.0226
0.0320
0.5694
0.1167
„Cross-section”
• Fama (1973)
• Chen (1983)
CAPM
Ri 0 1ˆ i i
Statistica t
0
1
R2
Statistica F
0.0199
-0.0014
0.000569
0.01025
2.3357
-0.1012
E[ Ri ] 0.0199 0.0014i
Principal Component Analysis
Correlation Matrix=X’ X
X’ X W = Λ W
1 2 ... k
Pm Xwm
P=XW
W’ = W-1
P’ P = W’ X’ X W = W’ W Λ = Λ
X=PW-1
n
i 1
i
/k
Kaiser Criterion
Valori proprii
Proportia de varianta
Proportia
cumulata
1
2
3.750
2.087
0.188
0.104
0.188
0.292
3
4
5
1.749
1.719
1.436
0.087
0.086
0.072
0.379
0.465
0.537
6
7
8
1.283
1.101
1.021
0.064
0.055
0.051
0.601
0.656
0.707
...
20
0.096
0.005
1.000
Cattell Test
Valorile proprii
Scree plot
4.000
3.500
3.000
2.500
2.000
1.500
1.000
0.500
0.000
1
3
5
7
9
11 13 15 17 19
Numarul componentelor
Vector 1
Vector 2
Vector 3
Vector 4
BET
0.2602
-0.489
-0.1858
-0.386
BETC
0.2755
-0.5093
-0.1904
-0.301
BUBID
0.5488
0.0788
-0.1121
0.1526
BUBOR
0.4917
0.264
-0.1518
0.0955
EXPORT
-0.1566
0.2045
-0.6878
-0.163
IMPORT
-0.2427
0.3079
-0.4558
-0.322
INDP
-0.1677
0.1501
0.4001
-0.642
INFL
0.3128
0.2716
0.2248
-0.423
USD
0.3223
0.439
0.0477
-0.081
n
FS jt Wij Z it
i1
FS jt 0 1 EC1t 2 EC2t 3 EC3t 4 EC4t jt
FACTOR
0
1
2
3
4
BET
EXPORT
INDP
USD
FS1
-0.337
13.110
0.748
-0.935
-4.752
p-values
0.250
0.000
0.708
0.748
0.517
FS2
0.424
-3.729
-4.707
-2.336
-8.050
p-values
0.173
0.055
0.030
0.450
0.302
FS3
0.036
1.090
4.874
3.754
-6.468
p-values
0.897
0.531
0.105
0.188
0.364
FS4
-0.070
-1.614
-0.960
-2.280
6.175
p-values
0.812
0.383
0.640
0.447
0.013
F
Prob.
15.292
0.0000
2.133
0.0930
2.150
0.0908
1.968
0.0871
FS jt 0 1 BETt 2 EXPORTt 3 INDPt 4USDt jt
APT
Ri 0 1bˆi1 2bˆi 2 3bˆi3 4bˆi 4 i
t
0
1
2
3
4
R2
F
0.01717
0.00046
0.00494
-0.00303
-0.00790
0.161
0.719
1.874
0.030
0.511
-0.319
-1.617
E[Ri ] 0.01717 0.00046bˆi1 0.00494bˆi 2 0.00303bˆi3 0.00790bˆi 4
.07
.06
.05
.04
.03
.02
.01
.00
-.01
5
10
RENTMED
15
20
25
30
RENTCAPM
35
40
45
RENTAPT
Residue Analysis
Ri Ei ( APT) i
Ri Ei (CAPM) i
A. APT residue analysis
i 0 1ˆi i
t
0
1
R2
0.0000
0.0000
0.000
0.0000
0.0000
B. CAPM residue analysis
i 0 1bˆi1 2bˆi 2 3bˆi3 4bˆi 4 i
0
t
1
2
3
4
-0.0028
0.0019 0.0048
-0.0032
-0.0079
-0.3077
0.1285 0.4984
-0.3377
-1.6327
R2
F
0.1605 0.7171