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Appendix C
Supplementary Data and Portfolio
Statistics
This section provides some supplementary data and portfolio statistics, which mainly
complement the observations in Section 13.6.
Similar to Table 13.5, Tables C.1, C.2, C.3, and C.4 show some descriptive
statistics on the NYSE (N) dataset, SP500 dataset, MSCI dataset, and DJIA dataset,
respectively.
Table C.5 illustrates the top ﬁve average allocation weights of the proposed strate-
gies on the datasets except NYSE (O). Connecting these weights with the descriptive
statistics, we can have similar observations as that of NYSE (O). That is, the pro-
posed algorithms put more weights on the volatile assets so as to exploit the volatility
of the assets, and most of the top average allocation weights of the mean reversion
algorithms are assets with negative autocorrelations, except DJIA.
187
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188 SUPPLEMENTARY DATA AND PORTFOLIO STATISTICS
Table C.1 Some descriptive statistics on the NYSE (N) dataset
Stat. 1 2 3 4 5 6 7 8
Cum 15.0504 3.7815 9.9188 32.7579 13.0692 9.1587 10.2382 9.3461
Mean 1.0006 1.0005 1.0005 1.0007 1.0007 1.0006 1.0005 1.0007
Std 0.0184 0.0237 0.0174 0.0163 0.0243 0.0203 0.0180 0.0251
Ac 0.0084 0.0321 0.0365 0.0140 0.0098 0.0134 0.0104 0.0060
910111213141516
Cum 12.3507 0.0407 16.8484 6.8311 19.7812 43.8699 19.6711 2.0467
Mean 1.0006 1.0002 1.0007 1.0005 1.0007 1.0007 1.0006 1.0010
Std 0.0185 0.0356 0.0246 0.0183 0.0221 0.0153 0.0157 0.0436
Ac 0.0193 0.0291 0.0177 0.0266 0.0145 0.0149 0.0507 0.0963
17 18 19 20 21 22 23
Cum 0.3934 28.7380 17.2551 83.5067 17.4584 10.4056 32.7829
Mean 1.0002 1.0007 1.0006 1.0009 1.0008 1.0006 1.0007
Std 0.0245 0.0179 0.0154 0.0181 0.0251 0.0226 0.0191
Ac 0.0206 0.0139 0.0368 0.0192 0.0055 0.0339 0.0478
Note: The top ﬁve of each statistics are highlighted. Each column denotes the index of an asset.
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SUPPLEMENTARY DATA AND PORTFOLIO STATISTICS 189
Table C.2 Some descriptive statistics on the SP500 dataset
Stat. 12345678
Cum 0.9381 1.4478 2.4279 1.1038 1.2034 1.2841 1.6480 1.3822
Mean 1.0002 1.0007 1.0010 1.0002 1.0004 1.0006 1.0006 1.0005
Std 0.0229 0.0280 0.0245 0.0180 0.0233 0.0273 0.0181 0.0223
Ac 0.0090 0.0103 0.0032 0.0363 0.0256 0.0033 0.0783 0.0510
9 10111213141516
Cum 1.4807 1.0293 1.0572 0.8625 1.1531 0.6044 1.3816 0.8419
Mean 1.0006 1.0002 1.0003 1.0005 1.0004 0.9998 1.0010 1.0001
Std 0.0255 0.0206 0.0215 0.0363 0.0247 0.0202 0.0392 0.0234
Ac 0.0389 0.0590 0.0182 0.0386 0.0063 0.0508 0.0618 0.0962
17 18 19 20 21 22 23 24
Cum 1.2405 3.7792 2.2260 1.1244 0.6523 1.1119 0.8263 1.8606
Mean 1.0004 1.0016 1.0013 1.0003 1.0000 1.0003 1.0000 1.0009
Std 0.0210 0.0323 0.0369 0.0213 0.0244 0.0212 0.0176 0.0296
Ac 0.0206 0.0431 0.0094 0.0755 0.0150 0.0017 0.0401 0.0229
25
Cum 0.8738
Mean 1.0002
Std 0.0242
Ac 0.0299
Note: The top ﬁve of each statistics are highlighted. Each column denotes the index of an asset.
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190 SUPPLEMENTARY DATA AND PORTFOLIO STATISTICS
Table C.3 Some descriptive statistics on the MSCI dataset
Stat. 12345678
Cum 0.9095 1.2541 0.8248 1.0638 1.0133 1.0242 1.3189 0.8063
Mean 1.0000 1.0005 1.0000 1.0002 1.0003 1.0002 1.0004 0.9999
Std 0.0164 0.0219 0.0190 0.0152 0.0242 0.0198 0.0180 0.0162
Ac 0.1305 0.0099 0.0426 0.0240 0.0105 0.0072 0.0082 0.0323
9 10111213141516
Cum 0.8742 0.7265 0.9160 0.6586 1.5040 0.2894 1.2153 0.5191
Mean 1.0003 0.9999 1.0001 0.9998 1.0005 0.9991 1.0003 0.9996
Std 0.0281 0.0178 0.0187 0.0196 0.0125 0.0256 0.0177 0.0232
Ac 0.0322 0.0415 0.0225 0.0103 0.0237 0.0188 0.0257 0.0624
17 18 19 20 21 22 23 24
Cum 0.9653 0.8714 0.8123 1.2018 1.1802 0.5670 0.5080 0.7285
Mean 1.0001 1.0001 1.0000 1.0004 1.0004 0.9996 0.9997 0.9998
Std 0.0192 0.0195 0.0220 0.0191 0.0202 0.0196 0.0250 0.0170
Ac 0.0228 0.0549 0.0324 0.0302 0.0275 0.0600 0.0410 0.1259
Note: The top ﬁve of each statistics are highlighted. Each column denotes the index of an asset.
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SUPPLEMENTARY DATA AND PORTFOLIO STATISTICS 191
Table C.4 Some descriptive statistics on the DJIA dataset
Stat. 1 2 345678
Cum 0.7085 0.5378 1.1414 1.1884 0.6870 0.7389 0.5449 1.1572
Mean 0.9997 0.9991 1.0004 1.0007 0.9996 0.9997 0.9993 1.0004
Std 0.0263 0.0260 0.0174 0.0269 0.0278 0.0256 0.0314 0.0161
Ac 0.0315 0.0094 0.0230 0.0691 0.0270 0.0961 0.0479 0.0895
9 10111213141516
Cum 0.5459 0.4287 0.7718 0.5806 0.6904 0.5323 0.5034 0.3608
Mean 0.9991 0.9988 0.9996 0.9992 0.9996 0.9992 0.9988 0.9990
Std 0.0256 0.0291 0.0166 0.0248 0.0268 0.0309 0.0198 0.0398
Ac 0.0597 0.0011 0.0280 0.0360 0.0066 0.0033 0.0240 0.0041
17 18 19 20 21 22 23 24
Cum 1.0191 0.6048 1.0863 0.8560 0.9178 0.9361 0.9787 0.8797
Mean 1.0003 0.9996 1.0003 1.0001 1.0001 1.0002 1.0002 1.0000
Std 0.0223 0.0357 0.0180 0.0264 0.0212 0.0249 0.0208 0.0202
Ac 0.0506 0.0208 0.0622 0.0963 0.0658 0.0257 0.0330 0.0578
25 26 27 28 29 30
Cum 0.5947 0.5197 0.6710 0.8309 0.9872 0.9311
Mean 0.9994 0.9995 0.9994 0.9998 1.0003 1.0001
Std 0.0281 0.0398 0.0197 0.0179 0.0238 0.0209
Ac 0.0426 0.0154 0.0873 0.0434 0.0335 0.0288
Note: The top ﬁve of each statistics are highlighted. Each column denotes the index of an asset.
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