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Finance and Economics Discussion Series: Data for paper 2010-45 ♣

The Information Content of High-Frequency Data for Estimating Equity Return Models and Forecasting Risk

Dobrislav Dobrev, Pawel Szerszen
First version: December 30, 2009
This version: July 25, 2010


Figure 1a: Relative error plots for five day VaR forecasts against the rank order of the underlying true forecasts for a two-factor log-SV model with leverage effects and jumps.

True forecast rank (quintiles) Relative forecast error (%): Daily Relative forecast error (%): HF - 5min
1st (Low) -0.044362036201112 -0.019643889242467
2nd -0.007584340977137 -0.00769967059475
3rd 0.059182093790093 0.035794718069146
4th 0.136136395736585 0.064015411380592
5th (High) 0.219711314124126 0.073151987962939
Return to Figure 1a

Figure 1b: Relative error plots for five day VaR forecasts against the rank order of the underlying true forecasts for a two-factor log-SV model with leverage effects and jumps.

True forecast rank (quintiles) Relative forecast error (%): Daily Relative forecast error (%): HF - 5min
1st (Low) -0.0777669138946591 -0.0365237593741274
2nd -0.0433546773085544 -0.0253403847993073
3rd 0.0360299012225693 0.0309588602276503
4th 0.155750262272605 0.0702435452103412
5th (High) 0.366354522556378 0.127143195770756
Return to Figure 1b

Figure 2a: One-percent and five-percent VaR forecasts for S&P 500 returns during the financial crisis of 2008.

date Return realizations VaR with Daily Data VaR with HF 5-min Data
2006-07-06 -0.0210286583154566 -0.0583549934075679 -0.0408809075436885
2006-07-13 0.000298500255184464 -0.0632761730309075 -0.0459810839734567
2006-07-20 0.00599545300309995 -0.061884613699287 -0.0493455463448506
2006-07-27 0.0138262671647402 -0.0615291182586822 -0.0467838549112012
2006-08-03 -0.020380651148656 -0.0566176361310204 -0.0372490008416785
2006-08-10 0.00298570808686643 -0.0498899231014961 -0.0413602928323181
2006-08-17 -0.00293608350596014 -0.0486393690183199 -0.0331106216535856
2006-08-24 0.00608231146733879 -0.046390561321091 -0.0308400026342448
2006-08-31 0.00877779520034655 -0.0387178448043756 -0.0273707334987576
2006-09-12 0.0010762770926232 -0.0418888124270177 -0.0277245089947506
2006-09-19 0.00542423663260938 -0.0365002917830235 -0.0295303789972145
2006-09-26 0.000455654804038641 -0.0389434048129895 -0.0334917734724358
2006-10-03 0.0255636515589255 -0.0355511454690604 -0.0308403196455457
2006-10-13 0.00218626645922165 -0.037331090907933 -0.0260966515168107
2006-10-20 0.0106668207837289 -0.033767777774155 -0.0231837691276351
2006-10-27 -0.0130511639070836 -0.0357606152922401 -0.0289627625333571
2006-11-03 0.020415072723953 -0.0353296677115276 -0.0320877795793923
2006-11-15 -0.0111360919566808 -0.0339993891757069 -0.0311104840507954
2006-11-27 0.0170473020425205 -0.0390805557825298 -0.0314339596272499
2006-12-04 0.000231079232228149 -0.0389224258621546 -0.0345457600782195
2006-12-11 -0.003810792525408 -0.0362512545834691 -0.0290886901772448
2006-12-18 0.00167199815562125 -0.0339830252226249 -0.0268153095827261
2006-12-28 -0.00581000498745143 -0.0338338428544988 -0.0266526105281493
2007-01-09 0.00914900463613411 -0.0331508669520884 -0.0360819188896067
2007-01-19 -0.0105375528355094 -0.0317058846217215 -0.0313555306543963
2007-01-26 0.0124423087856657 -0.0374993074991658 -0.0320587924910916
2007-02-02 -0.0089008539193684 -0.0357235192613205 -0.0276582914907981
2007-02-09 0.0110707810924622 -0.0341950222660975 -0.0282416917537014
2007-02-21 -0.034108465477425 -0.0329534837602159 -0.0260583817796761
2007-02-28 0.00504450878844026 -0.0374421836119268 -0.0433690654423451
2007-03-07 -0.00917993295098596 -0.0479172533045219 -0.0494952760092814
2007-03-14 0.0266404441322101 -0.0582515879475233 -0.0538273474890789
2007-03-21 -0.00621880660309687 -0.0621208840778613 -0.0425216082926339
2007-03-28 0.00163338836368226 -0.0570615552408495 -0.0396170963020257
2007-04-04 0.0125763605520056 -0.0510504988440961 -0.0323258869520674
2007-04-16 0.0064992795661864 -0.0501043481080308 -0.0278497639597815
2007-04-23 -0.00596718649019595 -0.0463712086266676 -0.0275982993431627
2007-04-30 0.00642079598012491 -0.046670556568224 -0.0310260108516426
2007-05-07 0.00182188941290279 -0.0413687953628802 -0.026426279280175
2007-05-14 0.00788246263002063 -0.0455944071370196 -0.0288396131782174
2007-05-21 -0.00499298710475687 -0.0404636012459078 -0.0298685689368732
2007-05-31 -0.0170331568962576 -0.0431622616650917 -0.0319167868610486
2007-06-07 0.0194817751644347 -0.0461054666693917 -0.0375852403800549
2007-06-14 -0.0120449475158845 -0.0469394558350047 -0.0382698874544942
2007-06-21 -0.00363786101266816 -0.0516746559644875 -0.0396504858571538
2007-06-28 -0.00292469701920994 -0.0520390545933836 -0.0489915591766911
2007-07-10 0.0246579925302146 -0.0556815006121468 -0.0418764897102266
2007-07-17 -0.0214059429376122 -0.0525231226771175 -0.0355151941692172
2007-07-24 -0.0378886159543597 -0.0620634325563098 -0.0442068608025274
2007-07-31 0.0139068057451594 -0.0712895413387135 -0.0706008143132961
2007-08-07 -0.0177582287062991 -0.0779292612573975 -0.0849979570122993
2007-08-14 -0.00397895843743351 -0.0892177110058135 -0.0914903730642259
2007-08-21 -0.0143131810038066 -0.0831456178748097 -0.0901621848469806
2007-08-28 0.0129728214976386 -0.0872527766011909 -0.062907484134277
2007-09-07 0.0126982597590312 -0.0871964335208542 -0.0612932979978748
2007-09-14 0.0146114786224004 -0.0804193129058332 -0.0508472463174684
2007-09-21 -0.00224591468973656 -0.0796798312434442 -0.0435856946027065
2007-09-28 0.0106645539393162 -0.0706284204383609 -0.0388456219490315
2007-10-10 -0.0275620825660139 -0.063984333388024 -0.0348054267318443
2007-10-17 -0.00126909981444862 -0.0610195217346847 -0.0450345639058411
2007-10-24 0.00421425562489425 -0.0656630174053397 -0.0626042469524521
2007-10-31 -0.0292433580768148 -0.0644091578162409 -0.0524269260468829
2007-11-07 -0.04027748817508 -0.0880854684699168 -0.0724592104601737
2007-11-19 0.0113865731785389 -0.0874286590899161 -0.0824981384359703
2007-11-29 0.0119452481741032 -0.0886112068214634 -0.0781033871487657
2007-12-06 -0.0344283952105128 -0.0824863677158602 -0.0552449571464426
2007-12-13 -0.0227196783976575 -0.08946701122138 -0.0635433130891897
2007-12-20 -0.0354596433287333 -0.0864094665281027 -0.0665175997448653
2008-01-04 -0.002472981833951 -0.0919640822080942 -0.0628128151632429
2008-01-11 0.00649844912844691 -0.0913846658178487 -0.0878657232376541
2008-01-23 -0.00369053907442984 -0.0998918112602965 -0.108709886252366
2008-01-30 0.00349585877465133 -0.0945815491138023 -0.0959166221754303
2008-02-06 0.0247314764069023 -0.107026980168605 -0.0868615022602196
2008-02-13 0.00380634939562885 -0.0920409738372727 -0.0763369876285911
2008-02-25 -0.00125629655350828 -0.0909701096026284 -0.0771730869274638
2008-03-03 -0.02223324769507 -0.0923222181410127 -0.0721161550274416
2008-03-10 0.00119993578722297 -0.0952463340107678 -0.087210120930074
2008-03-17 -0.0249961275856085 -0.0989442728521394 -0.100315778697323
2008-03-27 0.0195820427354916 -0.10664423466051 -0.0850567564384062
2008-04-03 -0.0112195095610921 -0.103127374544917 -0.0692693077659994
2008-04-10 0.00386756939835098 -0.091965357395626 -0.0578033297715117
2008-04-17 0.00560625197281534 -0.0900623438700212 -0.052334339785793
2008-04-24 0.0111977780445049 -0.0817071797426602 -0.0563968547463804
2008-05-01 -0.0129045285600363 -0.0767064667815605 -0.0537401326115793
2008-05-08 0.0173704220844359 -0.0765851052417531 -0.0558565551585413
2008-05-15 -0.0221694093812937 -0.070916380473822 -0.0472165284033049
2008-05-22 -0.0109761578476469 -0.0722220712066136 -0.0520470815856365
2008-06-03 -0.00356663781104488 -0.0670131992039126 -0.0546005104730773
2008-06-10 -0.0146168310815944 -0.0808751126722195 -0.0658173594986941
2008-06-17 -0.0133334582148728 -0.0784327248822449 -0.064417869123559
2008-06-24 -0.00417481436137304 -0.0780758119501319 -0.0645197544413868
2008-07-01 -0.0224144132184275 -0.0846726464962597 -0.0773520248380109
2008-07-11 0.00879526582153048 -0.0865985760600141 -0.0957742519252384
2008-07-18 -0.00614449054829433 -0.0891376002501993 -0.0870440471373842
2008-07-25 -0.00147514508030189 -0.0911167521447054 -0.0752206486924792
2008-08-01 0.0327045977648758 -0.0933618807716514 -0.0728992726062114
2008-08-08 0.0151154773223418 -0.0966121749438834 -0.0646604456885572
2008-08-15 0.000113690049502901 -0.0893645171070537 -0.0645054292041501
2008-08-22 0.00437628011560093 -0.0829323108306356 -0.058110806175523
2008-09-03 -0.0535887318524234 -0.084479520588396 -0.0625308247535567
2008-09-10 0.0420558901731942 -0.106542993017059 -0.0822332007310804
2008-09-17 -0.0384599851596062 -0.132339494811048 -0.132886982556569
2008-09-24 0.0214308140882575 -0.138118640966662 -0.132452808910084
2008-10-01 -0.130329786694844 -0.159549770359313 -0.137126081823025
2008-10-08 -0.069658652514407 -0.178970280720953 -0.222918122662331
2008-10-20 -0.0224054172568108 -0.205551366100746 -0.23002113337741
2008-10-27 0.0688629057382035 -0.216705657074377 -0.272510318116227
2008-11-03 0.021408141073877 -0.199235820785731 -0.197637459671048
2008-11-13 -0.12958649652647 -0.230814731551201 -0.222608370429068
2008-11-20 0.016733025895386 -0.262231209690478 -0.266579190845284
2008-12-02 0.0822038372249357 -0.282939101025188 -0.235805566882916
2008-12-09 0.030653124718059 -0.252929116498541 -0.207096307367685
2008-12-16 -0.073723328480021 -0.224030579683722 -0.173736247617085
2008-12-23 -0.0011670103099872 -0.198086085023918 -0.145274776330781
2009-01-07 -0.0429534181831074 -0.175894699253343 -0.109668521254001
2009-01-14 0.0620604494763361 -0.173725341909202 -0.119970703251889
2009-01-26 -0.0170117133686546 -0.153318275953573 -0.144949769786833
2009-02-02 0.0522145708663287 -0.160735256608777 -0.128847495338575
2009-02-09 -0.0471979640034774 -0.139724151103002 -0.113104647444389
2009-02-19 -0.040058078949984 -0.152029652288202 -0.134870875776988
Return to Figure 2a

Figure 2b: One-percent and five-percent VaR forecasts for S&P 500 returns during the financial crisis of 2008.

date Return realizations VaR with Daily Data VaR with HF 5-min Data
2006-07-06 -0.0210286583154566 -0.0370037885958211 -0.0250194577030272
2006-07-13 0.000298500255184464 -0.0404098956472142 -0.0284865015186116
2006-07-20 0.00599545300309995 -0.0393354868939801 -0.030782536455408
2006-07-27 0.0138262671647402 -0.0390135014393512 -0.0290096741668329
2006-08-03 -0.020380651148656 -0.0360236839340078 -0.0225844602435919
2006-08-10 0.00298570808686643 -0.0313466551516045 -0.0253082542115301
2006-08-17 -0.00293608350596014 -0.0306725142047987 -0.0197665292541019
2006-08-24 0.00608231146733879 -0.0289447631751418 -0.0182258873130908
2006-08-31 0.00877779520034655 -0.0239281859053164 -0.0158760542395566
2006-09-12 0.0010762770926232 -0.0260836872153355 -0.0161795404123115
2006-09-19 0.00542423663260938 -0.0223676768911621 -0.0173807039190609
2006-09-26 0.000455654804038641 -0.0241762071660269 -0.0200362678821565
2006-10-03 0.0255636515589255 -0.0219551479930482 -0.0182581637723924
2006-10-13 0.00218626645922165 -0.0230710416139932 -0.0150526747515053
2006-10-20 0.0106668207837289 -0.0205676047532192 -0.0130721546070957
2006-10-27 -0.0130511639070836 -0.0220980717364909 -0.0169480518155888
2006-11-03 0.020415072723953 -0.0218307334326412 -0.0190890421860917
2006-11-15 -0.0111360919566808 -0.0209197893769178 -0.0184020353659979
2006-11-27 0.0170473020425205 -0.0243129223453453 -0.018645094621871
2006-12-04 0.000231079232228149 -0.0241610719289625 -0.0207203954525195
2006-12-11 -0.003810792525408 -0.0221961034713993 -0.0170516863547396
2006-12-18 0.00167199815562125 -0.0208090439995534 -0.0155291074434474
2006-12-28 -0.00581000498745143 -0.0207041923454079 -0.0154232234035351
2007-01-09 0.00914900463613411 -0.0202551885347895 -0.0217859889064259
2007-01-19 -0.0105375528355094 -0.0192870622931831 -0.0186030879036644
2007-01-26 0.0124423087856657 -0.0232096550801558 -0.0191104088525406
2007-02-02 -0.0089008539193684 -0.0219657706895112 -0.0160882785796433
2007-02-09 0.0110707810924622 -0.0210215288401317 -0.0164918269134735
2007-02-21 -0.034108465477425 -0.0203695935137544 -0.0150193006239483
2007-02-28 0.00504450878844026 -0.0224596515332049 -0.0266703760579705
2007-03-07 -0.00917993295098596 -0.0293843382788787 -0.0308365388342183
2007-03-14 0.0266404441322101 -0.0363928078788385 -0.0337616363028001
2007-03-21 -0.00621880660309687 -0.0394991748437523 -0.0260749770826089
2007-03-28 0.00163338836368226 -0.0360348632493784 -0.0240760670864967
2007-04-04 0.0125763605520056 -0.0317422301968264 -0.0191741017506703
2007-04-16 0.0064992795661864 -0.0310672982924728 -0.0161697530068144
2007-04-23 -0.00596718649019595 -0.0290031668504103 -0.0160256283090789
2007-04-30 0.00642079598012491 -0.0291152386056459 -0.0183468437230253
2007-05-07 0.00182188941290279 -0.0256894454631252 -0.0152027791887849
2007-05-14 0.00788246263002063 -0.0284218464856289 -0.0168162585966536
2007-05-21 -0.00499298710475687 -0.0249277976233959 -0.017524256759275
2007-05-31 -0.0170331568962576 -0.0268400059797454 -0.0189144424923563
2007-06-07 0.0194817751644347 -0.0287747582396671 -0.022732144711848
2007-06-14 -0.0120449475158845 -0.029440061254184 -0.0231901457653561
2007-06-21 -0.00363786101266816 -0.0324120334956227 -0.0240991569939764
2007-06-28 -0.00292469701920994 -0.0326275338494994 -0.0304326142818995
2007-07-10 0.0246579925302146 -0.0350539446749021 -0.025627691179288
2007-07-17 -0.0214059429376122 -0.0332005980003671 -0.0213183681611632
2007-07-24 -0.0378886159543597 -0.0393643421473289 -0.0272114855347986
2007-07-31 0.0139068057451594 -0.0448404510151914 -0.0450524487912461
2007-08-07 -0.0177582287062991 -0.0499241555933644 -0.0548002473570604
2007-08-14 -0.00397895843743351 -0.056877192345754 -0.0592785315040351
2007-08-21 -0.0143131810038066 -0.0529791883615457 -0.05835000202966
2007-08-28 0.0129728214976386 -0.0560421083805055 -0.0398715287248463
2007-09-07 0.0126982597590312 -0.055904676268217 -0.0387611523083683
2007-09-14 0.0146114786224004 -0.051433767577868 -0.031648874778192
2007-09-21 -0.00224591468973656 -0.0508980696263761 -0.026761126435908
2007-09-28 0.0106645539393162 -0.0448333196760483 -0.0235515698664609
2007-10-10 -0.0275620825660139 -0.0406106801782128 -0.020836051235643
2007-10-17 -0.00126909981444862 -0.0383744022962157 -0.0277764974632681
2007-10-24 0.00421425562489425 -0.0419169025526999 -0.0396086610681746
2007-10-31 -0.0292433580768148 -0.0407367814518717 -0.0326813411369055
2007-11-07 -0.04027748817508 -0.0568505941846525 -0.0462780287393994
2007-11-19 0.0113865731785389 -0.0561820981528268 -0.0531835760641931
2007-11-29 0.0119452481741032 -0.0563694861803281 -0.0501500154761008
2007-12-06 -0.0344283952105128 -0.0522907726047546 -0.0346063523654653
2007-12-13 -0.0227196783976575 -0.0574934351768549 -0.0402705300720816
2007-12-20 -0.0354596433287333 -0.0553525944508279 -0.0422740566516167
2008-01-04 -0.002472981833951 -0.0591461134819268 -0.0397687561158608
2008-01-11 0.00649844912844691 -0.0590102089895356 -0.0567060979508022
2008-01-23 -0.00369053907442984 -0.0645374492842023 -0.0710019848454847
2008-01-30 0.00349585877465133 -0.0610421499738038 -0.0623042804861603
2008-02-06 0.0247314764069023 -0.068852157065475 -0.056051618024128
2008-02-13 0.00380634939562885 -0.0590366292401224 -0.0488850809829259
2008-02-25 -0.00125629655350828 -0.0582331197813814 -0.0495080104216493
2008-03-03 -0.02223324769507 -0.0596897149417829 -0.0460129323267781
2008-03-10 0.00119993578722297 -0.0612773267241667 -0.0562313950495697
2008-03-17 -0.0249961275856085 -0.0637694827205843 -0.0652304619318396
2008-03-27 0.0195820427354916 -0.0690063459998409 -0.0548864407183752
2008-04-03 -0.0112195095610921 -0.0665363815724996 -0.0441448784764247
2008-04-10 0.00386756939835098 -0.0589327367080169 -0.0364018007901461
2008-04-17 0.00560625197281534 -0.0584059675614375 -0.0327053678895912
2008-04-24 0.0111977780445049 -0.0519776661589613 -0.0353667759874145
2008-05-01 -0.0129045285600363 -0.0488454463731809 -0.0336121507545776
2008-05-08 0.0173704220844359 -0.0493206396540983 -0.0350500305130293
2008-05-15 -0.0221694093812937 -0.0455394384804287 -0.0292026319199385
2008-05-22 -0.0109761578476469 -0.0459552772411324 -0.032466801588492
2008-06-03 -0.00356663781104488 -0.0426772983379195 -0.0341926683203657
2008-06-10 -0.0146168310815944 -0.0523270597369522 -0.0417951014393326
2008-06-17 -0.0133334582148728 -0.0503581732694289 -0.0409098582216686
2008-06-24 -0.00417481436137304 -0.0501007798519877 -0.0409930491700092
2008-07-01 -0.0224144132184275 -0.054635944504362 -0.0496763274748703
2008-07-11 0.00879526582153048 -0.0558940917472033 -0.0622137644595569
2008-07-18 -0.00614449054829433 -0.0570277819428122 -0.0562127952930255
2008-07-25 -0.00147514508030189 -0.0587949015987033 -0.0482857193399126
2008-08-01 0.0327045977648758 -0.0597958250109353 -0.0466470512816104
2008-08-08 0.0151154773223418 -0.0626005902601544 -0.0410497492709594
2008-08-15 0.000113690049502901 -0.057178855242998 -0.0409537918129772
2008-08-22 0.00437628011560093 -0.0532683771960941 -0.0366250056539912
2008-09-03 -0.0535887318524234 -0.054427575991714 -0.0396199881009615
2008-09-10 0.0420558901731942 -0.0690588221104464 -0.0529513764836619
2008-09-17 -0.0384599851596062 -0.0864188895187225 -0.0874087580755448
2008-09-24 0.0214308140882575 -0.0904620362462098 -0.0871441811824556
2008-10-01 -0.130329786694844 -0.1029895085491 -0.0903608339799476
2008-10-08 -0.069658652514407 -0.117581123904069 -0.148947960997512
2008-10-20 -0.0224054172568108 -0.135016153545468 -0.153571958385373
2008-10-27 0.0688629057382035 -0.141151654129651 -0.182970538343119
2008-11-03 0.021408141073877 -0.12916919297712 -0.13165949458696
2008-11-13 -0.12958649652647 -0.151665437326353 -0.148507596234497
2008-11-20 0.016733025895386 -0.17140939732524 -0.178759267538625
2008-12-02 0.0822038372249357 -0.1851068403932 -0.157636852633251
2008-12-09 0.030653124718059 -0.16631361099946 -0.138154572480818
2008-12-16 -0.073723328480021 -0.147793010026557 -0.115070485753945
2008-12-23 -0.0011670103099872 -0.129247884110665 -0.0958471614058653
2009-01-07 -0.0429534181831074 -0.113999093455623 -0.0716897725787659
2009-01-14 0.0620604494763361 -0.112669956209507 -0.0786288037390763
2009-01-26 -0.0170117133686546 -0.0990062288068311 -0.0956232598412244
2009-02-02 0.0522145708663287 -0.104815497058818 -0.0846997459613824
2009-02-09 -0.0471979640034774 -0.0911802696315687 -0.0738969609696092
2009-02-19 -0.040058078949984 -0.0990283455213469 -0.0887292230278636
Return to Figure 2b

Figure 3a: One-percent and five-percent VaR forecasts for Google returns during the financial crisis of 2008.

date Return realizations VaR with Daily Data VaR with HF 5-min Data
2006-12-08 -0.00759284612867006 -0.0919566146364111 -0.0827532756877324
2006-12-15 -0.0288364211551202 -0.0762549649165755 -0.0613547569043044
2006-12-27 0.0263959464529289 -0.104800930519472 -0.0887717047830207
2007-01-08 -0.000298878226270505 -0.110392695969312 -0.100476984820472
2007-01-18 0.000548216133845703 -0.107729874942338 -0.0969032952835233
2007-01-25 -0.0135419434426756 -0.123463659053874 -0.100843628752083
2007-02-01 -0.0220368274410143 -0.129186874247906 -0.119755857236028
2007-02-08 -0.0207923530390151 -0.116042695290039 -0.0985495020285092
2007-02-15 -0.050171209308932 -0.104239637313408 -0.0850829705861487
2007-02-27 0.00987915425145303 -0.110206271992068 -0.0913324609439119
2007-03-07 -0.0167020113746219 -0.118469871572265 -0.100904396189241
2007-03-14 0.0188620170388125 -0.111231696458518 -0.098361242924046
2007-03-21 0.0116945114835221 -0.11085735039201 -0.0863330789122206
2007-03-28 0.0194255802831225 -0.0957923600657746 -0.0837007071160952
2007-04-04 0.0124817209661479 -0.101651705662559 -0.077275692794114
2007-04-16 0.0107534122316202 -0.0935543057094536 -0.0749339217598308
2007-04-23 -0.0160200332588978 -0.0936936756962538 -0.0914230220276821
2007-04-30 -0.0091179890551103 -0.0866887110348384 -0.0764992074824165
2007-05-07 -0.0118404448864124 -0.0810923990473184 -0.0722730557914311
2007-05-14 0.0190373668934902 -0.0836995748013037 -0.0739518692092908
2007-05-21 0.0296517831285603 -0.0901620496641797 -0.0773166421914747
2007-05-31 0.033974193287942 -0.0893417591915017 -0.100135708384754
2007-06-07 -0.0236731155630454 -0.0937417352620197 -0.112877726138195
2007-06-14 0.0217054095883849 -0.0825276275378008 -0.0917640346155003
2007-06-21 0.021034766310843 -0.08377592340216 -0.0912565983925093
2007-06-28 0.0132749090030364 -0.0826279589458404 -0.0976481088731573
2007-07-10 0.0212585104696998 -0.0707622465489234 -0.0800413599831176
2007-07-17 -0.0770732895760962 -0.0634351916177556 -0.0830327701699598
2007-07-24 -0.00727030909036541 -0.0865790924077655 -0.0933486236191102
2007-07-31 0.0106942464627096 -0.0754152115301146 -0.104174819552879
2007-08-07 -0.0142091540597926 -0.0784555770428319 -0.0956196959033009
2007-08-14 -0.00270841398432431 -0.086275551100443 -0.0891314718198843
2007-08-21 -0.000157806490119539 -0.0923062147533627 -0.0996941427645675
2007-08-28 -0.00258661196866927 -0.0836715253440254 -0.0845450455342608
2007-09-07 0.0178806202597739 -0.0774938357402325 -0.0812559303706022
2007-09-14 0.0575749438359987 -0.0735356565686256 -0.0756193384284484
2007-09-21 0.0129764248295696 -0.0886503760155626 -0.0868252390223699
2007-09-28 0.0362804004949491 -0.0791020286753646 -0.0807658280653525
2007-10-10 0.0135662611579293 -0.0887607801580943 -0.0865319012446924
2007-10-17 0.0636288839529722 -0.110337934360664 -0.112164497751899
2007-10-24 0.0445991640092625 -0.1170098325164 -0.128300722317255
2007-10-31 0.0354913760050952 -0.114492841022497 -0.117574602518591
2007-11-07 -0.107376449190697 -0.117403098101354 -0.126953382904179
2007-11-19 0.0648366402675229 -0.125257458546729 -0.154938480782926
2007-11-29 0.0263029560701702 -0.130892166836717 -0.164629135504664
2007-12-06 -0.0299982764260842 -0.128206087979728 -0.138832637781698
2007-12-13 -0.00688778141061963 -0.113064484350738 -0.120532846707086
2007-12-20 -0.0437248904305887 -0.110427117525803 -0.120099291276568
2008-01-04 -0.0279568425742069 -0.114024859482052 -0.113072096220954
2008-01-11 -0.124490328914548 -0.115394783438742 -0.147124591294111
2008-01-23 -0.0021102006139615 -0.149666753305471 -0.202705495391654
2008-01-30 -0.0876590441968073 -0.134378212742492 -0.188222691256708
2008-02-06 0.0619877569567877 -0.169122495681101 -0.167136842849094
2008-02-13 -0.0490851841817983 -0.153269415631569 -0.146787904842735
2008-02-25 -0.0616435688534598 -0.147421826708391 -0.137341491894271
2008-03-03 -0.0998055347667298 -0.14255247864926 -0.152894022488484
2008-03-10 0.0147514757748939 -0.154305090364158 -0.158005256092758
2008-03-17 -0.0072242164412637 -0.164977257874236 -0.174433991064961
2008-03-27 0.024832327021439 -0.169348046657473 -0.155844083107324
2008-04-03 0.0286891838830621 -0.167734639482143 -0.157727942790727
2008-04-10 -0.0413506576085645 -0.152743208225046 -0.147774835004945
2008-04-17 0.18795946591611 -0.1367111798463 -0.143459603683837
2008-04-24 0.0886147663912724 -0.136153902298928 -0.139982291642338
2008-05-01 -0.0175399816644555 -0.143683203165612 -0.151594978092608
2008-05-08 -0.00292191816829202 -0.133678856736426 -0.137835166423342
2008-05-15 -0.0561828178293058 -0.121607463232865 -0.12294469901034
2008-05-22 0.0118960378872555 -0.126554948422489 -0.13088517599591
2008-06-03 -0.0236104370589492 -0.123426704072194 -0.124026446639497
2008-06-10 0.02690066612025 -0.126323076206705 -0.138108833156775
2008-06-17 -0.0481746690386216 -0.123210398867616 -0.136913238094268
2008-06-24 -0.0147438330170158 -0.114537619093044 -0.121378611944383
2008-07-01 -0.0326656062363768 -0.119667795111158 -0.143588156964636
2008-07-11 -0.10363397489457 -0.116251661299539 -0.150074016314326
2008-07-18 0.0211890621316322 -0.158735185308093 -0.166724557162659
2008-07-25 -0.0492569784148281 -0.160072336878054 -0.154480433781426
2008-08-01 0.0556423078212093 -0.146240034524819 -0.147609676048827
2008-08-08 0.0304424866263797 -0.151832320474639 -0.142595825867989
2008-08-15 -0.0385171087634747 -0.128805777216968 -0.117773498272219
2008-08-22 -0.0376829941197421 -0.119009150760961 -0.114183150015656
2008-09-03 -0.116664527457477 -0.110996679248043 -0.117232251438626
2008-09-10 0.00242160844217942 -0.134980377565671 -0.158004335187701
2008-09-17 0.0496477221799995 -0.176117205204922 -0.19082797861686
2008-09-24 0.0121006682566508 -0.165983599623469 -0.20546689139938
2008-10-03 -0.225582951969318 -0.204170008921658 -0.263955740183931
2008-10-15 0.0470318408858836 -0.234769888914244 -0.32765748738425
2008-10-22 0.00961619895682209 -0.226564496047889 -0.307786542942255
2008-10-29 -0.0466075813092045 -0.266956883019172 -0.331548791566004
2008-11-05 -0.0038355350384035 -0.278320974052889 -0.259929317388398
2008-11-17 -0.153059826647002 -0.25876323791299 -0.312868676522474
2008-11-24 0.0292311017063402 -0.259076327934361 -0.356635828931991
2008-12-04 0.0882144493630134 -0.293072435229409 -0.324500635327115
2008-12-11 0.0340442384116366 -0.26555330358575 -0.313485263827763
2008-12-18 -0.0320730039719458 -0.253080074997266 -0.239400072111193
2008-12-30 -0.0194290748077118 -0.212476075424783 -0.176443393799662
2009-01-09 0.0156105296747192 -0.200567333471296 -0.167844592941705
2009-01-21 0.140563014434515 -0.215362337700058 -0.203794316929944
2009-01-28 -0.0165527201979927 -0.227590533883346 -0.193942264812996
2009-02-04 0.0429549329058119 -0.179133710635549 -0.181636608020533
2009-02-11 -0.023283803820536 -0.206543625056232 -0.186379398535886
2009-02-23 -0.00931060094087199 -0.207668064069995 -0.195972040475141
2009-03-02 -0.117498403407921 -0.192890650768268 -0.209747110677478
2009-03-09 0.0942970132440855 -0.204156839259934 -0.231375815803186
2009-03-16 0.0854340803363911 -0.19379469181602 -0.217951631447872
2009-03-23 -0.0160413440786881 -0.198112623406326 -0.181781714809197
2009-03-30 0.0700518706713315 -0.176373334968004 -0.156459731588936
2009-04-06 0.0139719609192048 -0.157387409617402 -0.151037620857254
2009-04-16 -0.0111471778597881 -0.159459499363177 -0.155672720360764
2009-04-23 0.0276067771916156 -0.144746150935694 -0.149104761690715
2009-04-30 0.00128797653989599 -0.127090941690805 -0.13583777232044
2009-05-07 -0.0227826451977826 -0.118870666020833 -0.128044189185177
2009-05-14 0.023047611037666 -0.123253884868761 -0.132270527535829
2009-05-21 0.0574414839154231 -0.108111555109863 -0.123942987746446
2009-06-02 0.0172511890550779 -0.104394954926596 -0.111721996959517
2009-06-09 -0.045763801695229 -0.101041345535562 -0.102101391099893
2009-06-16 -0.0255331984172579 -0.0970049421566682 -0.10260244028612
2009-06-23 0.0391979554291663 -0.106067769230315 -0.115055913685506
2009-06-30 0.00405758574906467 -0.101649294553603 -0.104973125745998
2009-07-10 0.036910149473607 -0.112545531362116 -0.111743795388566
2009-07-17 0.0378591231929573 -0.128402378051453 -0.124103685340324
2009-07-24 -0.00799932361908129 -0.121139981640425 -0.123036888668745
Return to Figure 3a

Figure 3b: One-percent and five-percent VaR forecasts for Google returns during the financial crisis of 2008.

date Return realizations VaR with Daily Data VaR with HF 5-min Data
2006-12-08 -0.00759284612867006 -0.0553291422748123 -0.0497122048048539
2006-12-15 -0.0288364211551202 -0.0445386003490088 -0.0351324814894523
2006-12-27 0.0263959464529289 -0.0652582911472151 -0.0541464175967735
2007-01-08 -0.000298878226270505 -0.0691235639960468 -0.062274889635554
2007-01-18 0.000548216133845703 -0.0675035878696933 -0.0599159153764761
2007-01-25 -0.0135419434426756 -0.0780808204659217 -0.0626555905309772
2007-02-01 -0.0220368274410143 -0.0823796193097511 -0.0757405370693444
2007-02-08 -0.0207923530390151 -0.0730746718236481 -0.0612760759300142
2007-02-15 -0.050171209308932 -0.0651753361978884 -0.0520297195764016
2007-02-27 0.00987915425145303 -0.06997088808336 -0.0566481346243021
2007-03-07 -0.0167020113746219 -0.0754510442245905 -0.0632543611314627
2007-03-14 0.0188620170388125 -0.0706043636309712 -0.0616097505123804
2007-03-21 0.0116945114835221 -0.0705345750591746 -0.0533587465276396
2007-03-28 0.0194255802831225 -0.06005247247986 -0.0516409402634181
2007-04-04 0.0124817209661479 -0.0639001819365695 -0.0470825825900339
2007-04-16 0.0107534122316202 -0.0578277956145926 -0.0453500967715624
2007-04-23 -0.0160200332588978 -0.0581335802547202 -0.0569961592602974
2007-04-30 -0.0091179890551103 -0.052889196711529 -0.0466931210655348
2007-05-07 -0.0118404448864124 -0.0495935652042365 -0.0440530026537799
2007-05-14 0.0190373668934902 -0.0511750387085712 -0.0452312729199849
2007-05-21 0.0296517831285603 -0.0559456314384372 -0.047672066894364
2007-05-31 0.033974193287942 -0.0552177514025896 -0.0634577696348636
2007-06-07 -0.0236731155630454 -0.0580214735555538 -0.0722088718580548
2007-06-14 0.0217054095883849 -0.0503302025700841 -0.0577855751229407
2007-06-21 0.021034766310843 -0.0510597079202625 -0.057404453888428
2007-06-28 0.0132749090030364 -0.05005166334762 -0.0618667937747654
2007-07-10 0.0212585104696998 -0.0419261735734642 -0.0495887681675394
2007-07-17 -0.0770732895760962 -0.0367330174905872 -0.0514667508491742
2007-07-24 -0.00727030909036541 -0.0523216728636152 -0.0587569010411456
2007-07-31 0.0106942464627096 -0.0449309663234727 -0.06628897548609
2007-08-07 -0.0142091540597926 -0.0473704403583244 -0.0605944021106711
2007-08-14 -0.00270841398432431 -0.0526387439305102 -0.0561153133247501
2007-08-21 -0.000157806490119539 -0.0573910255162183 -0.0634737242672752
2007-08-28 -0.00258661196866927 -0.0514540162523012 -0.0529175455823966
2007-09-07 0.0178806202597739 -0.0469227442387249 -0.0506936950540658
2007-09-14 0.0575749438359987 -0.0437124421634568 -0.046758327849288
2007-09-21 0.0129764248295696 -0.0549395665233462 -0.054315534354846
2007-09-28 0.0362804004949491 -0.0475372385229697 -0.0501038438836841
2007-10-10 0.0135662611579293 -0.0538760198626701 -0.0539777313155039
2007-10-17 0.0636288839529722 -0.0692445900606888 -0.0718224593248958
2007-10-24 0.0445991640092625 -0.074122823195099 -0.0828186967413072
2007-10-31 0.0354913760050952 -0.0722545370590003 -0.0754969426146305
2007-11-07 -0.107376449190697 -0.0735730739750269 -0.0818689027160651
2007-11-19 0.0648366402675229 -0.0794588383373744 -0.101218532589507
2007-11-29 0.0263029560701702 -0.0837140513281466 -0.108060995042429
2007-12-06 -0.0299982764260842 -0.0814728196341585 -0.089983173316829
2007-12-13 -0.00688778141061963 -0.0711147437144701 -0.0773715000635598
2007-12-20 -0.0437248904305887 -0.0696428941577681 -0.0769680809798684
2008-01-04 -0.0279568425742069 -0.0724698302545738 -0.0721874363564445
2008-01-11 -0.124490328914548 -0.0734508267710736 -0.0953449637717148
2008-01-23 -0.0021102006139615 -0.0964731755186563 -0.132948478471249
2008-01-30 -0.0876590441968073 -0.0848256281260736 -0.123347396729118
2008-02-06 0.0619877569567877 -0.108656556788179 -0.108898105554865
2008-02-13 -0.0490851841817983 -0.0987327321675475 -0.0947861271794808
2008-02-25 -0.0616435688534598 -0.094238726651412 -0.0886550308824653
2008-03-03 -0.0998055347667298 -0.0912494153715643 -0.0993263600911447
2008-03-10 0.0147514757748939 -0.0995842109954984 -0.102835048678771
2008-03-17 -0.0072242164412637 -0.105901511091214 -0.114274384198422
2008-03-27 0.024832327021439 -0.109981686775244 -0.101576153678
2008-04-03 0.0286891838830621 -0.108607816577153 -0.102822713813514
2008-04-10 -0.0413506576085645 -0.0985239854513395 -0.095999490355765
2008-04-17 0.18795946591611 -0.0872051730430583 -0.0931936108605745
2008-04-24 0.0886147663912724 -0.0870443880129576 -0.0907609535136557
2008-05-01 -0.0175399816644555 -0.0927997844121545 -0.098698526097955
2008-05-08 -0.00292191816829202 -0.0860041925503891 -0.089261619080173
2008-05-15 -0.0561828178293058 -0.0770093721680431 -0.079035032699936
2008-05-22 0.0118960378872555 -0.0806775983480718 -0.0844452986078851
2008-06-03 -0.0236104370589492 -0.0785439192700837 -0.079750451695213
2008-06-10 0.02690066612025 -0.0810259492775837 -0.0895150910713393
2008-06-17 -0.0481746690386216 -0.0787739725431056 -0.0887505378866101
2008-06-24 -0.0147438330170158 -0.0725243177752684 -0.0780920642665387
2008-07-01 -0.0326656062363768 -0.0762765309380554 -0.0934387419755755
2008-07-11 -0.10363397489457 -0.0742732097880005 -0.097784390330154
2008-07-18 0.0211890621316322 -0.101744640066409 -0.109349097183752
2008-07-25 -0.0492569784148281 -0.103513111537084 -0.101114995487468
2008-08-01 0.0556423078212093 -0.0941186547610799 -0.0962981876127392
2008-08-08 0.0304424866263797 -0.0988155240552193 -0.0928046631099335
2008-08-15 -0.0385171087634747 -0.083126496665058 -0.0755365669146263
2008-08-22 -0.0376829941197421 -0.0759450257293972 -0.073309362035061
2008-09-03 -0.116664527457477 -0.070394777454238 -0.0753711907047521
2008-09-10 0.00242160844217942 -0.0867202034610402 -0.103221702371621
2008-09-17 0.0496477221799995 -0.115465204436928 -0.126047677360968
2008-09-24 0.0121006682566508 -0.108510275713938 -0.135924957091172
2008-10-03 -0.225582951969318 -0.134032941573954 -0.175224518908643
2008-10-15 0.0470318408858836 -0.154171125010917 -0.218030209000606
2008-10-22 0.00961619895682209 -0.149551025793149 -0.205011233477383
2008-10-29 -0.0466075813092045 -0.1762671031235 -0.220373117935117
2008-11-05 -0.0038355350384035 -0.183431413793315 -0.172044465702444
2008-11-17 -0.153059826647002 -0.171106577914208 -0.208058424690251
2008-11-24 0.0292311017063402 -0.170671200539499 -0.237546970441536
2008-12-04 0.0882144493630134 -0.193768278268972 -0.216004497097046
2008-12-11 0.0340442384116366 -0.175025088430822 -0.208941409794736
2008-12-18 -0.0320730039719458 -0.166883207805511 -0.158360622595315
2008-12-30 -0.0194290748077118 -0.13868580988303 -0.115509047774267
2009-01-09 0.0156105296747192 -0.131316751561079 -0.109837016962379
2009-01-21 0.140563014434515 -0.141560228573897 -0.134610049623268
2009-01-28 -0.0165527201979927 -0.149636889285186 -0.127618368273767
2009-02-04 0.0429549329058119 -0.116049958331569 -0.119229458764973
2009-02-11 -0.023283803820536 -0.136163363699436 -0.122436104896034
2009-02-23 -0.00931060094087199 -0.136891436338774 -0.129052124082349
2009-03-02 -0.117498403407921 -0.12678501533299 -0.13874342713538
2009-03-09 0.0942970132440855 -0.134988995631513 -0.153077651208671
2009-03-16 0.0854340803363911 -0.127742694283022 -0.143986660634423
2009-03-23 -0.0160413440786881 -0.131131509204738 -0.119155544559007
2009-03-30 0.0700518706713315 -0.114936865871743 -0.101950508830023
2009-04-06 0.0139719609192048 -0.102169302682007 -0.0982678081800552
2009-04-16 -0.0111471778597881 -0.10378743372952 -0.101556876207277
2009-04-23 0.0276067771916156 -0.0937454972453893 -0.0969781886060794
2009-04-30 0.00128797653989599 -0.0813541850885979 -0.0878413569802012
2009-05-07 -0.0227826451977826 -0.0758849449191774 -0.0825081693454837
2009-05-14 0.023047611037666 -0.0795021592670277 -0.0854269365813193
2009-05-21 0.0574414839154231 -0.0684553809540924 -0.0796964074259818
2009-06-02 0.0172511890550779 -0.0661745539508124 -0.0711878938785692
2009-06-09 -0.045763801695229 -0.0634067483922816 -0.06446724935453
2009-06-16 -0.0255331984172579 -0.0609697904882393 -0.0649738557907808
2009-06-23 0.0391979554291663 -0.0676053126982494 -0.0736832941892523
2009-06-30 0.00405758574906467 -0.0645282577552831 -0.0665999059065073
2009-07-10 0.036910149473607 -0.0720784113753304 -0.0714203929733658
2009-07-17 0.0378591231929573 -0.0832148160149218 -0.0798445816471852
2009-07-24 -0.00799932361908129 -0.0779002839346646 -0.079034878883033
Return to Figure 3b
♣ This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text
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Last update: September 7, 2010