COVID crash: a study of volatility spillovers from stocks to us indexes and from us indexes to cryptocurrencies
Abstract
During market crashes, panic ensues, investors run to cover and usually only in the aftermath questions arise: How? How much? In which markets? Where did it start? This work seeks to answer some of these questions by quantifying the volatility spillovers from stocks to indexes, but also indexes to cryptocurrency. Not only there is a quantification by variance ratios of the contribution of one asset to another but as well a demonstration of the irregularity and uniqueness of these spillovers compared to other moments in the market’s history. The results from this work shed some light in the intricate relationship of causal effects in volatility such as which stocks contribute the most to the variance of each index and how much of a grip do US indexes have on the overall stability of the cryptocurrencies market. To achieve this, a relatively recent method was employed, described by Christiansen and Bekaert et al., but with some customization to adjust to the particular cases, allowing to perform variance decomposition based on multiple applications of AR-GARCH family models. Since the method relies on sums of decomposed variance, the greatest challenge is to produce variables (time series) independent from each other, and thereby, ignore covariance terms that would interfere with the validity of the analysis. On US indexes to cryptocurrency, the dummy variables were found significant and relevant to the overall modelling of the data, indicating that the period of the market crash is important to future models which otherwise would incur in significant bias that would change the results by orders of magnitude on the variance ratio. On stocks to US indexes, the dummy variables were found to be insignificant at the final results level (conditional correlations and variance ratios), however, not on most individual prices and returns. The period of the market crash is clear graphically by finding a major dip of all conditional correlations, which indicates that no single stock had a major influence during this time and that it was an phenomenon which affected all stocks. Stocks with individual movements that had more influence on the index continued to have the relevance during the market crash. During market crashes, this behavior is expected and this work adds confirmation. By comparing results from both cases, a relationship between eventual spikes in stocks and trend changes in cryptocurrency becomes apparent. This work does not clarify the reason as to why it happens but only its consequence and the cause seems to be exogenous to both cryptocurrency, indexes and possibly stocks. Further work is needed to explain it.
Full text
MMAA
Mes ado em Mé odos Analí icos A ançados
Mas e P og am in Ad anced Analy ics
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão da In o mação
Uni e sidade No a de Lisboa
COVID CRASH: A STUDY OF VOLATILITY
SPILLOVERS FROM STOCKS TO US
INDEXES AND FROM US INDEXES TO
CRYPTOCURRENCIES
Ped o Ma ia F agoso de Almeida Ca alho
Disse a ion p esen ed as pa ial equi emen o
ob aining he Mas e ’s deg ee in Da a Science and
Ad anced Analy ics, wi h majo in Da a Science
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade NOVA de Lisboa
COVID CRASH: A STUDY OF VOLATILITY SPILLOVERS
FROM STOCKS TO US INDEXES AND FROM US INDEXES
TO CRYPTOCURRENCIES
by
Ped o Ma ia F agoso de Almeida Ca alho
Disse a ion p esen ed as pa ial equi emen o ob aining he
Mas e ’s deg ee in Da a Science and Ad anced Analy ics, wi h
majo in Da a Science
Ad ise : B uno Damásio
No embe , 2021
Co id C ash: A S udy o Vola ili y Spillo e s om S ocks o US Indexes and
om US Indexes o C yp ocu encies
Copy igh © Ped o Ma ia F agoso de Almeida Ca alho, NOVA In o ma ion Manage-
men School, NOVA Uni e si y Lisbon.
The NOVA In o ma ion Managemen School and he NOVA Uni e si y Lisbon ha e
he igh , pe pe ual and wi hou geog aphical bounda ies, o ile and publish his dis-
se a ion h ough p in ed copies ep oduced on pape o on digi al o m, o by any
o he means known o ha may be in en ed, and o dissemina e h ough scien i ic
eposi o ies and admi i s copying and dis ibu ion o non-comme cial, educa ional
o esea ch pu poses, as long as c edi is gi en o he au ho and edi o .
This documen was c ea ed wi h he (pd /Xe/Lua)L
A
T
E
X p ocesso and he NOVA hesis empla e ( 6.6.7) Lou enço,
2021.
To OT.
Acknowledgemen s
I would like o hank my Supe iso , P o esso B uno Damásio, o his pa ience, sha -
ing o esou ces and knowledge which we e inc edibly use ul o me, no only o he
pu pose o his hesis bu o o e all unde s anding his new en i onmen and analysis
which I e y much in end o con inue de eloping and wo king on.
I app ecia ed g ea ly e e yone who hea d me complain o mon hs abou s ock
esiduals no being o hogonal o hei unwa e ing pa ience, e en when no ully
g asping he subjec .
I could no pass he oppo uni y o hank he en i e Ad anced Analy ics eam a
CGD o hei sugges ions and unde s anding.
Finally, I am g a e ul o e e yone who missed me because I was busy p oducing
his hesis and ye suppo ed me.
ii
e a p esen e disse ação o nece con i mação.
Compa ando esul ados de ambos os casos, uma elação en e alguns choques em
acções e al e ações de ends eme ge. Es a disse ação não cla i ica a causa e apenas
documen a uma consequência da mesma pois apa en a se ex e na a c ip omoedas,
acções e índices.
Pala as-cha e: ola ili y, spillo e s, c ip omoedas, indices, decomposição da a iân-
cia, au o eg essão, he e osquedacidade, GARCH, a iância condicional, co elação con-
dicional, queda de me cado, COVID-19
xi
Con en s
Lis o Figu es x ii
Lis o Tables xxiii
Glossa y xx
Ac onyms xx ii
1 In oduc ion 1
1.1 S uc u e ................................... 1
1.1.1 US Indexes - C yp ocu encies ................... 1
1.1.2 S ocks - US Indexes ......................... 2
2 Me hodology 3
2.1 P e ious Wo ks and Scien i ic Basis .................... 3
2.1.1 US Indexes - C yp ocu encies ................... 4
2.1.2 S ocks - US Indexes ......................... 6
3 Da a, Empi ical S a egy and Resul s 9
3.1 Da a ...................................... 9
3.1.1 US Indexes - C yp ocu encies ................... 9
3.1.2 S ocks - US Indexes ......................... 11
3.2 Empi ical S a egy .............................. 11
3.2.1 US Indexes - C yp ocu encies ................... 11
3.2.2 S ocks - US Indexes ......................... 12
3.3 Resul s .................................... 16
3.3.1 US Indexes - C yp ocu encies ................... 17
3.3.2 S ocks - US Indexes ......................... 17
3.3.3 Compa a i e Assessmen ...................... 19
4 Conclusion 21
x
Bibliog aphy 23
Appendices
A Appendix 1 25
A.1 DJI ....................................... 26
A.1.1 Index model ............................. 26
A.1.2 BTC .................................. 26
A.1.3 ETH .................................. 29
A.1.4 XRP .................................. 32
A.1.5 XMR ................................. 35
A.2 GSPC ..................................... 38
A.2.1 Index model ............................. 38
A.2.2 BTC .................................. 38
A.2.3 ETH .................................. 41
A.2.4 XRP .................................. 44
A.2.5 XMR ................................. 47
A.3 NDX ...................................... 50
A.3.1 Index model ............................. 50
A.3.2 BTC .................................. 50
A.3.3 ETH .................................. 53
A.3.4 XRP .................................. 56
A.3.5 XMR ................................. 59
B Appendix 2 63
B.1 DJI ....................................... 63
B.2 NDX ...................................... 81
x i
Lis o Figu es
3.1 DJI Va iance (black), DJI P ice (blue) and de ended log-BTC P ice ( ed) . 20
A.1 Va iance Ra io o DJI-BTC ........................... 28
A.2 Va iance Ra io o DJI-BTC wi h dummy a iables .............. 28
A.3 Va iance Ra io o DJI-ETH ........................... 31
A.4 Va iance Ra io o DJI-ETH wi h dummy a iables .............. 31
A.5 Va iance Ra io o DJI-XRP ........................... 34
A.6 Va iance Ra io o DJI-XRP wi h dummy a iables .............. 34
A.7 Va iance Ra io o DJI-XMR ........................... 37
A.8 Va iance Ra io o DJI-XMR wi h dummy a iables ............. 37
A.9 Va iance Ra io o GSPC-BTC .......................... 40
A.10 Va iance Ra io o GSPC-BTC wi h dummy a iables ............ 40
A.11 Va iance Ra io o GSPC-ETH .......................... 43
A.12 Va iance Ra io o GSPC-ETH wi h dummy a iables ............ 43
A.13 Va iance Ra io o GSPC-XRP .......................... 46
A.14 Va iance Ra io o GSPC-XRP wi h dummy a iables ............ 46
A.15 Va iance Ra io o GSPC-XMR ......................... 49
A.16 Va iance Ra io o GSPC-XMR wi h dummy a iables ............ 49
A.17 Va iance Ra io o NDX-BTC .......................... 52
A.18 Va iance Ra io o NDX-BTC wi h dummy a iables ............. 52
A.19 Va iance Ra io o NDX-ETH .......................... 55
A.20 Va iance Ra io o NDX-ETH wi h dummy a iables ............. 55
A.21 Va iance Ra io o NDX-XRP .......................... 58
A.22 Va iance Ra io o NDX-XRP wi h dummy a iables ............. 58
A.23 Va iance Ra io o NDX-XMR .......................... 61
A.24 Va iance Ra io o NDX-XMR wi h dummy a iables ............. 61
B.1 Condi ional Co ela ion DJI-MMM ...................... 66
B.2 Condi ional Co ela ion DJI-AXP ....................... 66
B.3 Condi ional Co ela ion DJI-AMGN ...................... 67
x ii
B.4 Condi ional Co ela ion DJI-AAPL ...................... 67
B.5 Condi ional Co ela ion DJI-BA ........................ 68
B.6 Condi ional Co ela ion DJI-CAT ....................... 68
B.7 Condi ional Co ela ion DJI-CVX ....................... 69
B.8 Condi ional Co ela ion DJI-CSCO ...................... 69
B.9 Condi ional Co ela ion DJI-KO ........................ 70
B.10 Condi ional Co ela ion DJI-DOW ...................... 70
B.11 Condi ional Co ela ion DJI-GS ........................ 71
B.12 Condi ional Co ela ion DJI-HD ........................ 71
B.13 Condi ional Co ela ion DJI-HON ....................... 72
B.14 Condi ional Co ela ion DJI-IBM ....................... 72
B.15 Condi ional Co ela ion DJI-INTC ...................... 73
B.16 Condi ional Co ela ion DJI-JNJ ........................ 73
B.17 Condi ional Co ela ion DJI-JPM ....................... 74
B.18 Condi ional Co ela ion DJI-MCD ....................... 74
B.19 Condi ional Co ela ion DJI-MRK ....................... 75
B.20 Condi ional Co ela ion DJI-MSFT ...................... 75
B.21 Condi ional Co ela ion DJI-NKE ....................... 76
B.22 Condi ional Co ela ion DJI-PG ........................ 76
B.23 Condi ional Co ela ion DJI-CRM ....................... 77
B.24 Condi ional Co ela ion DJI-TRV ....................... 77
B.25 Condi ional Co ela ion DJI-UNH ....................... 78
B.26 Condi ional Co ela ion DJI-VZ ........................ 78
B.27 Condi ional Co ela ion DJI-V ......................... 79
B.28 Condi ional Co ela ion DJI-WMT ...................... 79
B.29 Condi ional Co ela ion DJI-WBA ....................... 80
B.30 Condi ional Co ela ion DJI-DIS ........................ 80
B.31 Condi ional Co ela ion NDX-AAPL ..................... 88
B.32 Condi ional Co ela ion NDX-ADBE ..................... 88
B.33 Condi ional Co ela ion NDX-ADI ...................... 89
B.34 Condi ional Co ela ion NDX-ADP ...................... 90
B.35 Condi ional Co ela ion NDX-ADSK ..................... 90
B.36 Condi ional Co ela ion NDX-AEP ...................... 91
B.37 Condi ional Co ela ion NDX-ALGN ..................... 91
B.38 Condi ional Co ela ion NDX-AMAT ..................... 92
B.39 Condi ional Co ela ion NDX-AMD ...................... 92
B.40 Condi ional Co ela ion NDX-AMGN ..................... 93
B.41 Condi ional Co ela ion NDX-AMZN ..................... 93
B.42 Condi ional Co ela ion NDX-ANSS ...................... 94
B.43 Condi ional Co ela ion NDX-ASML ..................... 94
B.44 Condi ional Co ela ion NDX-ATVI ...................... 95
x iii
B.45 Condi ional Co ela ion NDX-AVGO ..................... 95
B.46 Condi ional Co ela ion NDX-BIDU ...................... 96
B.47 Condi ional Co ela ion NDX-BIIB ...................... 96
B.48 Condi ional Co ela ion NDX-BKNG ..................... 97
B.49 Condi ional Co ela ion NDX-CDNS ..................... 97
B.50 Condi ional Co ela ion NDX-CDW ...................... 98
B.51 Condi ional Co ela ion NDX-CERN ..................... 98
B.52 Condi ional Co ela ion NDX-CHKP ..................... 99
B.53 Condi ional Co ela ion NDX-CHTR ..................... 99
B.54 Condi ional Co ela ion NDX-CMCSA .................... 100
B.55 Condi ional Co ela ion NDX-COST ..................... 100
B.56 Condi ional Co ela ion NDX-CPRT ..................... 101
B.57 Condi ional Co ela ion NDX-CRWD ..................... 101
B.58 Condi ional Co ela ion NDX-CSCO ..................... 102
B.59 Condi ional Co ela ion NDX-CSX ...................... 102
B.60 Condi ional Co ela ion NDX-CTAS ...................... 103
B.61 Condi ional Co ela ion NDX-CTSH ..................... 103
B.62 Condi ional Co ela ion NDX-DLTR ..................... 104
B.63 Condi ional Co ela ion NDX-DOCU ..................... 104
B.64 Condi ional Co ela ion NDX-DXCM ..................... 105
B.65 Condi ional Co ela ion NDX-EA ....................... 105
B.66 Condi ional Co ela ion NDX-EBAY ...................... 106
B.67 Condi ional Co ela ion NDX-EXC ...................... 106
B.68 Condi ional Co ela ion NDX-FAST ...................... 107
B.69 Condi ional Co ela ion NDX-FB ....................... 107
B.70 Condi ional Co ela ion NDX-FISV ...................... 108
B.71 Condi ional Co ela ion NDX-FOX ...................... 108
B.72 Condi ional Co ela ion NDX-FOXA ..................... 109
B.73 Condi ional Co ela ion NDX-GILD ...................... 109
B.74 Condi ional Co ela ion NDX-GOOG ..................... 110
B.75 Condi ional Co ela ion NDX-GOOGL .................... 110
B.76 Condi ional Co ela ion NDX-HON ...................... 111
B.77 Condi ional Co ela ion NDX-IDXX ...................... 111
B.78 Condi ional Co ela ion NDX-ILMN ..................... 112
B.79 Condi ional Co ela ion NDX-INCY ...................... 112
B.80 Condi ional Co ela ion NDX-INTC ...................... 113
B.81 Condi ional Co ela ion NDX-INTU ...................... 113
B.82 Condi ional Co ela ion NDX-ISRG ...................... 114
B.83 Condi ional Co ela ion NDX-JD ....................... 114
B.84 Condi ional Co ela ion NDX-KDP ...................... 115
B.85 Condi ional Co ela ion NDX-KHC ...................... 115
xix
B.86 Condi ional Co ela ion NDX-KLAC ..................... 116
B.87 Condi ional Co ela ion NDX-LRCX ..................... 116
B.88 Condi ional Co ela ion NDX-LULU ..................... 117
B.89 Condi ional Co ela ion NDX-MAR ...................... 117
B.90 Condi ional Co ela ion NDX-MCHP ..................... 118
B.91 Condi ional Co ela ion NDX-MDLZ ..................... 118
B.92 Condi ional Co ela ion NDX-MELI ...................... 119
B.93 Condi ional Co ela ion NDX-MNST ..................... 119
B.94 Condi ional Co ela ion NDX-MRNA ..................... 120
B.95 Condi ional Co ela ion NDX-MRVL ..................... 120
B.96 Condi ional Co ela ion NDX-MSFT ..................... 121
B.97 Condi ional Co ela ion NDX-MTCH ..................... 121
B.98 Condi ional Co ela ion NDX-MU ....................... 122
B.99 Condi ional Co ela ion NDX-NFLX ..................... 122
B.100Condi ional Co ela ion NDX-NTES ...................... 123
B.101Condi ional Co ela ion NDX-NVDA ..................... 123
B.102Condi ional Co ela ion NDX-NXPI ...................... 124
B.103Condi ional Co ela ion NDX-OKTA ..................... 124
B.104Condi ional Co ela ion NDX-ORLY ..................... 125
B.105Condi ional Co ela ion NDX-PAYX ...................... 125
B.106Condi ional Co ela ion NDX-PCAR ..................... 126
B.107Condi ional Co ela ion NDX-PDD ...................... 126
B.108Condi ional Co ela ion NDX-PEP ...................... 127
B.109Condi ional Co ela ion NDX-PTON ..................... 127
B.110Condi ional Co ela ion NDX-PYPL ...................... 128
B.111Condi ional Co ela ion NDX-QCOM ..................... 128
B.112Condi ional Co ela ion NDX-REGN ..................... 129
B.113Condi ional Co ela ion NDX-ROST ..................... 129
B.114Condi ional Co ela ion NDX-SBUX ..................... 130
B.115Condi ional Co ela ion NDX-SGEN ..................... 130
B.116Condi ional Co ela ion NDX-SIRI ...................... 131
B.117Condi ional Co ela ion NDX-SNPS ...................... 131
B.118Condi ional Co ela ion NDX-SPLK ...................... 132
B.119Condi ional Co ela ion NDX-SWKS ..................... 132
B.120Condi ional Co ela ion NDX-TCOM ..................... 133
B.121Condi ional Co ela ion NDX-TEAM ..................... 133
B.122Condi ional Co ela ion NDX-TEAM ..................... 134
B.123Condi ional Co ela ion NDX-TMUS ..................... 134
B.124Condi ional Co ela ion NDX-TSLA ...................... 135
B.125Condi ional Co ela ion NDX-TXN ...................... 135
B.126Condi ional Co ela ion NDX-VRSK ...................... 136
xx
B.127Condi ional Co ela ion NDX-VRSN ..................... 136
B.128Condi ional Co ela ion NDX-VRTX ..................... 137
B.129Condi ional Co ela ion NDX-WBA ...................... 137
B.130Condi ional Co ela ion NDX-WDAY ..................... 138
B.131Condi ional Co ela ion NDX-XEL ...................... 138
B.132Condi ional Co ela ion NDX-XLNX ..................... 139
B.133Condi ional Co ela ion NDX-ZM ....................... 139
xxi
Lis o Tables
A.1 Pa ame e Es ima es o he GARCH(1, 1) (DJI) ................ 26
A.2 Pa ame e Es ima es o he GARCH(1, 1) (DJI-BTC) ............. 26
A.3 Pa ame e Es ima es o he GARCH(1, 1) (DJI-BTC wi h dummy a .) . . 27
A.4 Pa ame e Es ima es o he GARCH(1, 1) ((DJI-ETH) ............ 29
A.5 Pa ame e Es ima es o he GARCH(1, 1) (DJI-ETH wi h dummy a .) . . 30
A.6 Pa ame e Es ima es o he GARCH(1, 1) (DJI-XRP) ............. 32
A.7 Pa ame e Es ima es o he GARCH(1, 1) (DJI-XRP wi h dummy a .) . . 33
A.8 Pa ame e Es ima es o he GARCH(1, 1) (DJI-XMR) ............ 35
A.9 Pa ame e Es ima es o he GARCH(1, 1) (DJI-XMR wi h dummy a .) . . 36
A.10 Pa ame e Es ima es o he GARCH(1, 1) (GSPC) .............. 38
A.11 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-BTC) ........... 38
A.12 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-BTC wi h dummy a .) . 39
A.13 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-ETH) ........... 41
A.14 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-ETH wi h dummy a .) . 42
A.15 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-XRP) ........... 44
A.16 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-XRP wi h dummy a .) . 45
A.17 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-XMR) ........... 47
A.18 Pa ame e Es ima es o he GARCH(1, 1) (GSPC-XMR wi h dummy a .) 48
A.19 Pa ame e Es ima es o he GARCH(1, 1) (NDX) ............... 50
A.20 Pa ame e Es ima es o he GARCH(1, 1) (NDX-BTC) ............ 50
A.21 Pa ame e Es ima es o he GARCH(1, 1) (NDX-BTC wi h dummy a .) . 51
A.22 Pa ame e Es ima es o he GARCH(1, 1) (NDX-ETH) ............ 53
A.23 Pa ame e Es ima es o he GARCH(1, 1) (NDX-ETH wi h dummy a .) . 54
A.24 Pa ame e Es ima es o he GARCH(1, 1) (NDX-XRP) ............ 56
A.25 Pa ame e Es ima es o he GARCH(1, 1) (NDX-XRP wi h dummy a .) . 57
A.26 Pa ame e Es ima es o he GARCH(1, 1) (NDX-XMR) ........... 59
A.27 Pa ame e Es ima es o he GARCH(1, 1) (NDX-XMR wi h dummy a .) . 60
B.1 Pa ame e Es ima es o he GARCH(1, 1) (DJI-S ocks) ........... 64
xxiii
CHAPTER 1. INTRODUCTION
compa e he ola ili y spillo e s o h ee e y ma u e and es ablished US s ock indexes
(Dow Jones, Nasdaq 100 and S anda d & Poo ’s 500) and he ou c yp ocu encies
(Bi coin, E he eum, Ripple and Mone o) du ing he Co id ma ke c ash and quan i y
he inancial con agion e ec s be ween hese asse s which a e e y di e en in na u e
bu seemingly in e connec ed as i will be demons a ed.
1.1.2 S ocks - US Indexes
The e olu ion o he majo US indexes a e a sign o he s a e and well-being o he o e -
all US (and po en ially global) ma ke . I is ele an o s udy and ecognize momen s
o s ess as soon as possible and in oduce no el me hodologiesp o iding new obse -
a ion angles, allowing eliable in o ma ion o come o ligh . The ecen pandemic
has been a s ess es o he esilience o he socie y, including he economic engines’,
companies, and hei abili y o adap o he new eali y. This has ansla ed o ins a-
bili y and inc eased ma ke ola ili yl, leading o an ex emely signi ican alue d op
o he indexes in Ma ch 30 h 2020. By quan i ying his ins abili y, he ma ke can ab-
so b he shock and become mo e esilien , whe he by making bold adjus men s o he
unc ion o he companies and ela ionships o inancial ins i u ions o h ough mo e
conse a i e app oaches o p ese e economic s abili y ha may s ill be cu en ly, as
o No embe 2021, a isk. The S ocks-US Indexes sec ion ocuses p ima ily on unex-
pec ed ola ili y o indexes and iden i ica ion o he companies ha o igina ed i , as
well as i s quan i ica ion. The me hodology p oposed o achie e his goal, in based on
decomposing ola ili y acco ding o he a ious indexes’ s ocks elying on he ideas o
Bekae e al. (2005) and Ch is iansen (2007). Al hough he e is much esea ch on his
opic, i is he au ho ’s belie ha me hods ypically used, such as CCC-GARCH and
DCC-GARCH models can be imp o ed, as his me hod p o ides dynamic condi ional
co ela ions (which a e impossible wi h CCC-GARCH).
2
2
Me hodology
2.1 P e ious Wo ks and Scien i ic Basis
The ypical app oach o his p oblem is wi h mul i a ia e GARCH model based solu-
ions, in pa icula DCC-GARCH models. Simila wo ks ha e been seen in li e a u e
using hese models as a basis bu hei use is discou aged by McAlee o some ex en
by p o iding e idence ha DCC does no sa is y he condi ion o a condi ional co -
ela ion ma ix and ha no unde lying s ochas ic p ocess leads o he DCC model.
This me hodology can p esen a mo e consis en op ion and a manne o add ess he
issues a isen in he a o emen ioned li e a u e (McAlee , 2019). An ex emely simila
wo k o pa o he p esen disse a ion includes Malho a and Gup a (2019), whe e
spillo e s a e quan i ied be ween Asian equi y ma ke s and c yp ocu ency, in pa
using he a o emen ioned models. The e is as well a wo k by Ume e al., whe e ola il-
i y spillo e s among EAGLE ma ke s (de eloping coun ies) a e desc ibed using DCC
(Engle, 2002) and BEKK-GARCH (Engle & K one , 2000) models o analyse he 2008
subp ime c isis (Ume e al., 2018).
The basis o me hod in he p esen disse a ion is p oposed in Bekae e al. (2005)
o de e mine ola ili y spillo e s be ween a ious ma ke s paying close a en ion o
egional in eg a ion o ola ili y spillo e s om majo globalized o egional ones,
consis ing o a wo-s ep model amewo k. This could be an assump ion o causali y, an
assump ion ha Ch is iansen, has aken and used, in a G ange sense (G ange , 1969),
o s udy ola ili y spillo e s in bonds ma ke s and desc ibed as essen ial. In ha wo k,
a e desc ibed and s udied ola ili y spillo e s om US ma ke s o Eu opean o egional
(coun y le el) ma ke s du ing he in oduc ion o he Eu o wi h dummy a iables and
o he simila exogenous means o e ospec i e co ec ion and es ing (Ch is iansen,
2007). Bo h hese wo ks a e based on he o hogonaliza ion o a iables h ough
eg ession, aking ad an age o he eg ession p ope y o o hogonal esiduals o hei
eg esso s, causing hei independence and so, consequen ly, ola ili y decomposi ion
is a simple p ocess by elimina ing he need o condi ional co ela ion models such as
DCC and BEKK.
3
CHAPTER 2. METHODOLOGY
The majo di e ence be ween bo h cases is how he mul iple a iables a e o ga-
nized in causali y low. In he c yp ocu ency case, a ime se ies (index) has in luence
o e o he ime se ies (c yp ocu ency). In s ocks, mul iple ime se ies (s ocks) ha e
in luence o a single one (index) which is an unde s a emen since he index is buil
by de ini ion h ough co-in eg a ion o s ocks. O cou se ha he weigh in each s ock
may ha e impo ance, bu i does no ully desc ibe he a iance spillo e s and a mo e
comple e s ochas ic analysis is equi ed.
2.1.1 US Indexes - C yp ocu encies
The e is a ema kable di e ence no only in he asse s hemsel es bu in how hese
ma ke s’ ime ames ope a e. Simply using one lag migh no p ope ly ake in o
accoun pas in o ma ion and make he models poo ly es ima ed du ing some pa ic-
ula momen s, especially weekends and Mondays. The a iables mus be unde he
usual cons ain s o s a iona i y and no mali y as well as causali y in a G ange sense
(G ange , 1969). Two ypes o models we e applied, an AR(k)-GARCH o he indexes
and an AR(1)-gj GARCH, a model desc ibed in Glos en e al., 1993 o he c yp ocu -
encies, whe e
k
is he lag a which G ange causali y is signi ican , bu o e he all
he i e a ions o he pai s o indexes and c yp ocu encies, ini ially, he lag
k
= 4 was
he only one used since i is signi ican o Bi coin and E he eum and i is also he lag
ha minimizes he p- alue o Ripple and Mone o. Howe e , his only p o ed e ec i e
when he synch oniza ion o he indexes’ and c yp ocu encies’ ime se ies was based
on a o wa d ill me hod. This b ough nonsensical changes in he da a, in pa icula
ola ili y i sel and as such he me hod had o be e hinked. A e changing he me hod
o deal wi h he synch oniza ion, he G ange causali y was ound signi ican a lag 2.
Models we e es ima ed on lag 1 and 2, and e y mino di e ences we e ound be ween
hem, as such, a model wi h lag 1 was p e e ed since i is he simple solu ion.
Since his wo k only has wo s eps, indexes in o c yp ocu encies, some o he
modelling amewo k om p e ious wo ks is no applied. And so, i begins wi h a
model speci ica ion o he index’s log e u ns:
RI, =c0,I +c1,IRI, −1+eI, (2.1)
The e o e m
eI,
is no mally dis ibu ed wi h mean 0 and i is assumed o ollow a
GARCH(1,1) on he esiduals:
σ2
I, =ωI+αIe2
I, −1+βIσ2
I, −1(2.2)
The nex equa ion p esen s he AR(1) es ima ion o he c yp ocu encies, using
index e u ns and he p e ious model’s esiduals. So we can assume ha an o hogo-
naliza ion be ween he indexes and c yp ocu encies will occu which will be essen ial
la e on, o i will be he only way ha he a ia ion a ios will make sense. The
eC,
e m shows ARCH e ec s, possibly making he model an AR(1)-GARCH bu he e is
4
2.1. PREVIOUS WORKS AND SCIENTIFIC BASIS
some asymme y in he da a o c yp ocu encies. A solu ion is p o ided by Chu and
Chan, whe e a gj GARCH is one o he wo mos iable models o es ima e wi h and
o e s a solu ion o his asymme y (Chu & Chan, 2017). The AR(1)-gj GARCH model
wi h he ex e nal eg esso s om he p e ious index es ima ion can be ully explained
now:
RC, =c0,C +c1,CRC, −1+ζC,1RI, −1+φCeI, +eC, (2.3)
whe e he gj GARCH(1,1),
σ2
C, =ωC+αC+γCIC, −1e2
C, −1+βCσ2
C, −1
IC, −1:=
0 i RC, −1≥µ
1 i RC, −1< µ
(2.4)
I is simple o ealize how he gj GARCH ope a es by sepa a ing he e u ns by
abo e o below he condi ional mean and helping o p ope ly es ima e when he e
is asymme y. These models culmina e in independen idiosync a ic shocks bu no
independen unexpec ed e u ns:
εUS, =eUS, (2.5)
εC, =φCeI, +eC, (2.6)
F om he p e ious equa ions, he condi ional a iance o he unexpec ed e u n
o he c yp ocu encies can be deduced, and his is only possible because
eI, −k
is
o hogonal due o he AR(k= 1) speci ica ion om equa ion 2.1.
hC, =E[ϵ2
C, |I −1] = φ2
Cσ2
I, +σ2
C, (2.7)
Now, we ha e all he ing edien s equi ed o de e mine a iance a ios om indexes
in o c yp ocu encies:
V R =φ2
Cσ2
I,
hC,
(2.8)
The p e ious equa ion akes alues om 0 o 1. This alue demons a es in lu-
ence o he index’s a iance on c yp ocu ency’s. The emainde o he alue up o 1
co esponds o own ola ili y mo emen s and pu e c yp ocu ency shocks o which
he index canno explain. Al hough, his equa ion demons a es cons an spillo e s o
which he coe icien s o he equa ion 2.5 demons a e he spillo e e ec s:
ζC,i =ζC∀
φC,i =φC∀
(2.9)
5
CHAPTER 2. METHODOLOGY
To unde s and he phenomena du ing he Co id ma ke c ash, he pa ame e s we e
se in his ashion:
ζC,i =ζC,0,i +ζC,1,iD
φC,i =φC,0,i +φC,1,iD
(2.10)
D
is a dummy a iable ha akes uni alue du ing he pe iod in which he ma ke
c ash occu ed, Feb ua y 20 h 2020 and Ap il 7 h o he same yea . This speci ica ion
was in oduced in equa ion 2.3 and hen e aced all he subsequen s eps o e ie e
he new a iance a ios.
2.1.2 S ocks - US Indexes
The daily e u ns may be ep esen ed as
RI, =
k
X
i=1
βiRs, +eI, (2.11)
whe e
Rs,
is he daily e u ns o s ock
s
a momen
,
βs
is he weigh o s ock
s
and
eI,
is an e o e m, which can be a measu emen o model accu acy and a iabili y o
βs
o e ime.
q
is he o al numbe o s ocks in each index. Le
F −1
be he in o ma ion
se gene a ed by he a ailable in o ma ion un il −1. Gi en ha
V a (I |F −1) =
q
X
i=1
β2
sV a (Rs, |F −1) + 2
q−1
X
s=1
q
X
j=s+1
Co (Rs, ,Rj, |F −1) (2.12)
i is clea ha he index’s a iance canno be decomposed using solely he e ms
V a
(
Rs, |F −1
). To o e come his p oblem, a me hod was de eloped based on a me hod-
ology by Ch is iansen, which was used o ex ac he ola ili y spillo e e ec s in bond
ma ke s. I is assumed ha he e u ns can be exp essed as
RI, =ζ +
q
X
s=1
ηses, +υ (2.13)
whe e
ζ
is
F −1
-measu able and may include a cons an , seasonal dummies and dy-
namic e ms such as ARMA amily models and o he s ock e u ns.
es,
a e o hogonal
shocks associa ed wi h each s ock and
υ
is he e o e m. And so, he condi ional
a iance o
RI,
can be decomposed in o he sum o indi idual shocks o each s ock
plus he a iance o he idiosync a ic e m υ ,
V a (RI, |F −1) =
q
X
s=1
η2
sV a (es, |F −1) + V a (υ |F −1) (2.14)
This is he exp ession o used o decompose he a iance. I pe mi s he examina ion
o he ela ionship and ola ili y spillo e s om s ocks o indexes as he condi ional
6
2.1. PREVIOUS WORKS AND SCIENTIFIC BASIS
a iance o each s ock can be di ec ly compa ed o he condi ional a iance o he
index. To enable his exp ession, wo issues s ill ha e o be esol ed: 1. he shocks
need o be es ima ed 2. hey mus be o hogonal.
The shock
es,
is unknown bu i can be es ima ed om he esiduals o
Rs,
on
µs,
:
Rs, =µs, +es, (2.15)
The e m
µs,
is
F −1
mensu able and may include a cons an , seasonal dummies, o
dynamic e ms, and any o he e ms ha may be co ela ed wi h
Rs,
. This p ocedu e
aims o emo e all he e ec s de ined in
µs,
om
Rs,
and o he e ec s so ha
es,
is
unco ela ed wi h ej, (j,s).
I is assumed
es, |F −1∼N
(0
,σ2
s,
) and
υ |F −1∼N
(0
,σ2
υ,
). A es based on Lag ange
mul iplie p inciple con i ms ha mos he e o s display GARCH ype e ec s.
To con i m he o hogonaliza ion o he s ock esiduals, a Lag ange mul iplie
s a is ic is conside ed
λLM
=
nPM
s=2 Ps−1
j=1 ˆ
ρ2
s,j
, o which
ˆ
ρs,j
=
Co
(
es,ej
). Unde he
null,
Ho
:
ˆ
ρi,j
= 0,
λLM
has a limi ing chi-squa ed dis ibu ion wi h
M
(
M−
1)
/
2 deg ees
o eedom.
Le
y
= (
1, ,..., q, ,I
),
µ
= (
µ1, ,...,µq, ,ω
),
u
=
Φe
whe e
Ψ
and
e
a e de ined as
ollows
u =
1 0 ... 0 0
0 1 ... 0 0
.
.
..
.
..
.
..
.
.
0 0 ... 1 0
η1η2... ηq1
| {z }
Ψ
e1
e2
.
.
.
eq,
υ
|{z}
e
(2.16)
The model can be succinc ly w i en as
y
=
µ
+
u
whe e
u
=
Ψe
(no e ha
Ψ
is a
iangula ma ix). The condi ional a iance o y is
H =V a (y |F −1) = V a (u |F −1) = Ψ Σ Ψ′=
=
σ2
1, 0... 0η1σ1,
0σ2
2, ... 0η2σ2,
.
.
..
.
..
.
..
.
.
0 0 ... σ2
1, ηqσq,
η1σ1, η1σ2, ... ηqσq, Pq
s=1 η2
iσ2
s, +σ2
υ,
(2.17)
whe e Σ := V a (e |F −1). I ollows ha
V a (I |F −1) =
q
X
i=1
η2
iσ2
i, +σ2
υ, (2.18)
Co (Rs, ,I |F −1) = ηiσ2
s,
qσ2
s, (Pq
s=1 η2
iσ2
s, +σ2
υ, )
=ηiσs,
qPq
s=1 η2
iσ2
s, +σ2
υ,
(2.19)
7
CHAPTER 2. METHODOLOGY
To inalize hese e ec s, and in a simila ashion o he p e ious case wi h c yp ocu -
encies, a dummy a iable will be inse ed and i s signi icance e i ied. The simples
and an e ec i e way is o apply an AR(1) model o condi ional a iances, a iance
a ios and condi ional co ela ions wi h a dummy a iable as exogenous wi h uni a y
alue du ing he Co id ma ke c ash and ze o du ing all emaining ime.
8
3
Da a, Empi ical S a egy and
Resul s
3.1 Da a
3.1.1 US Indexes - C yp ocu encies
The da a used o his case has been comp ised o h ee indices:
• Dow Jones Indus ial (Dow Jones Indus ial Index (DJI))
• S anda d & Poo ’s 500 (SP500 o S anda d & Poo ’s 500 Index (SP500) (GSPC))
• NASDAQ 100 (Nasdaq 100 Index (NDX))
And also included ou c yp ocu encies:
• Bi coin (Bi coin (BTC))
• E he , colloquially known by he chain name E he eum (E he eum (ETH))
• Ripple (Ripple (XRP))
• Mone o (Mone o (XMR))
All he a o emen ioned da a was e ie ed by making API eques s o yahoo inance
da a o close adjus ed p ices. The indexes’ da a was e ie ed om 2002 and he
c yp ocu encies om hei ea lies eco d lis ing on yahoo inance. The da a was
p ocessed in o daily loga i hmic e u ns and all da a was cas ed in o a ime se ies da a
s uc u e bu he e is p esen ed an uncommon challenge: he da a does no ma ch em-
po ally. This happens because while he s ock ma ke s a e no open du ing weekends
and holidays, c yp ocu encies a e pe manen ly open and so his posed a challenge
on how o synch onize he da a. A solu ion is clea : joining he da a om each index
and each c yp ocu ency so ha no only hey ha e he same beginning ( he e we e
no c yp ocu encies in 2002), bu also he indexes’ ime se ies will display a missing
9
CHAPTER 3. DATA, EMPIRICAL STRATEGY AND RESULTS
alue on non-business days, and hence accoun ing o missing days in he o iginal
da a, while he c yp ocu encies’ will display a alue. A me hod was o be conside ed
o ill hese missing alues in o de o no lose da a.
Le index da a be a ime se ies o daily close adjus ed p ices wi h alues only on
business days. I can be conside ed ha he e a e h ee op ions o illing: 1. ill wi h
ze o, 2. in e pola e, 3. o wa d ill. Filling wi h ze o p esen s a nonsensical shock and
change o he ime se ies in an a i icial manne which would ende mos analysis
useless, e en wi h a dummy a iable, so his me hod is unaccep able.
In e pola ing he non-business days, using F iday and Monday alues o example,
could b ing good esul s and ie he alues in a somewha con inuous ashion du ing
hese days. Bu in a ime se ies sense i is inapp op ia e, i means he e is an in o -
ma ion leak om u u e alues o he p ice a
,becoming dependen on
+
k,k >
0,
c ea ing a non-causal sys em and incu bias in la e expe imen a ion.
Conside ing he p e ious wo issues, a o wa d ill seems o be he bes op ion,
a oids c ea ing nonsense da a which would happen wi h a ze o ill, and allows he
con inua ion o a causal sys em which would no happen wi h in e pola ion. This
me hod o illing seems o be he one ha minimizes impac on he p ice ime se ies.
Al hough he pa ag aphs abo e con ain me hods o deal wi h he null alues on
p ice, he da a is loga i hmic e u ns, bu he logic can be ansla ed in o his da a.
Since he e u n is a dimensionless coe icien o di e en ia ion o p ice a
and
−
1, i
he e is no change in p ice wi h o wa d ill hen he e u n is ze o. And so, in dealing
wi h e u ns wi h he a o emen ioned da a, he null alues we e illed wi h ze o. La e ,
i will be explained why his me hod was no used.
On he second i e a ion o models, he e u ns and esiduals o he a o emen ioned
equa ions we e simply lagged and in oduced in he AR(1)-gj GARCH c yp ocu ency
models on he nex s ep as exogenous a iables in equa ions 2.3 and 2.4.
The e is also a simila issue in he a iances. Since he modelling o he indexes was
no made o espec he ime ame o he c yp ocu encies bu o solely he indexes
hemsel es, he a iances would ha e missing alues on non-business days simila ly
o p ice da a. I he p e ious me hod was used, simply illing wi h ze o, he a iance
a io would no make sense because i would be ze o as well on hose same days, which
is as i saying, o example, ha any amoun o ola ili y on F iday in indexes is no
spilled du ing he weekend o c yp ocu encies, which is unaccep able. Al hough he
p ices a e no obse able, o e en i he ma ke s a e closed, he e is a change in he
p ice and making supposi ions can o e w i e his and c ea e dispa i ies be ween he
p esen ed wo k and he phenomenon i sel by in oducing bias h ough he new da a.
Models we e c ea ed using i and hey had a qui ky beha io by ea u ing a e y high
impo ance o AR(3) and AR(4) coe icien s, which is somewha s ange. How can i
be expec ed, in a high speed ansac ion en i onmen , o ind s a is ical signi icance
om h ee o ou days ago, p obably due o weekend e ec s, on a Thu sday o F iday
in de imen o he immedia ely p e ious day?
10
3.2. EMPIRICAL STRATEGY
The inal solu ion is clea : any ows con aining missing alues mus be d opped.
This means ha a synch oniza ion had o be made a he p ice le el and no a he
e u ns’ since i would pai index e u ns om F iday o Monday while c yp ocu en-
cies would ha e om Sunday o Monday. Al hough he e is some loss o da a, he e
is no inse ed da a no only on he e u ns bu also he ola ili y which was he mos
p oblema ic da a inse ion. This was he inal da a used o his wo k.
3.1.2 S ocks - US Indexes
He e he app oach is somewha di e en han he p e ious case, bu he indexes in
s udy a e s ill he same: DJI,GSPC and NDX. The da a is as well daily loga i hmic
e u ns o close adjus ed p ices o indexes and all he s ocks ha comp ise hem which
o he sake o b e i y a comple e lis ing will be wi hhold o he e we e used hund eds
o unique s ocks. Bu he e we e wo issues wi h he da a: 1. he e was no a simple
au oma ed way o e ie e he all he s ocks o each index 2. index composi ion
changes o e ime which could ende he me hod used useless since he da a would
no ma ch wi h he index.
To sol e he i s issue, websc apping was used. This allowed o e ie e he up-
da ed composi ion o each index and hei espec i e icke s, and so he au oma ed
download o he da a was possible.
Fo he second issue, a comp omise had o be made. Ins ead o using da a om
2002 simila ly o he p e ious case, he da a s a s om 2018, and so, a g ea deal o
majo changes o he indexes we e a oided bu s ill e aining he objec i e o his wo k,
since he ma ke c ash in s udy occu ed only in he i s and second qua e s o 2020.
Despi e he al eady as amoun o a iables, mo e we e added o mi iga e issues
wi h model es ima ion, which include he addi ion o seasonal dummies, speci ically
day-o - he-week and mon hly, and subsec ions o he o iginal s ock e u ns, an expla-
na ion o his will be imely gi en.
La e , his da a was d opped and p ice da a was used in he models since log-
e u ns did no p o ide an app op ia e o hogonaliza ion o esiduals. This change
will be discussed and explained la e on.
3.2 Empi ical S a egy
3.2.1 US Indexes - C yp ocu encies
The causali y equisi e could be ul illed in a G ange sense in Bi coin and in E he eum
a a 5% signi icance a lag 2. Fo Ripple and Mone o i is no pa icula ly signi ican ,
p- alues be ween 0.10 and 0.20, bu his me hod will s ill be applied and he esul s
will be e alua ed.
11
CHAPTER 3. DATA, EMPIRICAL STRATEGY AND RESULTS
causali y ela ionship om he index o s ocks, which was ound ex emely signi ican
in DJI, and could ende a cyclical e ec on he p ice and he index i sel which spills
in o he s ocks ha comp ise i . Du ing he o hogonaliza ion his in o ma ion could
be los since i is sha ed by mos o he s ocks. The lack o his cha ac e is ic could be
one eason as o why NDX s ocks a e much mo e independen om each o he and
p o ide la ge independen mo emen s. 2. he indexes hemsel es a e di e en , while
DJI is a p ice-a e age index, NDX is ma ke capi aliza ion-a e age, his could ha e a
non- i ial in luence on he p ice mo emen o NDX by ha ing supply independence.
3. he models used o o hogonalize he esiduals a e sligh ly di e en , while in DJI
an ARIMA(2,1,0)-GARCH(1,1) wi h lag 1 and lag 2 s ock exogenous a iables was
needed o achie e he signi icance in he
λLM
s a is ic, in NDX i was ARIMA(1,1,0)-
GARCH(1,1) wi h lag 1 exogenous a iables. Mo e explana o y a iables could mean
ha each s ock p ice is much mo e explained in DJI han in NDX and so a educ ion
in he magni ude o a iance o he s ock esiduals. Fu he wo k could be necessa y
o ully unde s and he eason why his happens.
3.3.2.1 DJI
Righ away, om analyzing he g aphs, i is possible o no ice ha du ing he ma ke
c ash in ea ly 2020, all he condi ional co ela ions a e low, and so i is possible o in e
ha a leas any speci ic s ocks do no ha e in luence o e he p ice o DJI bu i was a
ma ke wide highly co ela ed p ice mo emen .
The e a e a ious g oups o s ocks sepa a ed in o o e all high, medium and low
condi ional co ela ions. Examining s ocks wi h high co ela ions, o example, BA
on igu e B.5 and INTC on igu e B.15, can be seen ha hese s ocks ha e a highe
coe icien ( able B.1) and ha hey a e signi ican , and hen he in e se is ue on he
s ocks wi h low condi ional co ela ions and as expec ed he medium g oup has hese
alues in be ween he o he wo g oups.
As p oposed, he condi ional co ela ions we e used o es ima e as AR(1) model
wi h an exogenous dummy a iable. The dummy a iables on able B.2 seem o be
mos ly insigni ican on he condi ional co ela ions, a iance a ios and o hogonal-
iza ion esidual e u ns wi h no ela ion o he alues ha cha ac e ize he es ima ion.
Bu on he esiduals hemsel es om o hogonaliza ion and he s anda d de ia ion o
he s ock esiduals appea o be mos ly signi ican . So, in a way, i was con i med ha
he e was an unexpec ed mo emen in he p ice o he s ocks du ing he ma ke c ash
pe iod, bu i did no cause a signi ican change on he esidual e u ns and so his
lack o signi icance ca ied on o he index model, al hough i is possible o isually
ecognize he pe iod when he c ash happened in he g aphs.
18
3.3. RESULTS
3.3.2.2 NDX
All he same conclusions ga he ed in DJI, can be applied o he NDX case excep
ha only he s ock’s s anda d de ia ion was conside ed somewha signi ican . Bu
he e is an in e es ing addi ion, he e a e clea ola ili y clus e s in he condi ional
co ela ions, indica ing pe iods whe e g oups o s ocks mo ed in andem bu ai ly
independen ly. I would be in e es ing o analyse in dep h wha happened in la e Q1
o ea ly Q2 2019 in hese s ocks since i is unclea in o e all news abou he ma ke
as o why i happened, also i was mos ly a local end in e sion o he p ice o hese
s ocks, in pa icula GOOGL wi h a 5% d op. The second majo ola ili y clus e
in he condi ional co ela ion g aphs is in la e Q3 o 2020. This spike was mos ly
composed by RGEN, a pha maceu ical company, and could co espond o specula ion
and eac ion o news abou he accines o he pandemic.
3.3.3 Compa a i e Assessmen
I is shown ha 2019 and Q3 2020 we e ele an momen s on he condi ional co ela-
ions o s ocks in o indexes, howe e , hese momen s coincide ela i ely well wi h ones
when he a iance a io o indexes in o c yp ocu encies we e low, which is ai ly un-
expec ed. How come some componen s su e ed enough ola ili y o accoun o such
a la ge po ion o he a iance o he index bu did no spill in o c yp ocu encies? I
should be analysed wi h mo e de ail, wi h a mo e localized app oach since i p obably
pe ains o a speci ic momen in ime whe e a gene alisa ion om hei assimila ion
o majo ading ma ke s would no apply. Wha is clea is ha he e we e momen s
o p ice allying in c yp ocu encies, in pa icula BTC (using his example because
his coin’s luc ua ions dic a e empi ically he s a e o he c yp ocu ency ma ke ) wi h
abou a 244% inc ease in p ice in he i s hal o 2019 and 550% in he second hal
o 2020, and so, coinciding wi h hese momen s. Th ee guesses can be in e ed: 1.
he model migh no p ope ly es ima e hese momen s since he p ice allying in BTC
seemed ela i ely impe ious o a d op in indexes on ea ly May in 2020, he e is he
possibili y o a di ec ela ionship om s ocks o c yp ocu encies, bypassing he in-
dexes 2. he e is a possibili y ha BTC own ola ili y was comple ely dominan du ing
his ime wi h li le o no ela ionship wi h indexes o equi y ma ke 3. could be a
signal o indica o o some so o a ela ionship be ween bo h ma ke s unaccoun ed
by he models, wi h some so o ex e nal e en o expec a ion which in luenced he
ma ke .
On he las conclusion, igu e 3.1 shows ha DJI a iance (wi h AR(1)-GARCH(1,1))
has some in luence on he p ice o BTC. No only he p ice d ops when he e is a spike
bu also seems o indica e a end e e sal on he p ice. The indexes seem o ha e a
delayed esponse owa ds he end e e sing e ec o c yp ocu encies, which could
indica e ha an e en , exogenous o he a iables, ook place. This e ec only hap-
pened a ew imes, bu ce ainly is wo h o de elop wo k o u he unde s and i
19
CHAPTER 3. DATA, EMPIRICAL STRATEGY AND RESULTS
Figu e 3.1: DJI Va iance (black), DJI P ice (blue) and de ended log-BTC P ice ( ed)
since i has he po en ial o be impo an on un a elling he unc ioning o c yp ocu -
ency ma ke cycles, which is o immense alue o in es o s no only in his ma ke
bu also in equi y. Pe haps his e ec coupled wi h he p e ious wo cases can be he
ounda ion, in a pu ely quan i a i e and echnical analysis sense, o he de elopmen
o asse po olios ha include c yp ocu ency and mu ually hedging he ola ili y
h oughou all he asse s in a hypo he ical po olio wi h he wo p e ious cases de-
sc ibing co ela ions and c oss-ma ke in luence on ola ili y in he o e all ma ke
and he men ioned end e e sing e ec explaining pa icula momen s o cyclical
impo ance, opening ways o sho o mid- e m in es men s a egies and long- e m
passi e in es men p esen -ma ke e icien solu ions.
20
4
Conclusion
I is he belie o he candida e ha hese esul s a e a nea success, alling sho in only
wo aspec s o ully achie ing he p oposed goals: 1. GSPC comp ises a a oo g ea
numbe o s ocks, ende ing compu a ionally hea y he use o o e all s ocks using
his me hodology wi h he a ailable esou ces. 2. he inabili y o use log- e u ns and
ha ing o pe o m eg essions on he p ice i sel and hen he use o a i hme ic e u ns
o u he wo k. Howe e , he e is a case o be made he e o he usage o a i hme ic
e u ns as a subs i u e o log- e u ns since hey a e equi alen a small alues.
I was shown ha he e is a signi ican di e ence be ween he spillo e s du ing he
Feb-Ap il 2020 ma ke c ash, o Co id c ash, and o he momen s in he c yp ocu ency
ma ke his o y be o e and a e his e en due o he signi icance o esidual dummy
a iables included in he a ious models. These ola ili y spillo e s we e quan i ied
using a iance a ios and hei models we e analyzed, p obing o insigh s.
I was shown a ha e en hough i was a auma ic occu ence, he pandemic e ec
was no ele an in he condi ional co ela ions be ween s ocks and US indexes due
in pa o he models es ima ion capabili y. I was shown ha no single s ock had a
decisi e ole in he ma ke c ash, whichwas a ma ke wide p ice mo emen , since his
e ec was almos comple ely missing om he index model es ima ion and pos e io
calcula ed condi ional co ela ions, and so, los du ing o hogonaliza ion.
I is e iden ha much o hese pa icula subjec s was no co e ed by his wo k,
including a deepe analysis o he ela ionship be ween hem. Ne e heless, his s udy
poin s owa d o index ola ili y, and s ock ola ili y, being ele an in a non- i ial
manne o c yp ocu ency o e en, in ac , beha ing in an unexpec ed ashion. This
la e conclusion, ha appea ed almos acciden ally sugges ed by he cases, is in he
candida e’s belie o be he mos in e es ing aspec o his wo k and has he po en ial
o change he way he inancial sec o ope a es wi h c yp ocu encies.
21
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24
A
Appendix 1
This appendix p esen s ables o he models es ima ed du ing he p oduc ion o he
Index - C yp o componen o his disse a ion. E e y pai has h ee ables, which a e
disc imina ed by index model, c yp o model and c yp o model wi h dummy a iables.
And so, his sec ion is comp ised o 27 ables (non- epea ed index models). The e a e
also wo g aphs pe pai , wi h and wi hou dummy a iables, o aling 24 g aphs.
25
APPENDIX A. APPENDIX 1
A.1 DJI
A.1.1 Index model
Table A.1: Pa ame e Es ima es o he GARCH(1, 1) (DJI)
Es ima e S d. E o alue P (>| |)
mu 0.084 0.015 5.462 0.00000
a 1 −0.044 0.027 −1.647 0.100
omega 0.044 0.007 5.978 0
alpha1 0.233 0.028 8.387 0
be a1 0.732 0.026 28.046 0
A.1.2 BTC
A.1.2.1 C yp o model
Table A.2: Pa ame e Es ima es o he GARCH(1, 1) (DJI-BTC)
Es ima e S d. E o alue P (>| |)
mu 0.245 0.096 2.542 0.011
a 1 0.028 0.029 0.976 0.329
RI, −1−0.022 0.112 −0.199 0.842
eI, 0.005 0.001 4.284 0.00002
omega 1.506 0.261 5.767 0
alpha1 0.140 0.026 5.453 0.00000
be a1 0.790 0.024 33.351 0
gamma1 0.028 0.030 0.932 0.351
26
A.1. DJI
A.1.2.2 C yp o model wi h dummy a iables
Table A.3: Pa ame e Es ima es o he GARCH(1, 1) (DJI-BTC wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.262 0.096 2.740 0.006
a 1 0.034 0.028 1.221 0.222
RI, −10.104 0.102 1.011 0.312
eI, 0.003 0.001 3.416 0.001
RI, −1D 0.027 0.344 0.079 0.937
eI, D 0.013 0.002 5.242 0.00000
omega 1.223 0.229 5.333 0.00000
alpha1 0.137 0.024 5.749 0
be a1 0.817 0.023 34.905 0
gamma1 −0.007 0.024 −0.282 0.778
27
APPENDIX A. APPENDIX 1
A.1.4.3 Va iance Ra io G aphs
Figu e A.5: Va iance Ra io o DJI-XRP
Figu e A.6: Va iance Ra io o DJI-XRP wi h dummy a iables
34
A.1. DJI
A.1.5 XMR
A.1.5.1 C yp o model
Table A.8: Pa ame e Es ima es o he GARCH(1, 1) (DJI-XMR)
Es ima e S d. E o alue P (>| |)
mu 0.275 0.150 1.830 0.067
a 1 −0.019 0.028 −0.661 0.509
RI, −10.029 0.142 0.207 0.836
eI, 0.008 0.001 5.474 0.00000
omega 3.209 0.723 4.438 0.00001
alpha1 0.175 0.025 6.910 0
be a1 0.821 0.022 36.989 0
gamma1 −0.078 0.025 −3.130 0.002
35
APPENDIX A. APPENDIX 1
A.1.5.2 C yp o model wi h dummy a iables
Table A.9: Pa ame e Es ima es o he GARCH(1, 1) (DJI-XMR wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.287 0.150 1.919 0.055
a 1 −0.013 0.028 −0.463 0.643
RI, −10.069 0.151 0.457 0.648
eI, 0.005 0.002 3.367 0.001
RI, −1D 0.285 0.382 0.748 0.454
eI, D 0.012 0.003 3.851 0.0001
omega 2.926 0.664 4.405 0.00001
alpha1 0.177 0.025 7.043 0
be a1 0.827 0.021 39.687 0
gamma1 −0.088 0.025 −3.549 0.0004
36
A.1. DJI
A.1.5.3 Va iance Ra io G aphs
Figu e A.7: Va iance Ra io o DJI-XMR
Figu e A.8: Va iance Ra io o DJI-XMR wi h dummy a iables
37
APPENDIX A. APPENDIX 1
A.2 GSPC
A.2.1 Index model
Table A.10: Pa ame e Es ima es o he GARCH(1, 1) (GSPC)
Es ima e S d. E o alue P (>| |)
mu 0.091 0.015 6.232 0
a 1 −0.083 0.027 −3.072 0.002
omega 0.044 0.007 6.423 0
alpha1 0.252 0.029 8.758 0
be a1 0.720 0.024 29.473 0
A.2.2 BTC
A.2.2.1 C yp o model
Table A.11: Pa ame e Es ima es o he GARCH(1, 1) (GSPC-BTC)
Es ima e S d. E o alue P (>| |)
mu 0.253 0.096 2.628 0.009
a 1 0.027 0.029 0.921 0.357
RI, −1−0.080 0.108 −0.738 0.460
eI, 0.005 0.001 4.573 0.00000
omega 1.487 0.260 5.716 0
alpha1 0.138 0.025 5.530 0.00000
be a1 0.792 0.024 33.613 0
gamma1 0.028 0.029 0.967 0.333
38
A.2. GSPC
A.2.2.2 C yp o model wi h dummy a iables
Table A.12: Pa ame e Es ima es o he GARCH(1, 1) (GSPC-BTC wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.266 0.096 2.776 0.006
a 1 0.034 0.028 1.212 0.225
RI, −10.085 0.103 0.825 0.409
eI, 0.004 0.001 3.747 0.0002
RI, −1D 0.019 0.368 0.052 0.959
eI, D 0.014 0.003 5.355 0.00000
omega 1.194 0.227 5.269 0.00000
alpha1 0.133 0.023 5.735 0
be a1 0.820 0.023 35.341 0
gamma1 −0.005 0.024 −0.204 0.839
39
APPENDIX A. APPENDIX 1
A.2.2.3 Va iance Ra io G aphs
Figu e A.9: Va iance Ra io o GSPC-BTC
Figu e A.10: Va iance Ra io o GSPC-BTC wi h dummy a iables
40
A.2. GSPC
A.2.3 ETH
A.2.3.1 C yp o model
Table A.13: Pa ame e Es ima es o he GARCH(1, 1) (GSPC-ETH)
Es ima e S d. E o alue P (>| |)
mu 0.301 0.171 1.763 0.078
a 1 0.026 0.032 0.812 0.417
RI, −10.126 0.190 0.665 0.506
eI, 0.012 0.002 7.003 0
omega 3.458 0.697 4.960 0.00000
alpha1 0.173 0.029 6.037 0
be a1 0.803 0.026 31.101 0
gamma1 −0.074 0.028 −2.635 0.008
41
APPENDIX A. APPENDIX 1
A.2.3.2 C yp o model wi h dummy a iables
Table A.14: Pa ame e Es ima es o he GARCH(1, 1) (GSPC-ETH wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.308 0.170 1.809 0.070
a 1 0.031 0.032 0.966 0.334
RI, −10.185 0.174 1.067 0.286
eI, 0.008 0.002 4.486 0.00001
RI, −1D 0.081 0.455 0.177 0.859
eI, D 0.015 0.004 4.176 0.00003
omega 3.142 0.645 4.870 0.00000
alpha1 0.174 0.028 6.183 0
be a1 0.808 0.025 32.147 0
gamma1 −0.077 0.027 −2.865 0.004
42
A.2. GSPC
A.2.3.3 Va iance Ra io G aphs
Figu e A.11: Va iance Ra io o GSPC-ETH
Figu e A.12: Va iance Ra io o GSPC-ETH wi h dummy a iables
43
APPENDIX A. APPENDIX 1
A.3 NDX
A.3.1 Index model
Table A.19: Pa ame e Es ima es o he GARCH(1, 1) (NDX)
Es ima e S d. E o alue P (>| |)
mu 0.109 0.020 5.400 0.00000
a 1 −0.060 0.026 −2.281 0.023
omega 0.070 0.013 5.565 0.00000
alpha1 0.181 0.024 7.642 0
be a1 0.777 0.025 31.287 0
A.3.2 BTC
A.3.2.1 C yp o model
Table A.20: Pa ame e Es ima es o he GARCH(1, 1) (NDX-BTC)
Es ima e S d. E o alue P (>| |)
mu 0.230 0.097 2.388 0.017
a 1 0.029 0.029 1.004 0.315
RI, −10.008 0.087 0.093 0.926
eI, 0.004 0.001 5.007 0.00000
omega 1.428 0.253 5.642 0.00000
alpha1 0.134 0.024 5.610 0.00000
be a1 0.796 0.023 34.678 0
gamma1 0.034 0.027 1.256 0.209
50
A.3. NDX
A.3.2.2 C yp o model wi h dummy a iables
Table A.21: Pa ame e Es ima es o he GARCH(1, 1) (NDX-BTC wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.256 0.096 2.674 0.008
a 1 0.034 0.027 1.221 0.222
RI, −10.076 0.082 0.928 0.353
eI, 0.004 0.001 4.391 0.00001
RI, −1D 0.329 0.380 0.865 0.387
eI, D 0.016 0.002 6.355 0
omega 1.105 0.216 5.129 0.00000
alpha1 0.128 0.023 5.693 0
be a1 0.829 0.023 36.622 0
gamma1 −0.006 0.023 −0.271 0.786
51
APPENDIX A. APPENDIX 1
A.3.2.3 Va iance Ra io G aphs
Figu e A.17: Va iance Ra io o NDX-BTC
Figu e A.18: Va iance Ra io o NDX-BTC wi h dummy a iables
52
A.3. NDX
A.3.3 ETH
A.3.3.1 C yp o model
Table A.22: Pa ame e Es ima es o he GARCH(1, 1) (NDX-ETH)
Es ima e S d. E o alue P (>| |)
mu 0.262 0.172 1.524 0.127
a 1 0.029 0.033 0.887 0.375
RI, −10.191 0.146 1.313 0.189
eI, 0.009 0.002 5.778 0
omega 3.593 0.721 4.986 0.00000
alpha1 0.177 0.030 6.003 0
be a1 0.795 0.026 30.078 0
gamma1 −0.068 0.030 −2.283 0.022
53
APPENDIX A. APPENDIX 1
A.3.3.2 C yp o model wi h dummy a iables
Table A.23: Pa ame e Es ima es o he GARCH(1, 1) (NDX-ETH wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu 0.278 0.170 1.635 0.102
a 1 0.031 0.032 0.958 0.338
RI, −10.184 0.136 1.349 0.177
eI, 0.006 0.001 4.486 0.00001
RI, −1D 0.337 0.435 0.777 0.437
eI, D 0.017 0.003 5.114 0.00000
omega 3.011 0.636 4.731 0.00000
alpha1 0.169 0.028 6.015 0
be a1 0.815 0.025 32.207 0
gamma1 −0.077 0.026 −2.980 0.003
54
A.3. NDX
A.3.3.3 Va iance Ra io G aphs
Figu e A.19: Va iance Ra io o NDX-ETH
Figu e A.20: Va iance Ra io o NDX-ETH wi h dummy a iables
55
APPENDIX A. APPENDIX 1
A.3.4 XRP
A.3.4.1 C yp o model
Table A.24: Pa ame e Es ima es o he GARCH(1, 1) (NDX-XRP)
Es ima e S d. E o alue P (>| |)
mu −0.137 0.137 −0.999 0.318
a 1 0.043 0.030 1.418 0.156
RI, −1−0.097 0.110 −0.884 0.377
eI, 0.007 0.001 6.894 0
omega 3.177 0.448 7.085 0
alpha1 0.332 0.043 7.787 0
be a1 0.744 0.025 30.009 0
gamma1 −0.204 0.040 −5.149 0.00000
56
A.3. NDX
A.3.4.2 C yp o model wi h dummy a iables
Table A.25: Pa ame e Es ima es o he GARCH(1, 1) (NDX-XRP wi h dummy a .)
Es ima e S d. E o alue P (>| |)
mu −0.103 0.138 −0.745 0.456
a 1 0.049 0.030 1.616 0.106
RI, −1−0.092 0.110 −0.835 0.404
eI, 0.005 0.001 4.999 0.00000
RI, −1D 0.509 0.302 1.686 0.092
eI, D 0.011 0.003 4.458 0.00001
omega 3.075 0.424 7.252 0
alpha1 0.328 0.043 7.558 0
be a1 0.751 0.025 30.378 0
gamma1 −0.215 0.039 −5.480 0.00000
57
APPENDIX A. APPENDIX 1
A.3.4.3 Va iance Ra io G aphs
Figu e A.21: Va iance Ra io o NDX-XRP
Figu e A.22: Va iance Ra io o NDX-XRP wi h dummy a iables
58
A.3. NDX
A.3.5 XMR
A.3.5.1 C yp o model
Table A.26: Pa ame e Es ima es o he GARCH(1, 1) (NDX-XMR)
Es ima e S d. E o alue P (>| |)
mu 0.257 0.151 1.708 0.088
a 1 −0.021 0.028 −0.755 0.450
RI, −10.056 0.125 0.449 0.653
eI, 0.006 0.001 4.889 0.00000
omega 3.325 0.751 4.426 0.00001
alpha1 0.173 0.025 6.849 0
be a1 0.819 0.023 35.585 0
gamma1 −0.073 0.025 −2.970 0.003
59
APPENDIX B. APPENDIX 2
Figu e B.1: Condi ional Co ela ion DJI-MMM
Figu e B.2: Condi ional Co ela ion DJI-AXP
66
B.1. DJI
Figu e B.3: Condi ional Co ela ion DJI-AMGN
Figu e B.4: Condi ional Co ela ion DJI-AAPL
67
APPENDIX B. APPENDIX 2
Figu e B.5: Condi ional Co ela ion DJI-BA
Figu e B.6: Condi ional Co ela ion DJI-CAT
68
B.1. DJI
Figu e B.7: Condi ional Co ela ion DJI-CVX
Figu e B.8: Condi ional Co ela ion DJI-CSCO
69
APPENDIX B. APPENDIX 2
Figu e B.9: Condi ional Co ela ion DJI-KO
Figu e B.10: Condi ional Co ela ion DJI-DOW
70
B.1. DJI
Figu e B.11: Condi ional Co ela ion DJI-GS
Figu e B.12: Condi ional Co ela ion DJI-HD
71
APPENDIX B. APPENDIX 2
Figu e B.13: Condi ional Co ela ion DJI-HON
Figu e B.14: Condi ional Co ela ion DJI-IBM
72
B.1. DJI
Figu e B.15: Condi ional Co ela ion DJI-INTC
Figu e B.16: Condi ional Co ela ion DJI-JNJ
73
APPENDIX B. APPENDIX 2
Figu e B.17: Condi ional Co ela ion DJI-JPM
Figu e B.18: Condi ional Co ela ion DJI-MCD
74
B.1. DJI
Figu e B.19: Condi ional Co ela ion DJI-MRK
Figu e B.20: Condi ional Co ela ion DJI-MSFT
75
APPENDIX B. APPENDIX 2
Table B.3: Pa ame e Es ima es o he GARCH(1, 1) (NDX-S ocks)
Es ima e S d. E o alue P (>| |)
mu 0.001 0.0004 2.587 0.010
a 1 −0.297 0.039 −7.587 0
AAPL 0.00001 0.00001 0.481 0.631
MSFT −0.00000 0.00000 −3.360 0.001
AMZN −0.00000 0.00000 −5.798 0
TSLA 0.00003 0.00001 1.941 0.052
GOOG −0.00002 0.00001 −1.481 0.138
FB −0.00003 0.00002 −1.748 0.080
GOOGL 0.00004 0.00003 1.046 0.296
NVDA −0.00000 0.00000 −1.825 0.068
PYPL −0.00003 0.0001 −0.470 0.638
ADBE 0.00001 0.00001 1.184 0.236
NFLX 0.00001 0.00001 1.339 0.180
CMCSA −0 0.00000 −0.012 0.991
CSCO −0.00001 0.00001 −1.160 0.246
INTC −0.0001 0.0001 −1.331 0.183
PEP 0.00001 0.00001 2.123 0.034
AVGO −0.00000 0.00001 −0.624 0.533
COST −0.00001 0.00000 −3.266 0.001
TXN −0.0001 0.00002 −5.900 0
TMUS 0.00000 0.00000 0.857 0.392
MRNA −0.00001 0.00001 −1.127 0.260
INTU 0.00000 0.00000 1.877 0.060
HON 0.00001 0.00002 0.401 0.688
QCOM −0.00005 0.00003 −1.694 0.090
CHTR −0.00000 0.00000 −0.851 0.395
SBUX −0.00000 0.00001 −0.317 0.751
AMD −0.00001 0.00001 −1.078 0.281
AMGN 0.00001 0.00001 1.001 0.317
ISRG −0.00001 0.00000 −2.427 0.015
AMAT −0.00000 0.00000 −0.558 0.577
BKNG 0.00001 0.00002 0.593 0.553
ADI −0.00000 0.00002 −0.222 0.824
GILD 0.00000 0.00001 0.658 0.510
ADP 0.00002 0.00001 1.548 0.122
MELI 0.00000 0.00002 0.012 0.990
MDLZ −0.00001 0.00003 −0.368 0.713
LRCX 0.00001 0.00001 1.334 0.182
MU 0.00000 0.00004 0.133 0.894
FISV −0.00001 0.00001 −0.805 0.421
CSX 0.00000 0.00000 1.084 0.278
REGN 0.00005 0.00001 3.382 0.001
ILMN 0.00000 0.00000 0.086 0.932
ZM −0.00000 0.00001 −0.294 0.769
ADSK 0.0001 0.00004 1.435 0.151
ASML −0.0001 0.00002 −2.535 0.011
ATVI 0.00001 0.00001 1.015 0.310
JD 0.0001 0.00003 3.756 0.0002
TEAM 0.00003 0.00003 1.181 0.238
82
B.2. NDX
Table B.4: Pa ame e Es ima es o he GARCH(1, 1) (NDX-S ocks) (con . 1)
Es ima e S d. E o alue P (>| |)
IDXX −0.00001 0.00001 −1.003 0.316
DXCM −0.00000 0.00000 −0.043 0.966
ALGN 0.00001 0.00000 1.487 0.137
NXPI 0.00000 0.00000 0.254 0.799
KLAC 0.00000 0.00000 0.153 0.878
LULU −0.00000 0.00000 −0.031 0.975
DOCU −0.00001 0.00001 −1.342 0.180
MRVL −0.00002 0.00003 −0.677 0.498
CRWD −0 0.00000 −0.0001 1.000
KDP −0.00001 0.00001 −1.700 0.089
MAR −0.00003 0.00002 −1.296 0.195
WDAY 0.0001 0.00004 1.566 0.117
EXC −0.00000 0.00000 −0.172 0.863
VRTX 0.0001 0.00003 3.210 0.001
MNST −0.00000 0.00001 −0.369 0.712
SNPS 0.00000 0.00000 0.931 0.352
EBAY −0.00001 0.00002 −0.713 0.476
KHC 0.00002 0.00001 1.858 0.063
MTCH 0.00000 0.00002 0.031 0.975
BIIB 0.00000 0.00003 0.045 0.964
ORLY 0.00000 0.00000 1.340 0.180
MCHP 0.00002 0.00001 1.604 0.109
CDNS 0.00004 0.00001 4.894 0.00000
WBA −0.00000 0.00000 −1.940 0.052
AEP 0.00000 0.00000 1.336 0.181
EA −0.00000 0.00001 −0.300 0.764
PAYX 0.00003 0.00003 1.167 0.243
CTAS −0.00002 0.00001 −1.624 0.104
CTSH −0.00002 0.00003 −0.705 0.481
ROST −0.00000 0.00001 −0.435 0.664
BIDU −0.00004 0.00002 −2.071 0.038
XLNX 0.00000 0.00001 0.727 0.467
PDD 0.00001 0.00002 0.371 0.711
KTA −0.00000 0.00000 −1.688 0.091
XEL 0.00001 0.00002 0.527 0.598
CPRT −0.00000 0.00002 −0.084 0.933
VRSK 0.00000 0.00000 4.005 0.0001
SGEN 0.00000 0.00000 0.420 0.674
ANSS 0.00001 0.00002 0.930 0.352
FAST −0.0001 0.00003 −1.952 0.051
PCAR 0.0001 0.00005 1.503 0.133
SWKS −0.00000 0.00001 −0.353 0.724
NTES −0.00001 0.00002 −0.343 0.732
CDW −0.00000 0.00002 −0.157 0.875
SIRI 0.00001 0.00002 0.350 0.726
SPLK −0.00001 0.00002 −0.552 0.581
PTON 0.00002 0.00003 0.520 0.603
83
APPENDIX B. APPENDIX 2
Table B.5: Pa ame e Es ima es o he GARCH(1, 1) (NDX-S ocks) (con . 2)
Es ima e S d. E o alue P (>| |)
VRSN 0.00000 0.00000 0.132 0.895
DLTR 0.00002 0.00003 0.770 0.441
CERN 0.00000 0.00001 0.066 0.948
TCOM −0.00000 0.00000 −0.401 0.688
INCY 0.00000 0.00001 0.592 0.554
CHKP 0.00002 0.00002 1.210 0.226
FOXA −0 0.00000 −0.001 1.000
FOX −0.00000 0.00000 −0.592 0.554
omega 0.00000 0.00000 1.423 0.155
alpha1 0.050 0.002 30.110 0
be a1 0.900 0.001 1,095.711 0
84
B.2. NDX
Table B.6: Signi icance o dummy a iables du ing he COVID-19 ma ke c ash on
Condi ional Co ela ion and Va iance Ra io, Re u ns o P ice Residuals o S ocks,
S ock P ice Residuals, S ock S anda d De ia ion om GARCH models
S ocks Cond. Co VR Re u ns on Residuals Residuals S ock s d.
AAPL 0.782 0.816 0.955 0.529 0.313
MSFT 0.845 0.600 0.995 0.637 0.129
AMZN 0.601 0.668 0.915 0.754 0.775
TSLA 0.935 0.831 0.722 0.991 0.912
GOOG 0.331 0.513 0.395 0.499 0.186
FB 0.224 0.360 0.781 0.515 0.608
GOOGL 0.036 0.207 0.747 0.721 0.978
NVDA 0.823 0.879 0.895 0.953 0.181
PYPL 0.486 0.875 0.348 0.761 0.907
ADBE 0.978 0.844 0.757 0.678 0.082
NFLX 0.419 0.505 0.506 0.790 0.593
CMCSA 0.992 0.999 0.853 0.517 0.001
CSCO 0.438 0.501 0.812 0.540 0.065
INTC 0.748 0.581 0.888 0.441 0.0000
PEP 0.032 0.097 0.863 0.646 0.013
AVGO 0.845 0.903 0.762 0.526 0.318
COST 0.343 0.848 0.789 0.694 0.076
TXN 0.713 0.734 0.660 0.459 0.300
TMUS 0.856 0.931 0.820 0.995 0.808
MRNA 0.092 0.082 0.604 0.899 0.016
INTU 0.830 0.802 0.871 0.687 0.289
HON 0.664 0.904 0.781 0.815 0.088
QCOM 0.602 0.608 0.343 0.650 0.367
CHTR 0.311 0.396 0.0000 0.681 0.513
SBUX 0.409 0.662 0.959 0.716 0.370
AMD 0.244 0.561 0.921 0.820 0.019
AMGN 0.409 0.534 0.991 0.678 0.731
ISRG 0.832 0.732 0.822 0.728 0.370
AMAT 0.710 0.963 0.780 0.647 0.291
BKNG 0.286 0.469 0.834 0.639 0.001
ADI 0.771 0.619 0.907 0.467 0.037
GILD 0.642 0.864 0.806 0.797 0.860
ADP 0.432 0.495 0.622 0.863 0.926
MELI 0.208 0.073 0.733 0.474 0.586
MDLZ 0.743 0.785 0.569 0.949 0.739
LRCX 0.302 0.715 0.542 0.626 0.0000
MU 0.950 0.887 0.678 0.396 0.041
FISV 0.633 0.461 0.767 0.825 0.003
CSX 0.746 0.802 0.895 0.641 0.085
REGN 0.531 0.476 0.863 0.457 0.004
ILMN 0.802 0.597 0.845 0.941 0.128
ZM 0.647 0.906 0.621 0.657 0.590
ADSK 0.880 0.690 0.947 0.833 0.468
ASML 0.173 0.867 0.933 0.596 0.0001
ATVI 0.768 0.522 0.897 0.952 0.198
JD 0.824 0.988 0.0001 0.788 0.955
TEAM 0.634 0.945 0.863 0.774 0.820
85
APPENDIX B. APPENDIX 2
Table B.7: Signi icance o dummy a iables du ing he COVID-19 ma ke c ash on
Condi ional Co ela ion and Va iance Ra io, Re u ns o P ice Residuals o S ocks,
S ock P ice Residuals, S ock S anda d De ia ion om GARCH models (con . 1)
S ocks Cond. Co VR Re u ns on Residuals Residuals S ock s d.
IDXX 0.582 0.539 0.886 0.333 0.301
DXCM 0.858 0.485 0.846 0.607 0.766
ALGN 0.873 0.930 0.845 0.879 0.680
NXPI 0.772 0.482 0.890 0.471 0.034
KLAC 0.758 0.588 0.848 0.656 0.231
LULU 0.972 0.736 0.886 0.761 0.703
DOCU 0.359 0.492 0.641 0.762 0.033
MRVL 0.865 0.719 0.687 0.617 0.769
CRWD 1.000 1.000 0.845 0.968 0.924
KDP 0.214 0.485 0.978 0.768 0.0001
MAR 0.046 0.143 0.762 0.570 0.0000
WDAY 0.548 0.975 0.857 0.678 0.252
EXC 0.633 0.453 0.901 0.563 0.009
VRTX 0.672 0.725 0.805 0.971 0.015
MNST 0.941 0.702 0.854 0.744 0.018
SNPS 0.796 0.664 0.785 0.654 0.207
EBAY 0.874 0.620 0.955 0.819 0.191
KHC 0.513 0.360 0.689 0.356 0.108
MTCH 0.830 0.753 0.580 0.573 0.288
BIIB 0.894 0.617 0.819 0.722 0.870
ORLY 0.717 0.836 0.917 0.782 0.046
MCHP 0.501 0.580 0.963 0.965 0.026
CDNS 0.604 0.625 0.852 0.579 0.163
WBA 0.661 0.367 0.850 0.724 0.002
AEP 0.196 0.155 0.848 0.424 0.0000
EA 0.867 0.842 0.778 0.645 0.416
PAYX 0.684 0.836 0.938 0.749 0.019
CTAS 0.245 0.455 0.984 0.492 0.573
CTSH 0.848 0.867 0.604 0.884 0.010
ROST 0.203 0.327 0.815 0.738 0.278
BIDU 0.163 0.534 0.529 0.528 0.949
XLNX 0.875 0.455 0.965 0.774 0.028
PDD 0.474 0.455 0.813 0.931 0.669
OKTA 0.502 0.494 0.946 0.953 0.617
XEL 0.754 0.619 0.837 0.714 0.852
CPRT 0.740 0.412 0.909 0.866 0.792
VRSK 0.556 0.643 0.792 0.965 0.781
SGEN 0.757 0.732 0.827 0.470 0.708
ANSS 0.240 0.453 0.901 0.637 0.010
FAST 0.702 0.646 0.831 0.799 0.745
PCAR 0.422 0.466 0.813 0.395 0.037
SWKS 0.577 0.425 0.895 0.473 0.798
NTES 0.422 0.406 0.910 0.450 0.514
CDW 0.873 0.835 0.701 0.942 0.843
SIRI 0.876 0.939 0.916 0.832 0.008
SPLK 0.445 0.567 0.843 0.713 0.001
PTON 0.269 0.912 0.996 0.814 0.286
86
B.2. NDX
Table B.8: Signi icance o dummy a iables du ing he COVID-19 ma ke c ash on
Condi ional Co ela ion and Va iance Ra io, Re u ns o P ice Residuals o S ocks,
S ock P ice Residuals, S ock S anda d De ia ion om GARCH models (con . 2)
S ocks Cond. Co VR Re u ns on Residuals Residuals S ock s d.
VRSN 0.543 0.477 0.876 0.516 0.156
DLTR 0.600 0.575 0.878 0.620 0.224
CERN 0.307 0.517 0.916 0.845 0.001
TCOM 0.494 0.606 0.694 0.662 0.567
INCY 0.999 0.809 0.811 0.846 0.988
CHKP 0.463 0.551 0.965 0.449 0.976
FOXA 1.000 1.000 0.844 0.794 0.927
FOX 0.711 0.472 0.927 0.509 0.420
87
APPENDIX B. APPENDIX 2
Figu e B.31: Condi ional Co ela ion NDX-AAPL
Figu e B.32: Condi ional Co ela ion NDX-ADBE
88
B.2. NDX
Figu e B.33: Condi ional Co ela ion NDX-ADI
89
APPENDIX B. APPENDIX 2
Figu e B.34: Condi ional Co ela ion NDX-ADP
Figu e B.35: Condi ional Co ela ion NDX-ADSK
90
B.2. NDX
Figu e B.36: Condi ional Co ela ion NDX-AEP
Figu e B.37: Condi ional Co ela ion NDX-ALGN
91
APPENDIX B. APPENDIX 2
Figu e B.50: Condi ional Co ela ion NDX-CDW
Figu e B.51: Condi ional Co ela ion NDX-CERN
98
B.2. NDX
Figu e B.52: Condi ional Co ela ion NDX-CHKP
Figu e B.53: Condi ional Co ela ion NDX-CHTR
99
APPENDIX B. APPENDIX 2
Figu e B.54: Condi ional Co ela ion NDX-CMCSA
Figu e B.55: Condi ional Co ela ion NDX-COST
100
B.2. NDX
Figu e B.56: Condi ional Co ela ion NDX-CPRT
Figu e B.57: Condi ional Co ela ion NDX-CRWD
101
APPENDIX B. APPENDIX 2
Figu e B.58: Condi ional Co ela ion NDX-CSCO
Figu e B.59: Condi ional Co ela ion NDX-CSX
102
B.2. NDX
Figu e B.60: Condi ional Co ela ion NDX-CTAS
Figu e B.61: Condi ional Co ela ion NDX-CTSH
103
APPENDIX B. APPENDIX 2
Figu e B.62: Condi ional Co ela ion NDX-DLTR
Figu e B.63: Condi ional Co ela ion NDX-DOCU
104
B.2. NDX
Figu e B.64: Condi ional Co ela ion NDX-DXCM
Figu e B.65: Condi ional Co ela ion NDX-EA
105
APPENDIX B. APPENDIX 2
Figu e B.66: Condi ional Co ela ion NDX-EBAY
Figu e B.67: Condi ional Co ela ion NDX-EXC
106
B.2. NDX
Figu e B.68: Condi ional Co ela ion NDX-FAST
Figu e B.69: Condi ional Co ela ion NDX-FB
107
APPENDIX B. APPENDIX 2
Figu e B.82: Condi ional Co ela ion NDX-ISRG
Figu e B.83: Condi ional Co ela ion NDX-JD
114
B.2. NDX
Figu e B.84: Condi ional Co ela ion NDX-KDP
Figu e B.85: Condi ional Co ela ion NDX-KHC
115
APPENDIX B. APPENDIX 2
Figu e B.86: Condi ional Co ela ion NDX-KLAC
Figu e B.87: Condi ional Co ela ion NDX-LRCX
116
B.2. NDX
Figu e B.88: Condi ional Co ela ion NDX-LULU
Figu e B.89: Condi ional Co ela ion NDX-MAR
117
APPENDIX B. APPENDIX 2
Figu e B.90: Condi ional Co ela ion NDX-MCHP
Figu e B.91: Condi ional Co ela ion NDX-MDLZ
118
B.2. NDX
Figu e B.92: Condi ional Co ela ion NDX-MELI
Figu e B.93: Condi ional Co ela ion NDX-MNST
119
APPENDIX B. APPENDIX 2
Figu e B.94: Condi ional Co ela ion NDX-MRNA
Figu e B.95: Condi ional Co ela ion NDX-MRVL
120
B.2. NDX
Figu e B.96: Condi ional Co ela ion NDX-MSFT
Figu e B.97: Condi ional Co ela ion NDX-MTCH
121
APPENDIX B. APPENDIX 2
Figu e B.98: Condi ional Co ela ion NDX-MU
Figu e B.99: Condi ional Co ela ion NDX-NFLX
122
B.2. NDX
Figu e B.100: Condi ional Co ela ion NDX-NTES
Figu e B.101: Condi ional Co ela ion NDX-NVDA
123