Nghien CM cau true phu thuoc cua thj tnrcmg chirng khoan, thi trirong vang va thj tru'ong ngoai teo* Viet Nam
Le Trung Thanh
Tnt&ng Dgi hoc Kinh te - Dgi hgc Qudc gia Hd Ndi Email: [email protected] Nguyin Diic Khuvng Sa Tdi chinh tinh Thdi Binh
Ngay nhan: 23/3/2016 Ngay nhan ban sua: 6/6/2016 Ngay duyet dang: 25/8/2016
Tom tat:
Copula la mot trong nhimg ly thuyet ngdy cdng dugc dp dung nhieu vdo ITnh vuc tdi chinh, dgc biet Id ddi v&i qudn tri riii ro. Bdi viit giai thieu cdc md hinh Copula dugc sie dung phd bien vd dp diing trong tinh todn gid tri tdn thdt danh muc bao gdm: cd phiiu, vdng vd ty gid VND/USD. Kit qud cua nghien cim cho thdy mdi tuang quan yeu giita ba thi trudng & Viet Nam vd cung cdp mot phucmg phdp mai hiiu qud trong da dgng hda danh muc cho nhd ddu tu.
Tir khda: Copula; cau tnic phy thupc; chung khoan; gia tri rui ro; ngoai te; vang.
Study of dependence structure of stock market, gold market and foreign exchange mar- ket In Vietnam
Abstract:
Copula is one of the most popular theories, which is increasingly applied in finance and espe- cially in risk management. This research introduces some basic useful copula and an applica- tion in the estimation of Value at Risk of a portfolio composed by stock, gold and VND/USD foreign exchange rates. The research results indicate a weak correlation of the three markets
in Vietnam and provide investors with an efficient approach in diversification portfolios.
Keywords: Copula: dependence structure; foreign exchange; gold; stock; Value at Risk.
1. Giffi thieu hon ctia Copula dugc thi hien trong Rong & Truck Khai niem ciu triic phu thupc (dependence (2014), Hotta & Palaro (2006), Ozun & Cifter structure) dugc hieu la khi yeu to nay thay dii tac dpng (2007).
mpt ylu khac cung thay ddi mpt mirc dp nhit dinh. Tai Viet Nam, cac nghien cuu sit dung Copula tap Hien nay mpt teong nhftng phuang phap do ludng su trung thi hien su phu thudc gifta cac c l philu va chi phu thupc dang dugc sit dung phd bien la Copula. s l thi trudng nhu Trin Trpng Nguyen & Nguyin
Tir dien Oxford dinh nghTa "copula" la mpt kit Thu Thiiy (2015), Hoang Diic Manh (2014) ma noi (connection, linking of words). Trong thing ke, chua cd su tham gia ciia thi trudng vang, thi trudng Copula la mpt dang ham sd ket hgp cac phan phii ngoai te hoac mdi chi nghien cuu tren mpt dang mo tich luy tao ra mdt ham phan phli da bien ding thdi hinh t-Copula nhu Do Nam Tung (2010). Trong khi nhung vln thi hien diy dii su phu thupc. Trong ITnh do, nghien cuu bing md hinh h l i quy toyIn tinh ciia vuc tai chinh. Copula dugc su dung d l nghien citu Dinh Thi Thanh Long & Nguyin Thu Trang (2008) cau true phu thupc gift^ cac thi trudng va quan tei rui cdn tin tai phuang sai cua sai s l thay ddi va to ro. Cac bang chung ve kha nang do ludng nii ro tit ta'ong quan.
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Viec chung minh t i n tai hay khdng mdt cau tnic phu thudc gdp phin quan trgng vao trong viee phdng ngita nii ro cho nha d i u tu. Do do, dya tren y todng ctia Reboredo (2013), bai vilt se nham tra ldi cac v i n d l : (i) cd t i n tai mdt mdi quan he rang budc nao giua thi trucmg chiing khoan, thi trudng vang va thi trudng ngoai te khdng? (ii) neu cac bien la dpc lap thi cd tdn tai mdt md hinh de the hien dugc ddng thdi phan phdi ciia cac bien khdng? (iii) cudi citng, vang hoac ddng ngoai te cd la mpt cdng cu giam thieu riii ro trong danh muc da dang hda riii ro cho thi trudng chitng khoan Viet Nam va theo tirng nhdm nganh hay khdng?
2. Tong q u a n nghien cuu, ca sd ly thuyet va phu'tmg p h a p nghien ciru
2.1. Cdc dgng md hinh Copula pho biin Gia sit X, Y la hai bien ngau nhien lien tuc vdi ham phan phli F(x)=P[X<=x], G(y)=P[Y<=y], theo dinh ly Sklar (1959) se tdn tai mpt ham sd Copula sao cho P[X<=x,Y<=y] = C(F(x),G(y)) tren khoang [0,1]. Khi dd, he sd 6 ciia ham C do ludng sy phu thudc giua cac phan phdi bien (marginal distribu- tions), hay la sy phu thupc giua cac bien.
Bang 1 gidi thieu cac dang md hinh copula phd biln dupe sir dung bao gdm: hp Ellipptical (Normal, Student-t) va Archemedean (Clayton, Gumbel, Frank). Cac Elliptical thudng md ta cau tnic ddi xung trong khi cac Archemedean lai md ta cau tnic lech trai hoac lech phai. Mpt gia tri he sd 9 cua Gumbel Copula cang ldn cang cho thay mite dp phu thudc gifta cac bien lech ben phai (duang) nhieu hon va toong ty he sd 5 cua Clayton cang Idn, cang phu thupc ve ben trai (am).
Trong dd O la mpt ham phan phdi tich liiy chuan
hda (standard normal cdf). <!>•' la nghich dao ciia O, 0''y la ham phan phli chuin da biln vdi he s l tuong quan la ma tran 2. t^ ^ la phan phli Stodent da biln vdi bac to' do v va ma tran tuong quan X-
2.2. Phucmg phdp u&c lugng
D I han chl phuang sai ciia sai sd thay ddi va to toong quan thudng gap d dft lieu tai chinh, eac phan phli bien dugc sit dung theo md hinh ARMA(m,n)- GARCH(p,q). Phin du thu dugc to md hinh se dugc chuin hda d l thilt lap he s l phu thudc. Mot sd nghien ciiu cho thiy ARMA(I,1)-GARCH(I,I) la md hinh don gian, phii hgp nhu Brooks & Persand (2002), BoUerslev & cdng su (1992). Yan (2007), Gregoire &
cpng sy (2008) lai d l xuit sit dung cac phan phli thyc nghiem. Iju diem cua phuang phap nay la don gian trong tinh toan bing each sit dung cac gia quan sat (pseudo-observations) theo cdng thitc:
U = thit hgng cita bien X.j ban ddu/(dd ddi cita mdu quan sdt-^1)
D I quylt dinh ring Copula nao phu hgp vdi du lieu, cin xem xet gia tri thdng ke Goodness of fit (GoF) dugc tinh bang hieu khoang each giua md hinh Copula dugc thiet lap va md hinh thyc nghiem (Genest & cgng sy, 2009). Mpt cau tnic phu thudc tdt ky vpng mgt gia tri thdng ke GoF cao va ngugc lai. Copula dang xem xet khdng md ta diing cau tnic phu thudc. Khi dft lieu phii hgp vdi nhieu md hinh Copula, lya chpn tdt un la md hinh cd gia tri udc lugng loglihood (LLH) ldn nhat, tieu chuan thdng tin AIC va BIC nhd nhit.
2.3. Tinh todn vd kiim tra gid tri tdn thdt rui ro (Value at Risk-VaR)
VaR la mdt thudc do dugc sit dung de dinh lupng nii ro thi trudng, cho biet khoan Id tdi da cd kha Bang 1: Cac dang mo hinh Copula pho bien
Copula Mo hinh Gia tri he so
Normal Stadent
C7u,,..uj)= <t>\( •I>-'(ui),-, <I>"Vd) t5;,v(u,,..Uj)=tx,v(r'v(U|),...,t-',(u<,)
[-L1]
[-1,1]
Clayton C f (ui tt,) = Ef^ittf* d + 1]-i/s 5>0
Gumbel Frank
Cfl''"(tti uf) = exp(Ef=i( ln( ud «]-i/«
(e-''"-l)(e-''"-l)^
CF(U,V,( -\n[l + '- (e-»-l)
e>i
Ngudn: Tdc gid tdng htyp theo Fang & cdng su (2002), Rong & Truck (2014)
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Bang 2: Kit qua phan tfch thong ke
Mean Std. Dev.
Skewness Kurtosis Jarque-Bera Probability Observations ADF Test p -value
VN-Index (VND -0,0013
0,0433 -0,4041 4,6199 52,5697 0,0000 385 -16,9233
0,0000
HN-Index (HNX) -0,0037 0,0524 -0,2113 4,8766 59,3567
0,0000 385 -17,7637
0,0000
Vang (VVN) 0,0019 0,0229 0,4550 15,6851 2.594 0,0000
385 -21,8785
0,0000
Tygla VND/USD
0,0009 0,0064 3,9677 57,5795 48.796 0,0000 385 -22,8402
0,0000 Nguon: Tdc gid tinh todn dua trin sd lieu thu thdp.
nang xay ra cua mpt tai san hay mpt danh muc dau to. Trong mpt khoang thdi gian At, VaR cua danh muc diu to tai thdi diem t, vdi khoang tin cay (1-a), a e (0, 1) dugc xac dinh: P( X^, < VaRj(a)) = a
Phan bl chung cua cac yeu td nii ro la can ban de dilu tra va tinh toan VaR. Necula (2010) cho rang viec su dung cac phan phdi chuan de md hinh hda lgi suit tai chinh cua cac tai san rieng le cd the danh gia thip rui ro ctia thi trudng. Bdi vay, md hinh
thich hgp khdng chi tao nen mdt phan phdi chung phil hgp ma cdn tao ra mdt mdi toong quan phi tuyln tinh (Samia & Chaker, 2013). Dilu nay, dugc tim thiy trong Copula, dac biet Copula cdn phu hgp vdi du lieu cd phan phoi lech dudi (skew t) khi xay ra khiing hoang.
Kit qua tinh toan VaR to md hinh se dugc kiem tra bing kilm dinh Kupiec va kiem dinh Christof- fersen (Christoffersen, 1998). Cac kiem dinh nay Bang 3: Ket qua u'dc lugng cac mo hinh Copula
VNl (thurc nghiem)
VNI (ARMA- GARCH)
HNX (thuc nghiem)
HNX (ARMA- GARCH)
Copula Normal Stadent t Clayton Gumbel Frank Normal Student t Clayton Gumbel Frank Nonnal Student t Clayton Gumbel Frank Normal Student t Clayton Gumbel Frank
GoF 0,00 0,09 0,01 0,01 0,01 0,00 0,07 0,01 0,01 0,01 0,00 0,05 0,01 0,01 0,01 0,00 0,12 0,03 0,04 0,02
He so -0,0060 0,1272 0,0053 1,0097 0,1617 0,0193 0,1445 0,0361 1,0102 0,0061 -0,0148 0,1255 0,0361 1,0102 0,0556 0,0069 0,1490 0,0297 1,0050 0,1721
p-value 0,82 0,04 0,84 0,00 0,31 0,47 0,01 0,28 0,00 0,98 0,59 0,05 0,28 0,00 0,73 0,82 0,01 0,37 0,00 0,38
LLK 0,02 22,70 0,02 0,36 0,49 0,20 25,41 0,69 0,37 0,00 0,12 16,76 0,69 0,37 0,05 0,02 18,23 0,47 0,07 0,34
AIC 1,96 -39,40 1,97 1,27 1,02 1,61 -44,82 0,62 1,26 2,00 1,76 -27,53 0,62 1,26 1,89 1,95 -30,45 1,06 1,85 1,32
BIC 5,91 -27,54 5,92 5,22 4,98 5,56 -32,96 4,57 5,21 5,95 5,71 -15,67 4,57 5,21 5,85 5,90 -18,59 5,02 5,81 5,28 Nguon: Tinh loan cita tdc gid.
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kinh t4Phal trien
Bang 4: Kit qua tinh toan va kilm dinh gia tri VaR Copula VaR
copula
VaR Lich sti'
Kiem dinh Kupiec
Kiem dinh
Christoffersen Khong/ Bac bo VNI
HNX
-5.6%
-5.5%
-7.4%
-9.5%
0,12 0,12
0,08 0,08
Khong Khong
Khong Khong Ngudn: Tinh todn ciia tdc gid.
tap trung vao xac suat ciia ty le that bai eiia md hinh tinh toan VaR. Mdt md hinh tinh VaR tdt la md hinh cd gia tii bac bd cang ldn. Cae tinh toan dugc thyc hien teen phan mem thdng ke R theo ma chuang tiinh eiia Roy (2011).
3. Ket qua va thao luan
Dft lieu gia cd phieu ditgc thu thap to' Sd Giao dich chiing khoan Thanh phd Hd Chi Minh va Sd Giao dich chimg khoan Thanh phd Ha Npi. Cd phieu cd khdi lugng giao dich Idn nhat se dugc chpn theo 20 nhdm nganh tiong thdi gian tu 1/1/2008 den 30/9/2015. Ty gia VND/USD va gia vang SJC dugc chgn dai dien cho thi trudng ngoai te va thi trudng vang do ty trgng giao djch Idn. Gia thu thap la gia ban ddng 50USD va gia ban 1 lupng vang. Tat ca du' lieu sau dd dugc luge giam thanh dft lieu theo toan de loai bd yeu td miia vy. Cac chudi lgi suat se dugc tinh logarit de phii hpp vdi cac md hinh tai chinh theo cdng thitc: r= ln(P/Pj,) vdi P, la gia tai thdi diem t. Danh muc cd ty trpng bang nhau. Ket qua thdng ke dugc teinh bay tai bang 2.
Bang 3 trinh bay ket qua udc lupng cac md hinh Copula. Ket qua cho thay he sd GoF ciia md hinh Copula t ldn hon 5%. Dtr lieu phu hop vdi md hinh Copula t cho ca chi sd VNI, HNX trong danh muc.
Gia tri LLK to md hinh Copula t ldn nhat, gia tri AIC va BIC nhd nhat cho thay md hinh phu hpp nhat. Phuang phap can bien su dung ARMA(1,I)- GARCH(I,1) hieu qua hon do cd he sd LLK ldn hon, AIC va BIC nhd hon.
Bang 4 cho thay ket qua udc lupng gia tri VaR to' md hinh copula thap hon so vdi phuang phap truyen thing thdng thudng ddi vdi ca trudng hgp danh muc ciia chi sd VNI va HNX. Nha dau to cin it ngudn vln diu to cho muc dich phdng ngira nii ro. Kit qua kilm dinh Kupiec va kiem dinh Christoffersen diu vugt qua muc y nghTa 5% cho thiy chip nhan gia thuylt H^; md hinh VaR la phii hgp.
4. Kit luan
Thyc hien vdi 119 ma cd philu dl nghien cuu ciu
tnic phu thudc giua thi tru'dng chiing khoan, thi trudng vang va thi tru'dng ngoai te. Mdt sd ket luan rut ra to' ket qua nghien cuu nhu sau:
(i). Cd 66 cd phieu phii hgp vdi t-Copula, 21 cd phieu phu hgp vdi Gumbel copula; 13 cd phieu phii hgp vdi Clayton copula; 18 cd phieu phit hgp vdi Noi-mal copula va chi cd 1 cd phieu phii hgp vdi Frank copula. Do dd viec sit dyng duy nhat t-Copula de do ludng sy phu thupe la chua phit hgp. Ket qua nay cdn cho thay cd phieu, vang va ngoai te cd mdi phy thudc ddi xirng va lech phai nhieu hon. Dieu nay cho thay danh muc gdm ba tai san cho muc Igi suat bien dpng khi thi trudng di len Idn hon so vdi mile giam khi thi tru'dng di xudng.
(ii). Cac nganh cd chung lya chpn md hinh Copula cd the dupe sir dung cho cac cd phieu thudc nhdm nganh. Cd 5 nhdm nganh cho cung lya chpn 1 md hinh copula: t-Copula (cao su, nang lugng, dau khi, thyc pham), Gumbel Copula (du lich). Xay dyng la nganh phiic tap nhat vdi viee ed nhieu lya chpn md hinh Copula. Tuy vay, khdng cd nhdm nganh nao phii hop hoan toan vdi Clayton Copula, nghia la muc giam khi thi trudng di xudng ldn hon miic tang khi thi trudng di len. Cac danh myc deu cho nhieu kha nang dem lai Igi suat duong, trong dd dau to ket hgp cd phieu nhung nganh du lich chiu it nii ro nhat, thu dugc lgi nhuan cao ban khi thi tru'dng di len.
(iii). Neu tinh ca chi sd VNI, HNX thi trong tdng sd 119 ma cd phieu cd 77 ma cd phieu (chiem 66,4%), udc lugng bang phuong phap thyc nghiem cho ket qua md hinh tdt hon so vdi phuang phap can bien. Dieu nay cho thay rang phuong phap thyc nghiem nen dugc ap dung do ky thuat tinh toan don gian. Ket qua nay cdn ham y viec su dung ARMA( 1,1 )-GARCH( 1,1) dl thi hien chudi lpi suit ciia cac cd phieu chua thuc sy phii hgp ddi vdi thj tru'dng Viet Nam.
(iv). Chung khoan, vang va ty gia VND/USD cd mdi tuong quan thap khi he sd ta'ong quan va he sd phu thudc nhd (khoang 12-14%). Su phu thupc dudi
Sd 231 thdng 9/2016 13
m\
d i l xitng duac thi hien bing t-Copula ehi ra ring Christoffersen la 11 danh myc. Ket qua nay cho thay vang va USD cd thi hoat ddng nhu mot kenh diu to md hinh tinh toan VaR to Copula tdt ban so vo, viec an toan hieu qua trong thdi ky c l philu cd biln dpng gia djnh phan phd. chuan cua chudt dti lieu teong tai manh. Bing chitng nay cung pht. hgp vd, vai trd chinh. Mdt gia trj VaR thap hon ham y nha dau to nhu mpt tai san phdng ngua cua vang. Kit qua cung cin it ngudn vdn cho boat ddng phong ngua mi ro thi hien tinh hftu ich cua vang trong danh muc vdi theo tieu chuan ciia Basel.
chung khoan va d i n g ngoai te khi giam dugc muc Bai vilt cho thiy su phu thudc yeu giua thj dp rili ro so vdi danh muc thuin toy c l philu. trudng chiing khoan, thj trudng vang va thj trudng
(v). Nghien ciru nay cd quan dilm toang d i n g ngoai te. Kit qua tinh toan gia tij VaR cho thiy Igi vdi Reboredo (2013) khi gia tij VaR cua danh muc ich trong viec sti dung vang va USD nham da dang diu tu bao g l m ca vang, ngoai te va chung khoan cd hda danh muc nii ro. De cd ket qua dugc tdt han gia tri thip ban so vdi phuong phap Ijch sit. Kit qua trong thdi gian tdi tac gia se md rdng viee sit dung kilm tra VaR theo kilm djnh khdng dilu kien cac md hinh Copula khac va sit dyng them sd lieu Kupiec tai mile y nghTa 5% chi cd 8 danh muc bac v l cac d i n g tiln p h i bien nhu Euro, Bang Anh, Yen bd md hinh, d i i vdi kilm dinh cd dilu kien Nhat va Nhan dan te.D
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