MO HINH GIA TRI CHIU RUI RO TRONG D A U Tii CO PHIEU DOI V 6 l V N - INDEX
D a t v a n de
TS. Vo Thi Thiiy Anh N g u y i n A n h Tung Dai h o c Kinh te Da Nang
De kiem soat hieu qua rui ro thi trQdng, thach thQc dat ra dd'i vdi cac dinh che tai chinh cung nhQ gidi hgc thuat la hinh t h a n h mdt phQOng phap khoa hgc nham iQgng hda mQc do tdn t h a t tai chinh cd the xay ra trong nhQng dieu kien nha't dinh ciia thi trQdng va cua nen kinh te. Da cd nhieu thQdc do dQgc phat trien nham iQgng hda, dQ bao tdn t h a t do rui ro thi trQdng gay ra. Tuy nhien, vQgt len each tiep can truyen thd'ng ve do iQdng rui ro thi trQdng, thQdc do Gia tri chiu rui ro (Value at Risk - VaR) da nhanh chdng dQgc cac td chQc tai chinh ldn cung nhQ gidi khoa bgc tai chinh cdng nhan va ap dung rdng rai.
Trong thQc t e , md h i n h VaR dQOc sQ d u n g de xac dinh va dQ bao mQc do t o n t h a t td'i da CO the xay r a trong dau tQ cd phie'u. Day la CO sd de xac dinh mQc vdn an t o a n r u i ro can t h i e t trQdc nguy co riii ro tQ thi trQdng chQng k h o a n gay ra. M a t k h a c , VaR cung la mgt chi tieu chuan mQc cung cap t h d n g tin ve rui ro t h i trQdng ma mdt dinh che t a i chinh hay m g t c a - n h a n t h a m gia dau tQ t r e n thi trQdng chQng k h o a n cd k h a n a n g gap p h a i . VaR cdn la cO sd de chi r a r a n g r u i ro ma cac n h a dau tQ p h a i ddi m a t cd n a m trong gidi b a n dQOc cho p h e p bdi ngudn vd'n dau tQ hay khdng.
T r e n co sd, each tie'p c a n t h a m so' b a n g cac md h i n h k i n h te iQOng chudi t h d i gian, b a i bao xac dinh md h i n h phu h o p de dQ b a o , iQgng h d a mQc do r u i ro, t h i trQdng b a n g thQdc do VaR dd'i vdi d a n h muc t h i trQdng (Vn-Index). .«:v ' ' . • Mo h i n h g i a t r i c h i u r i i i r o
ThU&c do VaR
ThQdc do VaR dQOc dinh nghia la thQdc do t d n t h a t ldn nha't cd k h a n a n g xay r a dd'i vdi gia t r i t h i trQdng ciia cac cdng cu t a i chinh cung nhQ dd'i vdi gia t r i ca d a n h muc cac cdng cu t a i chinh t r o n g tQOng lai, vdi mgt
mQc xac sua't xac dinh trQdc, x e t t r o n g mdt k h o a n g t h d i gian nha't dinh.
Ve mat toan hgc, thQdc do VaR dQgc dinh nghia:
P [ F , - F o < F a R ] = l - a ( l )
Trong dd: VaR - gia tri chiu rui ro, V^ - gia tri bien tai hay ban dau cua mgt danh muc; V,. - gia tri tQOng lai cua danh muc sau mdt khoang thdi gian nha't dinh, dQgc xac dinh: V,, = V e"'^; a - xac suat gia thi trQdng ciia tai san hay danh muc khdng vQgt qua VaR.
TQ (1), thQdc do VaR cd the dQgc viet dQdi dang ty sua't ldi tQc cua tai san nhQ sau:
P[r,{T)< \f{r)dr- (2)
Vdi R ; (T) la ty suat lgi tQc (TSLT) t h a p nha't cua cd phieu sau khoang thdi gian x n h a t dinh vdi xac sua't tQong Qng 1 - a; r (T) la TSLT lien tuc cua CO phieu trong khoang thdi gian x, dQOc xac dinh: R^ (x) = I n (F^JP), P^: gia thi trQdng cd phidu t a i thdi diem t, f(r) la h a m m a t do p h a n phdi xac suat ciia TSLT. Theo dd VaR dQOc xac dinh:
FaR = V, -V -V ,'-:(^) 1 (3)
NhQ vay: thQdc do VaR phu thudc vao hai yeu td' chinh:
- Ky d a n h gia: la k h o a n g t h d i gian a n dinh de dQ bao sQ thay ddi gia tri thi trQdng cua danh muc cd the xay ra. Viec iQa chgn ky d a n h gia dQa t r e n nguyen t a c can dd'i giQa chi phi va lgi ich. Tbeo Uy Ban Basel, ky d a n h gia dQgc iQa chgn la 10 ngay kinh doanh [2], trong khi theo quan diem ciia RiskMetrics ky d a n h gia n e n dQgc iQa chgn 01 n g a y k i n h doanh do'i vdi cac danh muc dau tQ n h i m muc dich mua b a n kie'm lgi n h u a n trong n g a n h a n va
nganhang
So 5 7 " T h a n g 12/2010
DIEN DAN TAI CHINH
ill
25 ngay k i n h doanh dd'i vdi muc dich dau tQ dai b a n [8].
- Xac sua't tdn t h a t cho trQdc dQgc iQa chgn bdi nha quan tri rui ro. DQdi gdc do an toan vdn, xac sua't tdn t h a t nen dQgc iQa chgn sao cho td'i thieu hda cac trQdng hgp gia tri tdn that thQc te vQgt qua dQ bao cua VaR. Theo de nghi cua Uy ban Basel xac sua't tdn that khdng vQgt qua VaR cho trQdc la 99%, trong khi RiskMectrics de nghi mQc 95% dd'i vdi muc dich mua ban l l n dau tQ.
Md hinh xdc dinh VaR trong ddu tU cd phieu De xac dinh VaR ddi vdi cd phieu, chung tdi sQ dung each tiep can theo phQOng phap tham sd' dQa tren cac md hinh kinh te iQgng tQ hdi quy trung binh trQgt vdi phQOng sai cua sai sd dQgc md ta bdi cac md hinh phQOng sai sai so thay ddi cd dieu kien tQ hdi quy vdi dang phan phdi xac sua't ciia nhiiu ngau nhien dQgc gia dinh la phan phdi sai sd tdng quat - GED cd cac dang tdng quat sau:
* Md hinh ARMA - GARCH:
r, =c + 2^(l>f,_j+e, +5]0,£,_,,£, =^,u,,u,~iid G£D{0,1). (4)
J.I i=i
vdi d i e u k i e n : K > O, 8, > O ai > O, '^(S,+a,)<\,p = mm{r,m),
va moduli cua nghiem cac phQOng trinh
l - X z V , = 0 , l - | ; z ^ ( 5 , + a . ) = 0
nam ngoai dQdng trdn don vi; r^ la TSLT lien tuc ciia cd phieu. H^ la phQOng sai cd dieu kien_TSLT ciia cd phie'u. TrQdng hgp (5 =0 vdi Vy = lr md hinh se cd dang ARMA(p,q) - ARCH(m).
r, =e + £^^);_^+£,+^0,£,_, £,=^ii,, u,~ iid GED{0.\). (5)
1
vc
•1-5.ln(A) = »' + I/5;ln('',-,) + I « ,
* Md hinh ARMA - TGARCH:
r,=c^Y,^,r,_j+E,+2^6,£,_,. e,=^ii,, ii,-iid GED(0,\). (6)
•s] (cl <=l
trong dd: I^^ =1 neu s^^ < 0 va I^^ =0 khi e^,^ > 0;
s la bac bat ddi xQng cua md hinh.
Trong md hinh (6) nhQng thdng tin tdt (s^ ^ > 0) va thong tin xa'u (e^.^ < 0) se cd nhQng tac dgng khac
nhau dd'i vdi phQOng sai cd dieu kien cua TSLT, tac ddng cua nhQng thong tin td't (cu sd'c dQOng) den do dao dgng la a, trong khi a n h hQdng cua nhQng thdng tin xau den do dao dgng se la Oj + 5.. Neu 5j > 0 nhQng thdng tin xa'u se lam gia t a n g dd dao dgng cua TSLT hay cdn ggi la hieu Qng ddn bay dd'i vdi bac thQ i. NhQ vay, ne'u 5^0 tbi tac dgng cua cac cu sd'c gia ca len do dao ddng cua TSLTcua cd phieu se khdng dd'i xQng.
* Md hinh ARMA - IGARCH:
r, =c + ^^,/;_, T £ , + i ^ e , £ , ^ , E,=^u,, u,~iid GED(0,\). (7)
"Z'^.''''-;^Z°'^'-"
E.5,+X«.=l- (S vdi dieu kien b a n che:
Mdt md hinh GARCH thda man (8) dQgc ggi la md hinh GARCH tich hop bac r, m. Ky hieu IGARCH(r,m). Vdi dieu kien (8) thi ^-t/{s,*a,)^o cd nghiem don vi. NhQ vay, md hinh IGARCH cho phep md ta dQgc phQong sai cd dieu kien cua chudi TSLT trong trQdng hgp chudi binh phQOng phan dQ cua md hinh mo ta chudi TSLT xua't hien nghiem don vi.
Cac md hinh t r e n la dang tdng quat, tuy thudc vao dac tinh cua tQng chudi dQ lieu ma md hinh se cd dang AR, MA hoac ARMA ket hop ARCH, GARCH, TGARCH, EGARCH hoac IGARCH.
Trong cac md hinh t r e n phan phdi xac suat dQgc sQ dung la phan phdi sai so' tdng quat, ky hieu GED (Generalized error distribution). Day la dang phan phdi xac suat cd tinh linh boat cao va bao quat dQOc sQ dung trong khoa hgc tai chinh de md ta dac tinh "leptokurtotic". Daniel B.Nelson (1991) la mgt trong nhQng ngQdi dau tien sQ dung phan phdi GED de md hinh hda phan phdi xac sua't TSLT (Ty sua't lgi tQc) cua cd phie'u. Phan phdi GED cd dang dieu va dQgc dinh nghia nhQ sau:
Hinh 1: Dang dieu phan phdi sai sd tdng quat - GED.
G E D d v = i . i
PDF 0.8 0.7
o.«
0.S 0.4 0.3 0.2 0.1 0
stributiou 5 and 2
—
Nguon; RiskMetrics Group (1996), "RiskMetricsTM Technical Document", J.P.Morgan/Reuters, New York.
Congnghe ngan hang yj
So 57 • Thang 12/2010
Dinh nghia bien ngau nhien t a i chinh ^' ' ' ' vdi z la bie'n ngSu nhien cd phan phdi GED chuan bda vdi: E fzj=0, Var (zJ = 1, ham mat do phan phdi xac sua't cua z^ se cd dang [5]:
/ ( . - ) = e x p r - l / 2 | r / A | ' l / / . . 2 ^ ' - ' ' " ' - ' r ( l / v ) . - ac < r < K , 0 < I - < X . ( 9 )
trong dd: X dQgc xac dmh: L ^ '/ ^ 'J ^' la ham Gamma, dQgc xac dinh: r{x)= \y'~'e~'dy.
Bie'n ngSu nhien i,c6£ii.i = 0 va iar(i',|i/„,) = (T,j„,vdiu,.:
la a- dai sd cua cac thdng tin den thdi diem t-1. Ham m a t dd phan phdi cd dieu kien cua ^, la ham mat do phan phdi xat sua't GED cd dieu kien vdi phQOng sai thay ddi tbeo thdi gian dQgc xac dinh [5]:
(j|^,,,) = vcxp|-l/2J5,/;..a^|..^j'j/;./7.,.,2i"""V(l/v). -r.<i<r..O<\ir.. (10)
tham sd "v" quy dinh do day cua dudi phan phdi.
TrQdng hgp: v < 2, dudi phan phdi GED se day hon so vdi phan phdi chuan. NgQgc lai khi v >
2, dudi phan phdi GED tha'p bon (mdng bOn) so vdi phan phd'i chuan. Khi v = 2, phan phdi GED se trung vdi phan phdi chuan. Khi v = co, pban phdi GED trd thanh phan phdi deu vdi khoang xac dinh [-31/2, 31/2] [5].
Kiem dinh do phu hpp md hinh xdc dinh VaR
Mgt md hinh xac dinh VaR dQgc xem la phu hgp neu thda man cac kiem dinh ve do phu hgp cua md hinh [8]. Hau h e t nhQng kiem dinh nay deu la kiem dinh hau mau (Backtesting). Nghia la, tren co sd sQ dung mgt sd cac quan sat khdng dQa vao md hinh de thQc bien kiem dinh do phu hgp cua md hinh. Trong pham vi bai bao, chung tdi sQ dung hai phQOng phap kiem dinh hau mau dd'i vdi do phu hgp cua cac md hinh xac dinh VaR: kiem dinh dQa tren tieu chuan cua Uy ban Basel [1] va kiem dinh bang thdng ke cua P.Kupiec (1995) [7] vdi sd' quan sat dung kiem dinh hau mfiu 250 quan sat.
Lfdfc liftfng v a k i e m dinh mo h i n h x a c d i n h VaR doi vdfi chudi VNI-Index (VNI)
Nguon dU lieu thUc hien U&c lUdng vd kiem dinh md hinh
De thQc hien qua trinh Qdc iQgng va kiem dinh cac md hinh xac dinh VaR dd'i vdi chudi VNI, chung tdi tien h a n h thu thap mfiu chi sd'VNI theo ngay (tQ ngay 28/07/2000 de'n ngay 15/11/2010) gdm: 2.411 quan s a t theo ngay. Trong dd: sQ
dung 2.161 quan s a t , tQ n g a y 28/07/2000 de'n 13/11/2009 de thQc b i e n qua t r i n h Qdc iQgng, kiem dinh cac t h a m so' cua md h i n h xac dinh VaR. Dd'i vdi 250 quan s a t cdn l a i (tQ ngay
16/11/2009 de'n 15/11/2010) d u n g k i e m dinh do phu h g p ciia md b i n b x a c d i n h VaR theo tieu chuan k i e m d i n h cua U y b a n Basel va thd'ng ke P.Kupiec (1995).
Dil li#u lich sii thay doi bien dp giao dpng gia ap dung do'i vdi San Giao dich Chxing khoan Tp. Ho Chi Minh (SGDCK TPHCM)
•^'gay hieu luc 28'07/2000
01/08/2000
13/06/2001
10/10/2001
11/OS/2002
02/01/2003
27/03/2008
07/04/2008
19/06/2008
18/08/2008 ddn nay
Bien dp ( - - ) 5 %
( - - ) 2 %
(+/-) 1%
{+,••-) 2 %
(+•'-) 3 %
(+/-) 5%
(W-) 1%
(+/-) 2%
(+/-) 3%
(-/-) 5%
Nguyin nhan
Giu: mite lliay doi gia dao dgng du nho, tranh soc cho thj trudng.
Thi truang giao djch lo lang vc dam ddng dau tu va siic mua vugt quii xa khoi lugng san siing bin.
Thj tnrdng giao djch muon khAng djnh dij trufmB du dieu kii;n d^ vjn hanh tron tru vii nhi dau lu chju Enich nhi^m v6 hiinh vi dAu lu. NAi rgng bicn dg dc iSng quyen l\r chii.
Dieu chinh sau gun 4 ttidng s^t giam sire mua vi gia tren loin Ihj (ruong, ngay sau dinh chi sd VNI li 571 didm vao thang 06/200!.
Dieu chinh de lim kiem sy soi dpng sau nhieu Ihang giao djch vcri kh6i lugng lliap, vi miic cung co phieu liing nhanh do vigc lang them cong ty niem ycl.
Nham lang linh hip dan cho Ihj trudng, l ^ g khi nSng Ihanh khoin cho Ihj Inrdng Irong dieu kign ciiu yeu hem cung.
N'ham on dinh tiim ly nha dau tu, h ^ chi; vigc ban thao co phieu vi cac ho^t dgng giii chap nhiim on dinh lai ho;il dgng ciia thj t n i ^ g khi thj truong lao ddc qua nhanh v i sau (Cdng vin so 467/UBCK-PTTT ngiy 25/03/2008).
Can cit vao diiSn bicn ciia ihj truong, tiim ly ciia nhi dau ttr cung nhu sau khi da trien kliai cie giii phip theo chi d^o cua Thii tuong Chinh phii l^i cdng vin s6 1909/VPCP-KrrK, Uy ban Chung khoin Nhi nudc cd cdng vin sd 529/UBCK-PTTT chap thuyin cho SGDCK TPHCM lym thdi dieu chinh bien dg dao dgng giii cd phieu, chiing chi quy dau tu.
Nham tang site hut ciia thj trudng sau khi thj trudng da dan ho^l dgng dn djnh. (Cdng vin so 1160/UBCK-PTTT ngiy 16/06/2008), Nham liing sire hiil, linh thanh khoin cua thj Irudng cung nhu Irinh nhimg thay ddi bat tiiudng trong dieu kien linh hinh kinh tc vT md da cd nhung chuyen bicn lich c^^c, lai suat, ty gia, nh^p sieu vi Ijim phii da CO lin higu tdt hon.
Nguon: Uy ban Chiing khodn Nhd nudc
Ke't qud U&c lUpng vd kiem dinh md hinh xdc dinh VaR theo ngdy ddi v&i chi sd VNI
C h u n g t d i sQ dung p h a n m e m eviews de Qdc iQOng va k i e m dinh cac mo h i n h : ARMA- GARCH, ARMA-EGARCH, ARMA-TGARCH, ARMA-IGARCH trong viec x a c dinh VaR dd'i vdi chi so' VNI. Theo each tie'p c a n tham sd', de Qdc iQOng md h i n h x a c d i n h VaR dau t i e n p h a i gia dinh trQdc d a n g p h a n phoi xac sua't ciia chudi TSLT. K i e m d i n h Jarque - Bera (JB) chi r a p h a n phd'i x a c sua't ciia chudi TSLT VNI k h d n g t u a n theo p h a n phd'i chua'n. Tuy n h i e n , t h d n g qua cac h e so' thd'ng k e : Kurtosis = 5,183 > 3 va s k n e w n e s s = -0,193 cho tha'y d a n g p h a n phd'i ciia TSLT VNI la g a n dd'i xQng va bi leptokurtotic. Do do, d a n g p h a n phd'i GED dQgc c h u n g t d i sQ dung de Qdc iQOng md h i n h .
nganhang
DIEN DAN TAI CHINH
ill
Dang cua cac md binh dQOc xac dinh thdng qua iQgc dd ham tQ tQOng quan (ACF) va tQ tQOng quan rieng phan (PACE) ddi vdi chudi TSLT VNI va binh phQOng chudi TSLT VNI. Sau nhieu lan thQc hien Udc iQgng, ke't qua cho tha'y md hinh ARMA(7, 6) - IGARCH(2, 3) vdi sQ bd sung bie'n ngoai sinh "Bien do dao dgng gia" - BDDD trong ca'u triic md binb IGARCH dQgc iQa chgn de dQ bao VaR dd'i vdi chi sd VNI. Cac tham sd Qdc iQgng deu cd mQc y nghia rat cao, cac kiem dinh tQ tQOng quan chudi va phQOng sai sai sd thay ddi theo thdi gian ddi vdi cac phan dQ chuan hda cua hinh deu cho tha'y md hinh khdng cdn tdn tai tQ tQOng quan chudi cung nhQ phQong sai sai so thay ddi. Ket luan nay cho thay dang cua md binb ARMA va IGARCH dQgc xac dinh la phu hgp. Cac kiem dinh hau mfiu theo tieu chuan cua Uy ban Basel va thd'ng ke P.Kupiec cung chi r a day la md hinh hoan toan .phu hgp va cd do tin cay cao de xac dinh VaR ddi vdi chi sd VNI.
Ke't qua Qdc iQgng va kiem dinh dQgc chi tie't tai bang sau: Md binb dQgc Qdc iQgng:
Ke't qua Qdc iQgng va kiem dinh mo hinh:
/;=0,1772r,.|+0,0023r, ,+0,5711;;J-0,2077r,., +0,3613/;.,-0,05l8r,., + £, +0,I523ir,^, -0,4834£,^, +0,1085e,., -0,2733£v,,
c,=hf-u„ u,-1.1.11 GED(0.].v), v=l,48015
A, =1,4819*,_,-0,7265A,_,+0,182i;i,_,+0,3262£,'_,-0,26374,+4,99.10-'SDDD
Ket qua dQ bao chi so' VNI va VNI tha'p n h a t cd the xay r a vdi mQc tin cay 99% trong 30 quan
sat tdi ke tQ ngay 15/11/2010 dQgc tdng hgp t a i bang sau:
Cdt VNI dQ bao la gia t r i dQ bao cua chi sd' VNI tQ md hinh Qdc iQOng, cot VNI tha'p nha't
Ngiky
16/1L'2010 17/1172010 18/11/2010 19/1L/2010 22/1172010 23/11/2010 24/lL'2010 25/1L/2 010 26/11/2010 29/11/2010 30/11/2010 01/12/2010 02/12/2010 03/12/2010 06/12/2010
VNI di^ b a o
431,55 424,24 424,94 431,21 424,11 424,89 432,44 434,34 441,20
439,32 448,92 452,87 453,80 454,33 455,66
VNI t h a p n h a t (99%) 418,90 411,98 414,72 419,34 412,10 414,44 420,26 423,48 429,19
428,97 435,56 440,75 444.02 446,04 447,92
N g a y
07/12/2010 08/12/2010 09/12/2010 10/12/2010 13/12/2010 14/12/2010 15/12/2010 16/12/2010 17/12/2010 20/12/2010 21/12/2010 22/12/2010 23/12/2010 24/12/2010 27/12/2010
VNI drf b a o 456,23 457.44 457,96 458.99 459,36 460,47 460.84 461,81 462,10 463.06 463.30 464.20 464,41 465,27 465,42
VNI t h a p n h a t (99^f)
448,67 450,06 450.82 452,12 452,77 454,13 454,74 455,91 456.42 457,56 457,98 459,04 459.40 460.40 460,68
N^l dung R"
R'' difiu chinh Akaike info critetion Log likelihood
PhSn vj phan phdi GED chu^n h i a tucmg i m g tham s6 V
= 1.48015 vdrixScsu^Hyo.
Thdng kfi Ki4m djnh ARCH b^c 5 cua R.F.Engle (1982) (N-P)R'
G\A trj I6i h^n cua phSn phdi chi binh phirong p = 5 bSc t y do l u c n g irng x&c su^t sai i^m io^i i: 1 %
Kel iu$n ve hi^n lup'ng phifcrng sai sai so thay ddi theo Ihoi gian ddi vin ph^n d u chuan h6a cua mo hinh.
Thdng k6 LB viri 36 dp tre ddi vdti phan dir chuan hoa cua mfl hinh.
G i i tit l<^ hgn cua phSn phdi chi binh phirong 36 b^c tg* do tirong irng x i c s u i l sai i^m iogi i; 1 % .
K^t l u | n v^ hi^d l u g n g l y tuong quan chufii ddi voi p h l n d u c h u i n hda cua mo hinh.
X i c s u l l Idn that thyc l 6 khflng virgl q u i VaIR d y b i o hay h^ s6 tin c^y irong mo hinh xac djnh VaR.
Sd t r u i n g bop ngogi 1$ trong mau 250 quan s i t . T i n suSl xuSt hi^n lar&ng hpp ngogi lg tr6n m^u kifem djnh 250 quan s i l
G\d tii th6ng kg Kupiec
Gid hj thdng k6 Chi binh p h u o n g 1 b$c lu- do vdi x i c sufll sai l i m logi 1 l i 1 0 % v i 5 %
Kht lu$n v^ dO phu hpp cua m6 hinh:
+ Theo ti§u c h u i n k i ^ djnh cua Basel
• Theo th6ng kg k i l m djnh P.Kupiec (1995)
ARMA(7,6) - IGARCH(2,3) 0.13565 0.13022 -6.00168 7227.021 -2.50649 3,20852 15,0863 C h i p nhgn gia Ihiet Ho: khong Idn Igi hign t u p n g p h u o n g sai cua sai sd ihgy doi theo thai gian doi vdri p h l n d u chuan hoa cua mo hinh tren c o s o m l u quan sat.
36.18026 58,61921 P h l n d u c h u i n hoa cOa mo hinh Id chu5i r&ihj tr^ng, md hinh phii hpp voi ly thuyet
1 % 4 1,6%
0,76914 2.70554 vd 3,84146
+ M6 hinh c6 xay ra t>6n trubng hpp ngogi le, Iheo ti&u c h u i n cua Dy ban Basel mo hinh d u ^ c xep vao vung xanh, dSy 1^ vung an todn voi dp nii ro cua mo hinh Id t h l p n h l l ,
+ Kh6ng t h i bdc bo gid thiet Ho ve xac s u i t x u l t hi^n t r u i n g h p p ngogi lg bang voi lan x u l t x u l t hi&n tdn I h i t thyc l l v i f p i qua VaR d y bao, hay h#
so tin cdy Irong mo hinh xac dinh VaR Id 1 % tren c p sir 250 quan sdt cua m l u kiem (Snh, Do do, mo hinh Id phd hpp iheo lieu c h u i n kiem dinh P.Kupiec Sai s 5 binh p h u o n g "trung binh d y bAo VaR n g i y cua chi j ^ ^ ^ ^ ^^
sA VNI (RMSE) irong 250 quan sAi. ' ' ^ ^ Sai s6 binh p h u o n g irung bmh d y b t o cJii s6 VNI theo ; ^ 2514 d i ' ngdy (RMSE) trong 250 quan s i t . '
(99%) la gia t r i VNI tha'p nha't cd t h e xay r a vdi k h a n a n g la 99%. Vi du: ngay 26/11/2010 gia tri VNI dQgc md hinh dQ bao la 441,20 diem va neu trong trQdng hgp VNI sut giam t h i md hinh se dQ bao k h a nang 99% VNI sut giam td'i da d a t de'n mQc 429,19 diem. So sanh vdi ke't qua VNI thQc de'n ngay 30/11/2010 cho tha'y RMSE dQ bao VNI la 1,32 diem va RMSE dd'i vdi dQ bao VaR cua VNI la 5,57 diem. De dang n h a n thay, cac ngay 17, 18/11 va 22 va 23/11 la nhQng ngay VNI dat mQc t h a p nhat. Day la nhQng phien dieu chinh cua thi trQdng va la day cua nhQng chu ky bien dgng trong ngan b a n cua VNI.
K e t l u a n riit r a tiif k e ' t q u a vCdc Ivtdng thxic n g h i e m
Qua ket qua Qdc iQOng, md hinh ARMA(7,6) - IGARCH(2,3) cd do tin cay cao. Cac kiem dinh nhieu trang, mQc y nghia cua cac tham sd, kiem dinh ARCH cua RF.Engle (1982) va do phu hgp eiia mo hinh cho thay day la md hinh hoan toan thda man cac dieu kien ve mat ly thuye't va phu hgp vdi tieu chuan cao nhat ciia Uy ban Basel. TQ ke't qua Qdc iQOng va kiem dinh cho phep di de'n mdt sd nhan xet sau:
Thii nhdt, md hinh IGARCH td ra phu hop de mo ta dgng hgc cua phQOng sai cd dieu kien ddi vod chudi TSLT chi so VNI. Cac nghien cQu ly thuyet ve md hinh IGARCH chi ra rang dd'i vcri cac chudi dQ heu dQOc md ta bdi IGARCH dieu dd ham y tdn tai cac nhan td anh hQ&ng ben vCftig lam thay ddi cau tnic dao dgng cua chudi dQ lieu [11]. Dd'i vdi chudi VNI, nhan td anh hQ&ng rd rang nhat la bien do dao dgng gia. TQ ket qua Qdc iQOng cho thay do nhay cua bien do dao dgng gia dd'i vdi phQong sai ed dieu kien ciia TSLT VNI dQgc md ta trong ca'u true md hinh IGARCH la 4,99.10-6 vdi mQc y nghia thd'ng ke p-value la 0,06%.
nganhangV
So 57•Thang 12/2010
Thii hai, TSLT cua chi sd VNI khdng tuan theo phan phd'i chuan ma tdn tai dac tinh leptokurtotic va fatail. Do dd, de dQ bao VaR dd'i vdi VNI thi phan phd'i GED phu hop hon so vdi phan phd'i chuan.
ThiX ba, md hinh Qdc iQgng VaR ddi vdi VNI da kiem dinh dQgc gia thuye't thi trQdng hieu qua va hieu Qng GARCH tren day TSLT ddi vdi Thi TrQdng ChQng khoan Viet Nam (TTCKVN) vdi dQ lieu dai dien la chi sd VNI. Theo dd, TTCKVN tdn tai hieu qua dang ye'u ddng thdi xac n h a n tdn tai hieu Qng GARCH. Ca hai van de nay deu ham y vai trd cua cac thong tin qua khQ ddi vdi viec dQ bao gia tren thi trQdng. Theo ca'u true ciia md hinh ARMA(7,6) - IGARCH(2,3) chi ra tac ddng cua cac quan sat qua khQ anh hQdng den gia tri dQ bao ciia chi sd VNI. Theo dd:
(i). TSLT cua chi sd VNI dQ bao chiu sQ chi phd'i bdi d i i n bien TSLT VNI trong bay quan sat trQdc dd. Trong dd, TSLT chi sd VNI cua n a m va bay quan sat trQdc cd tQOng quan cimg chieu vdi TSLT chi sd VNI dQ bao. Tuy nhien, mQc do nhay cam cua thdng tin phan anh vao gia tri dQ bao cua TSLT giam dan theo thdi gian. Thdng tin cua nam quan sat trQdc dd cd mQc do nhay cam cao hon so vdi bay quan sat trQdc. Dieu nay, the hien qua dau va do ldn cac he sd Qdc iQgng (j cua rt-j trong md hinh.
(iii). Do dao ddng dQ bao cua TSLT chi sd VNI phu thudc vao binh phQOng TSLT, mQc do dao dgng cua TSLT cua chi sd VNI trong 1 va 2 quan sat trQdc dd. Ddng thdi, ca'u true phQOng trinh phQOng sai cung chi rd n h a n td bien do dao ddng gia cd anh hQdng cd y nghia den do dao ddng cua TSLT chi sd VNI.
NhQ vay, de dQ bao VaR dd'i vdi chi so' VNI, md hinh dang IGARCH td ra phu hgp va dQ bao td't hon so vdi cac dang khac thudc ldp md hinh GARCH. Nguyen nhan la do cau true phQong sai cua TSLT chi sd VNI khdng chi phu thuge vao cac bien ndi sinh ma cdn chiu tac ddng m a n h bdi cac nhan td ngoai sinh. Trong dieu kien thi trQdng chQng khoan Viet Nam, dang chu y la nhan td': bien do dao dgng gia chQng khoan dQgc xem la hanh vi nan thi trQdng cua chinh phii.
Mdt he qua cd the dQOc suy ra tQ ket qua Qdc iQOng: dd'i vdi nhQng thi trQdng chQng khoan mdi, chiu sQ dieu tie't manh bdi chinh phu, nOi ma cac quyet dinh dau tQ thQdng hi chi phd'i bdi tam ly "bay dan" thi ca'u true phQOng sai cua TSLT ciia cac cd phieu nhieu kha nang bi thay ddi bdi tac ddng cua cac n h a n td' ngoai sinh va xua't hien nhQng dao ddng cQc bien hay tdn tai
nganhang
dac tinh "fat tail" trong phan phdi xac sua't TSLT cua cac cd phie'u. De xac dinh VaR dd'i vdi cac cd phieu trong dieu kien nay thi cac md hinh dang IGARCH vdi sQ bd sung cac bien ngoai sinh se dQgc Qu tien iQa chgn"
Tai lieu tham khao
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