Download - [Nh] Detai Ueh500 2012
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MC LC
DANH MC CC T VIT TT ............................................................................................. iv
DANH MC BNG BIU .......................................................................................................... v
DANH MC HNH ..................................................................................................................... vi
LI M U ............................................................................................................................... 1
1. L DO CHN TI ........................................................................................................ 1
2. MC TIU NGHIN CU ................................................................................................. 2
3. PHNG PHP NGHIN CU ........................................................................................ 2
4. NI DUNG NGHIN CU ................................................................................................. 3
5. NGHA NGHIN CU CNG TRNH .......................................................................... 4
6. HNG PHT TRIN TI .......................................................................................... 5
1. GII THIU ............................................................................................................................ 6
2. TNG QUAN CC NGHIN CU ...................................................................................... 6
3. KHUNG L THUYT C S V M HNH VALUE AT RISK ...................................... 12
3.1 Khi nim gi tr ti ri ro ................................................................................................ 12
3.2 Cc m hnh tnh VaR ...................................................................................................... 14
3.3 D bo phng sai : .......................................................................................................... 16
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3.3.1 M hnh tham s : ..................................................................................................... 16
3.3.2 M hnh phi tham s ................................................................................................. 18
3.4 Backtesting VaRs .............................................................................................................. 19
3.4.1 Kim nh Unconditional Coverage ......................................................................... 20
3.4.2 Kim nh tnh c lp ............................................................................................. 21
3.4.3 Kim nh Conditional Coverage ............................................................................. 23
4. P DNG M HNH VALUE AT RISK LNG HA RI RO T GI TRONG
KINH DOANH NGOI HI ..................................................................................................... 24
4.1 Khung l thuyt c s v vn ri ro trong kinh doanh ngoi hi ................................. 24
4.1.1 c im ca kinh doanh ngoi hi trn th trng forex: ...................................... 24
4.1.2 Cc loi ri ro nguyn nhn pht sinh ri ro trong giao dch kinh doanh ngoi
hi..25
4.1.3 Vn trng thi ngoi hi (exchange position) ...................................................... 27
4.1.4 Vn qun tr ri ro trong kinh doanh ngoi hi ................................................... 28
4.2 D liu v xy dng m hnh thc nghim ...................................................................... 29
5. KT QU THC NGHIM : .............................................................................................. 30
5.1 Kt qu xc nh VaR cho tng cp tin t ring l: ........................................................ 30
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5.2 Xc nh hn mc u t, li nhun v thua l tch ly ca danh mc da vo gi tr
VaR ....................................................................................................................................... 32
5.3 Kim tra m hnh Backtesting VaRs .............................................................................. 34
5.4 Xc nh VaR cho c danh mc...................................................................................... 39
5. KT LUN ......................................................................................................................... 41
DANH MC TI LIU THAM KHO .................................................................................... a
PH LC .................................................................................................................................... d
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DANH MC CC T VIT TT
ADF Augmented Dickey-Fuller test
GARCH T hi quy phng sai thay i c iu
kin tng qut
HS Historical Simulation model
P/L Profit/loss distribution
TSSL T sut sinh li
VaR Value at risk
VAR-COVAR Ma trn phng sai- hip phng sai
EVT Extreme Value Theory
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DANH MC BNG BIU
Bng 2.1: Tng hp cc m hnh VaR truyn thng
Bng 3.1: Tng hp cc phng php tnh VaR ph bin
Bng 4.1: Tng hp cc giao dch lm pht sinh trng thi ngoi hi
Bng 4.2: Thng k m t thu nhp ca cc cp tin t trong giai on 1/11/2006-1/11/2012
Bng 4.3: Kim nh ADF test v tnh dng ca cc bin
Bng 4.4: Kt qu o lng bin ng ca cc cp t gi bng m hnh GARCH (1,1)
Bng 5.1: Kt qu tnh VaR cho tng cp tin t (n v %)
Bng 5.2: Kt qu tnh VaR cho tng cp tin t ring l (n v USD)
Bng 5.3: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t GBP/USD
Bng 5.4: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t EUR/USD
Bng 5.5: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t CAD/USD
Bng 5.6: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t AUD/USD
Bng 5.7: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t CHF/USD
Bng 5.8: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t NZD/USD
Bng 5.9: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t JPY/USD
Bng 5.10: Ma trn phng sai ca cc bin
Bng 5.11: Ma trn tng quan gia cc bin
Bng 5.12: Kt qu tnh VaR cho ton danh mc
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DANH MC HNH
Hnh 3.1: Xc nh gi tr VaR t th phn phi xc sut ca chui thu nhp
Hnh 4.1: Biu phn phi tn sut ca cc cp tin t
Hnh 4.2: Bin ng t gi hng ngy ca cc cp tin t
Hnh 5.1: Kt qu d bo VaR cho tng cp tin t ring l
Hnh 5.2: Kt qu P/L tch ly hng ngy ca tng cp tin t
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LI M U
1. L DO CHN TI
Forex l mt th trng u t y tim nng nhng li cha ng ri ro cao thng qua
bin giao ng ln ca cc mc gi v nhng lc n by. S xut hin ca nhn t
ri ro t ra nhu cu cp thit cho cc ch th tham gia th trng l: Cn phi c
mt cng c lng ha nhng nh hng ca ri ro, kim sot v phn b chng
mt cch hp l nhm t c mc tiu li nhun trong iu kin th trng lun bin
ng khng ngng. gii quyt vn ny, hng lot cc m hnh ton hc phc tp
vi s kt hp ca cc l thuyt v xc sut, ti u ha v c lng ra i. Trong
, gii ti chnh hin i c bit ch ti m hnh Gi tr ti ri ro (VaR), v y
cng l m hnh c ng dng rng ri trong qun tr ri ro ti cc ngn hng ln trn
th gii nh Goldman Sachs, J.P. MorganTuy nhin, tri qua hn mt thp k hnh
thnh v pht trin m hnh ny cng bc l mt s thiu st nht nh v bn thn
VaR, tuy l mt cng c qun tr ri ro tt nhng hiu qu s dng li chu tc ng rt
ln bi mc ch, trnh hiu bit cng nh kinh nghim ca ngi s dng. Chnh v
vy m vn t ra y l: VaR l g v s nguy him nh th no nu khng hiu
v s dng ng chc nng ca n? M hnh VaR no c kh nng d bo ri ro mt
cch chnh xc? u l nhng sai lm thng gp khi s dng VaR ? VaR c p
dng ra sao trong vic phng nga nhng ri ro pht sinh trong qu trnh kinh doanh
ngoi hi? Xut pht t nhng nhu cu ny, bi nghin cu tin hnh ng dng m
hnh Value at risk trong lng ha ri ro kinh doanh ngoi hi trn th trng forex,
thng qua nhm to c s khoa hc cho vic ra quyt nh, phn b danh mc u
t, hn ch n mc thp nht nhng nh hng xu do ri ro gy ra. T gp phn
nng cao hiu qu ca nghip v kinh doanh ngoi hi ti h thng cc ngn hng
thng mi Vit Nam.
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2. MC TIU NGHIN CU
V mt nh tnh, ti tp trung nghin cu cc l thuyt v hot ng kinh doanh
ngoi hi trn th trng Forex. Nhng im c th ca th trng ny, cc loi ri
ro pht sinh trong giao dch kinh doanh ngoi hi. Vn v trng thi ngoi hi,
xc nh v duy tr mc trng thi ngoi hi hp l. Phn tch nguyn nhn pht sinh
ri ro v cc vn ch yu trong qun tr ri ro kinh doanh ngoi hi
V mt nh lng, ti tin hnh ng dng m hnh value at risk vo vic lng
ha ri ro trong kinh doanh ngoi hi. T kt qu thc nghim, ti tp trung lm
r mt s vn sau:
Quy trnh thc nghim ng dng VaR trong o lng ri ro t gi l g ?
Lm th no lng ha chnh xc nhng bin ng ca d liu ti chnh
(chui t gi) vi 2 c th c bn ca chng l bin ng theo nhm v hin
tng fat tail ?
Gi tr VaR c s dng ra sao trong thc tin u t c th l vic xc
nh hn mc u t ti a v li nhun/thua l (P/L) tch ly d kin
Vn xy dng tiu chun kim nh la chn m hnh VaR thch hp
vi chui d liu nghin cu
3. PHNG PHP NGHIN CU
Phng php nghin cu ca ti c th c chia lm phn :
- i vi nhng mc tiu nh tnh, bi nghin cu ch yu s dng phng php
thng k, m t, so snh, phn tch v tng hp vi mc ch trnh by nhng
vn l thuyt nh: cc c im c trng ca th trng ngoi hi, vic xc
nh v duy tr mt trng thi ngoi hi hp l, nhng li ch v ri ro no
thng pht sinh trong qu trnh kinh doanh ngoi hi.
- i vi vic nh lng, bi nghin cu s dng m hnh gi tr ti ri ro
(Value at risk) : (1) lng ha nhng bin ng t gi qua cch tip cn tham
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s (m hnh riskmetrics, GARCH (1,1)) v phi tham s ( m hnh Historical
Simulation), (2) o lng cc khon l tim nng thng qua gi tr VaR v (3)
xc nh cc mc li nhun/ thua l tch ly (P/L) theo thi gian v hn mc
u t ti a cho tng cp tin t ring r cng nh cho ton danh mc. V cui
cng l vn kim nh tnh thch hp ca m hnh qua xy dng php th
Backtesting VaRs
4. NI DUNG NGHIN CU
ti tp trung vo 3 ni dung nghin cu sau :
Th nht l tng quan v hot ng kinh doanh ngoi hi trn th trng forex ca cc
ngn hng thng mi. Phn tch cc c im c trng ca th trng ny t
rt ra c cc tng kt v nhng li ch v ri ro s pht sinh khi tham gia vo th
trng ny:
- Tng quan v cc giao dch kinh doanh ngoi hi
- Li ch ca kinh doanh ngoi hi trn Forex
- Trng thi ngoi hi
- Vn qun tr ri ro trong kinh doanh ngoi hi
Th hai l
- Tng quan cc nghin cu v m hnh Value at risk
- Khung l thuyt c s v m hnh Value at risk
- Cc phng php tnh VaR
- Vn d bo phng sai : Cc m hnh tham s ( RiskMetric, GARCH(1,1))
v phi tham s (Historical Simulation Model)
- Kim tra mc ph hp ca m hnh qua php th Backtesting
Th ba l xy dng m hnh v kt qu thc nghim
- La chn h thng bin chui thi gian d liu, xy dng m hnh
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- D Bo VaR cho tng cp tin t ring l v cho c danh mc. T phn tch
tc ng ca vic a dng ha u t trong gim thiu ri ro ton danh mc
- Xc nh hn mc u t, li nhun v thua l tch ly ca danh mc da vo
gi tr VaR
- Kim nh mc ph hp ca cc m hnh VaR xy dng bng vic s
dng php th Backtesting
- Kt lun v cc xut lu khi p dng m hnh VaR trong qu trnh qun tr
ri ro kinh doanh ngoi hi
5. NGHA NGHIN CU CNG TRNH
Ba ng gp quan trng ca ti l :
- V mt l lun, ti h thng c mt s nghin cu v vn lng ha
ri ro cho chui d liu ti chnh, cc vn pht sinh v cc hng nghin cu
mi, ch ra c 2 im c th ca phn phi d liu ti chnh l bin ng
theo nhm v hin tng fat tail, cng cc khung l thuyt c s, cc m hnh
gii quyt ang c p dng v tip tc nghin cu pht trin. i vi i
tng nghin cu l ri ro t gi, ti cng khi qut c cc im chnh
trong qun tr ri ro t gi nh cung cp mt ci nhn h thng v ri ro t gi,
nguyn nhn pht sinh, cc yu t nh hng, vn xc nh v duy tr trng
thi ngoi hi hp l v cc nn tng c s trong qun tr ri ro kinh doanh ngoi
hi.
- V mt thc tin, ti tin hnh xy dng mt m hnh lng ha cc bin
ng t gi, o lng cc khong l tim nng v xc nh hn mc u t
thng qua gi tr VaR. ng thi cng a ra c cc tiu chun kim nh
la chn m hnh VaR thch hp cho danh mc u t. T hn ch n mc
thp nht nhng nh hng xu do ri ro gy ra v gp phn nng cao hiu qu
ca nghip v kinh doanh ngoi hi ti h thng cc ngn hng thng mi Vit
Nam.
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- Ngoi ra, ti cn cung cp c s l thuyt v phng php lun cho cc
nghin cu tip theo Vit Nam. ng thi n cng cung cp thm mt tnh
hung nghin cu cho cc mn hc nh: Thanh ton quc t, Qun tr ri ro,
Kinh t lng ng dng v phng php nghin cu.
6. HNG PHT TRIN TI
ti c th m rng theo hng, o lng cc gi tr vt mc cho nhng s kin
Black swan thng qua cch tip cn l thuyt gi tr vt mc Extreme Value Theory
(EVT). S dng phn b Pareto xc nh t trng danh mc ti u v xc nh phn
phi cho ton b danh mc thng qua hm copula of portfolio
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1. GII THIU
L th trng ton cu vi khi lng giao dch khng l cng s ng o v a dng
ca s lng thnh phn tham gia. Forex c xem l mt mi trng u t y ha
hn. Song, cng vi kh nng kim li ln th mc ri ro m nh u t phi gnh
chu cng tng theo do tc ng n t 2 yu t c th chnh ca th trng ny l: bin
dao ng gi ln v lc n by mnh. Ri ro y c xem l nhng bin ng
ngoi k vng. iu c ngha l, n l mt c tnh gn vi th trng, chng ta
khng th loi b n m ch c th hn ch n mc thp nht nhng nh hng xu do
n gy ra thng qua lng ha cc bt trc bng cng c xc sut. T nhu cu ny
thc y cc nh nghin cu v gii thc t kho st, xut v pht trin nhng m
hnh qun tr ri ro thch hp. Qun tr ri ro trn c s nhng m hnh Value-at-Risk
(VaR - gi tr chu ri ro) nhanh chng tr thnh mt ch hc thut nng v nhn
c s quan tm c bit ca nhiu nh u t cng nh cc t chc ti chnh ln. Tuy
nhin, tri qua hn mt thp k hnh thnh v pht trin VaR cng bc l nhng thiu
st nht nh. Trong 2 vn ng ch nht l: (1) VaR hu nh ch c kho st
trong iu kin th trng n nh. iu ny t ra cu hi: Liu rng VaR c cn duy
tr c mc d bo chnh xc trong iu kin th trng c s dao ng mnh di
s tc ng ca nhng s kin black swan ang xut hin ngy mt nhiu ? (2) Vic
o lng VaR truyn thng thng phi da vo nhng gi nh phn phi chun ca
chui d liu. Song, nhng kho st thc t cho thy, y l mt gi nh phi thc t v
cc chui d liu t ga thng c hin tng fat tail tc l nhng kh nng mt vn
ln tp trung nhiu pha ui ca th phn phi. Vy th gii nghin cu ti chnh
c nhng hng gii quyt nh th no i vi vn ny? Nhm i tm li gii cho
nhng cu hi t ra, bi nghin cu tin hnh phn tch v tng hp t cc khung l
thuyt c s v m hnh VaR cng nh vn qun tr ri ro kinh doanh ngoi hi, kt
hp vi hng lot cc nghin cu thc nghim trong sut nhng bc pht trin ca lnh
vc lng ha ri ro a ra c c th ca cc ri ro t gi pht sinh. Quy trnh p
dng VaR trong lng ha ri ro kinh doanh ngoi hi v nhng iu cn lu khi p
dng VaR trong thc tin u t. ng thi, hng n nhng mc tiu nh lng, bi
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nghin cu cng tin hnh xy dng m hnh VaR cho danh mc tin t gm 7 ng
tin c doanh s giao dch ln nht trn th trng Forex. Bin ng s c o lng
thng qua c 2 cch tip cn l tham s v phi tham s. Vn la chn khung thi gian
v tin cy s c kim nh qua php th Backtesting VaRs. Cui cng, gi tr VaR
s c nghin cu trong 2 trng hp l vi tng cp t gi ring l v vi ton b
danh mc u t. Vic phn tch s c tin hnh lm r li ch thu c t vic a
dng ha u t.
2. TNG QUAN CC NGHIN CU
Hng lot cc cng trnh nghin cu tp trung vo vn m hnh ha ri ro th
trng, trong hu ht u da vo cch tip cn m hnh gi tr ti ri ro VAR.
Nghin cu ca Hendricks (1996) tin hnh phn tch 12 m hnh VAR khc nhau khi
tnh ton da trn chui d liu qu kh cho thu nhp t gi (exchange rate returns) v
tm thy rng phng php m phng qu kh (historical simulation) cho kt qu tt
hn mc 95% so vi 99% hoc tin cy cao hn v phng php trung bnh trt
c trng s ly tha cho kt qu ng tin cy hn khi s dng nhn t phn r bng 4
i vi chui d liu hng ngy.
Barone-Adesi and Giannopoulos (2000) kim nh phng php m phng qu kh
cho chui thi gian t 1/1997- 12/1999 vi danh mc u t S&P 100 bao gm c cc
quyn chn . H kt lun rng c th xc nh VAR bng c 2 cch l s dng phng
php phng sai hip phng sai hoc k thut m phng qu kh. Vic s dng phng
php thng k v c im ca ti sn ti chnh s nh hng n tin cy ca gi tr
VaR c tnh. Hendricks (1996) trong nghin cu ca mnh chn ngu nhin 1000
danh mc quyn chn tin t kim nh tnh hiu qu ca m hnh VAR . Mc tiu
ca nghin cu ny l chng minh v so snh s ging nhau gia ri ro o lng bng
VAR v ri ro thc t pht sinh. ng tin hnh o lng ri ro th trng vi 3 phng
php c bn : (1) trung bnh trt, (2) trung bnh trt c trng s ly tha v (3)
phng php m phng qu kh. Da vo tng phng php cp trn cho ra cc
kt qu VAR khc nhau v ng vn cha th i n kt lun v mt phng php o
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lng VAR ti u. Trong kim nh ny ng cng ch ra rng vic la chn tin cy
khc nhau cng c nh hng ln n kt qu VAR o lng c. Nghin cu ca
Vlaar (1998) tin hnh chn mu 25 danh mc u t khc nhau cha tri phiu chnh
ph H Lan k hn 12 nm v 8 nm tin hnh o lng vi 3 m hnh VAR khc
nhau (bnh qun qu kh, Monte Carlo v phng sai hip phng sai). ng thi, da
trn tin cy l 99% v thi gian d liu l 10 ngy. Kt qu cho thy : mt l, phng
php bnh qun qu kh ch cho kt qu tt khi v ch khi thu thp c mu d liu
ln. Hai l, Monte Carlo i hi cn thc hin php lp nhiu c th xc nh VaR
chnh xc. Ba l, da vo gi nh phn phi chun v m hnh phng sai thay i theo
thi gian, khi kt hp Monte Carlo v phng php phng sai hip phng sai cho
kt qu tt hn so vi cc trng hp cn li .
Nghin cu ca Duffie and Pan (1997) a ra ci nhn tng quan c s l thuyt ca cc
m hnh VaR c s dng trong lng ha ri ro th trng, kha cnh kinh t lng
cng nh nhng ng dng thc t ca n. Jorion (2001) a ra mt nghin cu hon
chnh v chi tit v gi tr ti ri ro, vic p dng n i vi nhng loi ri ro v danh
mc u t khc nhau. Ngoi ra, ng cng ch ra nhng by thng gp i vi cc m
hnh ny. Engel and Gizycki (1999) pht trin nhng nghin cu ca Hendricks v
xut nhng kim nh mi v chnh xc v tnh hiu qu ca m hnh VaR thit lp.
Trong mt nghin cu khc, Rockafellar and Uryasev (2002) tip cn theo hng gi
tr ti ri ro c iu kin nh l mt phng php o lng v gii quyt nhng thiu st
trong cch tnh VAR truyn thng, ch yu l vn thiu tnh cht ch v gii hn
thng tin cung cp bi VAR (VAR khng th cho bit nhng khon l qu mc vt
ngng gii hn nht nh). ng thi, h cng ra c phng php ti u ha cch
o lng VaR c iu kin CVaR. Kt qu t Cng trnh ca Alexander (2001) cung
cp mt ci nhn ton din v cc m hnh lng ha ri ro th trng, ng thi ng
cng a ra nhng v d in hnh v cch p dng chng trong thc t bng cc phn
mm khc nhau. Cch tip cn VaR ca Kaplanski and Levy (2009) li ch yu tp
trung vo vic nhng qui nh hin thi cho php s dng cc m hnh qun l ri ro
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ni b. iu ny dn n cc ngn hng thng mi hot ng vi mt mc ri ro vt
ngng v bp mo cu trc phn b vn ca mnh.
Phng php o lng VAR chun thng c tin hnh da trn cc gi nh v s
phn b xc sut. Mt trong nhng gi nh ph bin nht l gi nh rng chui d liu
chy VAR c phn phi chun. Gi nh phn phi chun p t mt vi gii hn ln
cc hm phn phi li nhun nh v tnh cn xng v quan trng hn l khng tnh n
cc nhn qu mc trong th phn phi. Tuy nhin, nhiu cng trnh nghin cu
nh Mandelbrot (1963), Fama (1963), Mussa (1979), Andersen et al. (1999) and
Manganelli and Engle (2001) ch ra rng nhng gi thit ny l gn nh phi thc t.
Theo nh kt qu nghin cu ca Hols and De Vries (1991), Huisman et al. (1997),
Huisman et al. (1998), Wagner and Marsh (2003) th nhng chui d liu ti chnh
thng c hin tng ui dy (fat tail). Hn th na chng cn chu nhng s bin
ng theo nhm (volatility clustering). iu ny hm rng mc d cc d liu th v
li nhun c th khng tng quan nhng li nhun bnh phng hoc li nhun tuyt
i s c hin tng t tng quan dng. gii quyt nhng kha cnh ny, mt vi
cch tip cn VAR thay th c s dng, nh l phn phi Student-t, m hnh
ARCH/GARCH c xut bi Engle (1982) and Bollerslev (1986), hoc chun hn
hp cng l mt phng php c thc hin trong nghin cu ca Duffie and Pan
(1997).
Nghin cu ca Simons (1996) nh ngha ri ro tng ng vi cc ti sn ti
chnh v ch ra 2 gii hn lin quan n VaR : th nht, VaR ch quan tm n 1
im trong th phn phi li nhun v thua l. Tuy nhin, iu cn thit l phi c
mt i din cho tt c cc phn phi trong hm. Th hai, VaR t ra kh yu khi o
lng chnh xc ri ro trong nhng iu kin th trng vt mc.
gii quyt vn ny, nhiu tc gi nh hng cc nghin cu ca h theo cch
tip cn l thuyt gi tr vt mc Extreme Value Theory (EVT). Vic o lng bng
EVT cho kt qu mnh khi p dng i vi cc lnh vc nh bo him v qun tr ri ro
ti chnh. Nghin cu ca Embrechts, Kluppelberg and Mikosch (1997) cng s dng
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cng c EVT nh gi hin tng fat tail vi cc chui d liu thi gian khc nhau.
Tng t , cc nghin cu ca Resnick (2007). McNeil (1997a, 1997b, 1998, 1999),
tp trung vo phng php POT bng cch s dng phn b Pareto tng qut o
lng nhng ngng bin ng vt mc. POT cng l phng php c s dng
trong cc nghin cu ca Matthys and Beirlant (2000), Blum and Dacorogna (2002),
Wagner and Marsh (2003).Trong , h so snh vic s dng phn phi t- student vi
cc m hnh o lng s bin ng GARCH-t. Nghin cu ca Brooks et al. (2003)
s dng phn b Pareto tng qut cho cc hp ng tng lai, Gonzalo and Olmo (2004)
s dng phng php m phng qu kh xc nh ngng ti u. Block Maxima l
phng php c s dng trong cc nghin cu Caserta and De Vries (2003). H tin
hnh phn ha cc phn tch ca mnh cho trng hp ti a v ti thiu ca ch s
AEX. Cng trnh ca Cotter and Dowd (2007) th s dng phng php ny ro snh
cc ri ro v pha ui i vi cc lnh gii hn v lnh th trng trong hm phn phi
li nhun kinh doanh ngoi hi. Robert, Segers and Ferro (2008) phn tch hin tng
fat tail cho d liu li nhun t ch s FTSE 100. Rt nhiu trong s cc nghin cu
ny v c nhng nghin cu khc s dng vic xc nh gi tr ti ri ro thit lp
khung EVT. Mt kt lun chung c rt ra t cc nghin cu l EVT l mt phng
php t ra kh hiu v c pht huy tnh ti u khi tin hnh o lng cc hng bin
ng vt mc trong chui d liu.
Bng 2.1 Tng hp cc m hnh VaR
Ngun :Extrem risk management, Christina Ray, The McGraw-Hill Companies, Inc
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Mc d VaR c cho l mt cng c hu ch nhm o lng ri ro th trng ca cc
danh mc u t, cc gii hn v thiu st t m hnh vn ang l vn gy nhiu
tranh ci . Nghin cu ca Dowd (1998) ch ra 3 gii hn chnh ca phng php tnh
VaR:
- Th nht, m hnh ny s dng d liu qu kh d bo cc hnh vi trong tng
lai
- Th hai, m hnh c xy dng da trn cc gi nh khng phi lun thch hp
trong tt c cc iu kin. V vy, ngi dng cn ht sc cn trng i vi nhng
gii hn ca m hnh v xc nh hm cho cc tnh ton ca mnh.
- Th ba, gi tr VaR d bo ch c th c s dng ra quyt nh ng khi
ngi dng c kin thc v khi nim gi tr ti ri ro cng nh qu trnh xy dng
m hnh
C v nh VaR l mt phng php c th c dng cho nhiu mc ch khc nhau :
nh gi ri ro, gii hn ri ro, thit lp cc ngng an ton vn, phn b vn ni b.
Tuy nhin, VaR vn cha phi l cu tr li hon ho cho cc thch thc t ra trong
qu trnh qun tr ri ro. Khng c mt l thuyt no tn ti chng mnh rng VaR l
cch o lng xp x m da vo n ta c th thit lp nhng quy tc ra quyt nh ti
u. VaR khng gip ta o lng c nhng s kin ri ro (nht l khi c khng hong
ti chnh hoc mt s v th trng) v vy cn c nhng kim nh stress tests b
tr thm, song song vi vic xc nh VaR. Th nht, v VaR khng th tnh n mc
thanh khon khc nhau gia cc cng c ti chnh nn cc gii hn v k hn v quyn
chn vn rt cn thit. Th hai, v VaR khng o lng ht cc thng tin th trng c
lin quan nn n ch c th l cng c tt khi c s dng bi cc nh qun tr ri ro c
kinh nghim. Tuy vy, VaR l mt cng c o lng ri ro mang nhiu ha hn, nht l
khi n l tm im m ra thi k nghin cu v pht trin mi trong lnh vc lng ha
v qun tr ri ro
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12
3. KHUNG L THUYT C S V M HNH VALUE AT RISK
3.1 Khi nim gi tr ti ri ro
VaR thng c nh ngha l khon l tim nng ti a ca mt danh mc hoc mt
ti sn qua mt khon thi gian v mt xc sut nh trc khi xy ra cc chuyn hng
ngoi mong i ln tng i ca cc bin th trng nh (gi c, li sut, t gi).
Var thng c xc nh theo n v Dollar $VaR. Trong :
Pr ($ thua l > $ Var) = p
S c (1-p) *100% ln khon l s nh hn gi tr VAR
xy dng m hnh cho log thu nhp, vic xc nh Var s da vo hm sau:
Pr (-RPF > VAR) = p
Pr ( RPF < - VAR ) = p
V vy VAR c nh ngha l con s m ta s nhn c khon log thu nhp t nht
vi xc sut p. iu ny hm rng chng ta c (1-p)*100% tin cy rng mc thu
nhp thu c s ln hn VAR.
$VaR = VPF (1- exp (-VaR))
Gi
l p.100% VaR cho thu nhp 1 ngy k tip v gi nh rng thu nhp c
phn phi chun vi trung bnh = 0 v lch chun l PF,t+1. Ta c :
Pr (RPF, t+1 < - VaRp
t+1) = p
Pr (RPF, t+1/ PF,t+1 < - VaRp
t+1/ PF,t+1) = p
Pr (zt+1 < - VaRp
t+1/ PF,t+1) = p
(- VaRpt+1/ PF,t+1) = p
Vi (*) l hm mt tch ly ca phn phi chun
- VaRp
t+1/ PF,t+1 = -1
(p)
VaRp
t+1 = -PF,t+1 -1
p
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13
Nu chn p = 0.01 ta c -1p = -1
0.01 = -2.33 v gi s lch chun d bo cho thu
nhp vo ngy mai l 2.5% ta c :
VaRp
t+1 = -PF,t+1 -1
p = -0.025(-2.33) = 0.05825
Kt qu ny c ngha l c 1% xc sut cho vic khon l ngy mai s vt mc 5.825%
gi tr danh mc ngy hm nay. Nu gi tr danh mc ngy hm nay l 2 triu dollar th
$ Var s l :
$VaR = VPF (1- exp (-VaR)) = 2000000 (1- exp (-0.05825)) = $ 113172
Hnh 3.1: Xc nh gi tr VaR t th phn phi xc sut ca chui thu nhp
Ngun : Elements of nancial risk management / Peter Christoffersen.2nd Edition
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14
3.2 Cc m hnh tnh VaR
tnh gi tr VaR, hin ti c kh nhiu m hnh khc nhau c s dng, trong
ph bin nht l 3 m hnh sau:
Mt l, m hnh m phng qu kh (Historical Simulation), trong gi nh rng thu
nhp kinh doanh ngoi hi trn v th ngoi hi s lp li cch thc phn phi ca n
trong qu kh
Hai l, m hnh phng sai- hip phng sai, trong gi nh thu nhp kinh doanh
ngoi hi trn tng v th ngoi hi lun c phn phi chun v nhng thay i trong gi
tr ca v th ngoi hi ph thuc tuyn tnh vo thu nhp ca tt c cc cp tin t ring
l.
Ba l, Monte Carlo vi gi thit thu nhp trong tng lai s c phn phi ngu nhin.
Bng 3.1 : Tng hp cc phng php tnh VaR ph bin
Phng
php Cch thc hin u im Khuyt im
Historical
Simulation
1.Tnh gi tr hin ti ca danh
mc u t
2. Tng hp tt c cc t sut sinh
li qu kh ca danh mc u t
ny theo tng h s ri ro
3. Xp cc t sut sinh li theo th
t t thp nht n cao nht
4. Tnh VaR theo tin cy v s
liu t sut sinh li qu kh.
- Thit k v p
dng d dng
- Khng cn gi
thuyt v quy lut
phn b
- i hi mt s
liu cc ln
- Tng lai c th
khng ging qu
kh
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15
Phng sai
Hip
phng sai
1.Tnh gi tr hin ti V0 ca danh
mc u t
2.T nhng d liu qu kh, tnh
t sut sinh li k vng m v
lch chun sut sinh li ca danh
mc u t
3.VaR c xc nh theo biu
thc sau y :
VaR = V0(m + zq)
- Thit k v p
dng d dng
- p dng cho
danh mc u t
bao gm chng
khon tuyn tnh
(nh c phiu)
- Tnh VaR khng
tt
cho nhng chng
khon phi tuyn
(quyn chn)
- t quan tm n
trng hp xu
nht; khng chng
minh c thuyt
v phn b chun
ca cc d liu
Monte
Carlo
1. M phng mt s lng rt ln
N bc lp
2. Cho mi bc lp i, i
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16
th t gi tr t thp nht n cao
nht.
4. Tnh VaR theo tin cy v t
l phn trm s liu ri..
5. ng thi tnh sai s tng ng
cho mi VaR, nu s lng N cng
cao th sai s cng nh.
Ngun : Tng hp t tc gi
3.3 D bo phng sai :
3.3.1 M hnh tham s :
Nhng m hnh nh RiskMetrics EWMA c pht hnh nm 1996 bi hng J.P.
Morgan hay ARCH-GARCH model xut trong nghin cu ca Engle (1982) and
Bollerslev (1986) i hi cn phi xc nh c cc tham s m t hnh vi bin ng
ca t gi . V vy chng c xp vo loi m hnh tham s
Vi cch tip cn RiskMetrics, bin ng pht sinh t m hnh m hnh trung bnh trt
c trng s ly tha, gip ta tnh n nhng nh hng ca thng tin trong qu kh n
thu nhp v phng sai.
2t+1 = 2
t + (1- ) R2
t
Trong t2 l phng sai ti thi im t, rt : thu nhp ti thi im t, : nhn t phn
r, thng c mc nh l 0.94 hay 0.97. Cch tip cn ny s dng gi nh phn d
c phn phi chun
M hnh RiskMetrics c mt s u im ni bt. u tin, n cho php tnh n s thay
i ca phng sai theo cch ph hp vi bin thu nhp quan st c. Nhng mc thu
nhp cng gn th cng nh hng nhiu n phng sai ang xem xt v < 1 v v th
tc ng ca cc tr ca bnh phng thu nhp s nh dn khi tr tng dn. Th hai,
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17
m hnh ny ch cha 1 bin tham s cn xc nh l . Khi c lng cho mt s
lng ln cc ti sn ti chnh RiskMetrics tm thy rng php c lng ny kh ging
nhng ti sn d liu cho. Do , n gin ha h mc nh h s = 0.94 cho mi
ti sn khi c lng phng sai hng ngy. Trong trng hp ny,khng nht thit
phi tin hnh php c lng . y l li th cho nhng danh mc u t qui m ln.
Th ba, vi nhng mu d liu t tng i cn thu thp tnh ton phng sai ngy k
tip. Trng s ca bnh phng thu nhp ngy hm nay l 1- = 0.06 v trng s l
phn r ly tha n (1- ) 99 = 0.000131 trn 100 tr ca bnh phng thu nhp. Sau
khi tnh n 100 tr ca bnh phng thu nhp, trng s tch ly l (1-) i-1
=
0.998. V vy 99,8 % ca trng s c tnh n. V vy, lng d liu cn thu thp
ch l 100 tr ca thu nhp tnh phng sai ca ngy tip theo 2t+1
M hnh GARCH
S dng m hnh t hi qui phng sai thay i c iu kin tng qut (GARCH),
phng sai d bo c th c din t nh sau :
2t+1 = + R2
t + 2
t vi +
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18
thc t l phng sai trung bnh di hn c khuynh hng n nh tng i qua thi
gian. Trong khi m hnh GARCH, ngc li li c th xc nh da hon ton vo 2
2t+1 = (1- ) 2 + R2t +
2t =
2 + (R2t -
2) + (2t - 2)
T y, phng sai d bo ca ngy k tip l trung bnh c trng s ca phng sai di
hn, bnh phng thu nhp ca ngy hm nay v phng sai hm nay. Ngha l phng
sai ca ngy k tip l phng sai trung bnh di hn cng (hoc tr) nhn t hiu chnh
khi bnh phng thu nhp hm nay ln (hoc nh) hn trung bnh di hn ca n v
cng (tr) nhn t hiu chnh khi phng sai ca ngy hm nay ln (hoc nh) hn
trung bnh di hn ca n.
3.3.2 M hnh phi tham s
Nhng m hnh ny khng i hi ta phi c lng cc tham s trong phng trnh m
t hnh vi bin ng ca t gi. Cch tip cn phi tham s ph bin nht l m hnh m
phng qu kh Historical Simulation (HS). M hnh ny khng p t bt c gi nh
no cho hm phn phi thu nhp, v y l mt trong nhng u im ln nht ca n
ngoi vic n l phng php tnh ton n gin nht. V c bn, trong m hnh ny cc
mc thu nhp s c sp xp theo th t tng dn v VaR s c xc nh nh sau:
Vi danh mc gm N cp tin t. Gi tr ton danh mc ti thi im t
Thu nhp di dng log ca danh mc ti thi im t :
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19
Gi chui d liu qu kh {RPF,t+1-t}m
t=1 l chui thu nhp dng log ca danh mc m
ngy trc th phn phi ca RPF,t+1 s c xc nh da vo biu tn s ca
chui {RPF,t+1-t}m
t=1
Gi tr VaR vi xc sut p s c xc nh t chui d liu qu kh nh sau:
Xc nh VaR theo phng php m phng qu kh gip ta khng phi quan tm n
cc gi nh phn phi cng nh khng phi thc hin cc php c lng. Do , loi
b tnh thiu chnh xc trong tnh ton. Mc d phng php ny c tnh n hin tng
fat tail tuy nhin n li ph thuc ch yu vo d liu qu kh v b qua cc s kin
ngoi mu, tc l n cho rng tng lai s li chnh xc nhng g qu kh din ra.
y cng l mt trong nhng yu im ln nht ca m hnh ny
3.4 Backtesting VaRs
Backtesting l mt php c lng da vo d liu thu nhp thc t nh gi mc
ph hp ca mt m hnh VaR. C th l, vi php th ny chng ta s tin hnh o
lng mc phn trm tht bi trong c lng VaR thng qua hm tn tht :
1, nu RPF,t+1 > -VaRp
t+1
0, nu RPF,t+1 < -VaRp
t+1
Lt+1 s bng 1 nu nh mc thua l thc t ngy ny ln hn mc thua l c lng
c t m hnh VaR. Trong trng hp cn li Lt+1 s bng 0.
Nhng trng hp trong mc thua l vt qu gi tr d bo l hon ton khng th
lng trc c v vy chng s c phn phi c lp trong chui thi gian nh mt
bin Bernoulli, nhn gi tr 1 vi xc sut p v gi tr 0 vi xc sut 1-p. Ta c :
H0: Lt+1 ~ i.i.d. Bernoulli (p)
Lt+1 =
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20
Hm phn phi Bernoulli:
f (Lt+1,p) = (1-p)1-I,t+1
pI,t+1
p c th nhn gi tr l 1% hoc 5% ty vo mc ngha la chn trong m hnh VaR
3.4.1 Kim nh Unconditional Coverage
kim tra s cn i gia tn s thc t ca nhng dao ng bt thng vi tn s
c d bo bi cc m hnh VaR. Bi nghin cu s dng kim nh Unconditional
Coverage test.
Gi l xc sut vt ngng thc t, ta c hm hp l ca chui bin Lt+1 ~ i.i.d.
Bernoulli ()
Trong T0 v T1 l s ln Lt+1 nhn gi tr 0 v 1 trong mu quan st, vi
l gi tr c lng ca
S dng c lng hp l ti a maximum likelihood (ML) cho hm hp l ny ta c
mc ti u:
Vi gi thit H0 : = p vi p l mc ngha c la chn trong m hnh VaR. Ta c :
kim nh gi thit ny bng cch kim nh t l hp l :
-
21
Mt cch tim cn, khi tng s quan st, T tin ti v cc LRuc s c phn phi 2
vi
bc t do bng 1
Gi tr LRuc cng ln th xc sut gi thit H0 b bc b cng cao. V d nh vi mc
ngha l 10%, gi tr ti hn t phn phi 21 l 2.7055. Nu gi tr kim nh LRuc ln
hn 2.7055 th ta bc b m hnh VaR ny ti mc ngha 10%
3.4.2 Kim nh tnh c lp
Vn v tnh c lp xy ra khi cc s ph v m hnh VaR trong mu din ra trong
cng mt khong thi gian. iu ny c ngha l v bn cht cc nh qun tr ri ro c
th d bo c rng nu hm nay c mt s ph v th xc sut xy ra s ph v vo
ngy mai s ln hn p.100%. Trong nhng tnh hung ny h nn gia tng gi tr VaR
h thp xc sut c iu kin ca s v xung gi tr p. Mc tiu ca kim nh
ny l nhm hnh thnh mt php th gip loi b cc m hnh VaR c hin tng ph
v theo nhm
Gi nh rng cc chui dao ng bt thng l ph thuc nhau theo thi gian v c
m t bng ma trn xc sut sau :
Ma trn ny c ngha l vi iu kin Lt =0, xc sut sau Lt+1 = 1 l 01
Xc sut xy ra dao ng bt thng ngy hm sau di iu kin ngy hm nay
c mt dao ng bt thng l
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22
Tng t, xc sut xy ra mt dao ng bt thng ngy hm sau di iu kin
hm nay khng xy ra dao ng bt thng
Vi T quan st , hm hp l s c xy dng nh sau :
Vi cc c lng:
T :
Ma trn s c vit li l ;
Vi vic gi nh cc chui ph v ny l ph thuc ta c 01 s khc vi 11
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23
Chng ta c bit ch ti trng hp ph thuc dng. Ngha l xc sut
mt s ph v ko theo mt s ph v (11) s ln hn xc sut s khng ph v
ko theo s ph v 01
Nu, xt trn kha cnh khc, cc chui ph v ny l c lp theo thi gian, ngha l
xc sut xy ra s ph v ca ngy mai khng ph thuc vo vic ngy hm nay c xy
ra ph v hay khng th ta c 01 = 11 =
Ta c th kim nh tnh c lp vi gi thit H0 : 01 = 11 v thit lp gi tr kim nh :
Trong mt mu quan st ln th LRind cng s c phn phi 2 vi bc t do l 1. Cc
bc kim nh tng t vi kim nh mc ngha
3.4.3 Kim nh Conditional Coverage
V c bn, vn cn quan tm trong nh gi mc ph hp ca m hnh VaR l
tnh c lp ca cc ln ph v v chnh xc ca s ln ph v trung bnh
kim nh ng thi 2 tnh cht ny ta s dng php kim nh mc ngha c iu
kin, vi gi tr kim nh c thit lp nh sau :
Vi gi thit H0 : 01 = 11 = p. ta c :
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24
V bn cht kim nh Kim nh Conditional Coverage l s tng hp ca 2 kim nh
Unconditional Coverage test v kim nh tnh c lp
4. P DNG M HNH VALUE AT RISK LNG HA RI RO T GI
TRONG KINH DOANH NGOI HI
4.1 Khung l thuyt c s v vn ri ro trong kinh doanh ngoi hi
4.1.1 c im ca kinh doanh ngoi hi trn th trng forex:
Th nht l ph giao dch thp v khng phi qua trung gian t lnh : nh u t giao
dch trc tip vi th trng trn cc phn mm giao dch vi sn v c cp nht
thng tin trc tip v gi v t gi cc cp tin t. iu ny lm gim chi ph giao dch,
thc y tin giao dch din ra nhanh chng v hn ch kh nng xy ra nhng hiu
lm trong qu trnh thc hin cc lnh giao dch.
Th hai l th trng giao dch 24h : nh vy m nh u t khng phi ch i th
trng ng v m ca, c th linh hot trong vic chn thi gian giao dch. ng thi,
c im ny cng cho php nhng ch th tham gia th trng vo v thot ra bt c
lc no.
Th ba l th trng c t sut n by (leverage trading) hp dn : thng mc cao
1:100 , 1:200 iu ny dn ti gia tng khong sinh li tim nng ca nh u t
Th t l th trng hot ng c lp, khng ai c kh nng nh hng th trng : l
th trng ton cu vi khi lng giap dch khng l cng vi s a dng thnh phn
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25
v ng o lc lng tham gia th trng dn ti khng ai c th iu khin v kim
sot c th trng trong di hn. C th l, s can thip ca ngn hng trung ng ch
c tc dng trong ngn hn v khng hiu qu. Ngn hng, qu u t, chnh ph, nh
u c, v cc nhm giao dch ch l mt thnh phn nh ca th trng ngoi hi.
Nhng phn tch ca cc chuyn gia ch mang tnh cht tham kho ch khng th tc
ng mnh ln th trng ny.
Th nm l th trng hot ng mang tnh xu hng (Trendiness) : trong mt nhng
khong thi gian lch s, tin t khng nh c tnh xu hng quan trng ca n.
Mi ng tin mang mt tnh cch ring v a ra ch mt xu hng, bt k nhng
nh hng v nhng c hi giao dch a dng trn th trng.
4.1.2 Cc loi ri ro nguyn nhn pht sinh ri ro trong giao dch kinh
doanh ngoi hi:
Phn loi theo hng tng qut
C 2 dng ri ro cn bn:
Ri ro h thng (systematic risks) : l loi ri ro c th nh hng n s bin ng ca
nhiu cp tin t. V d nh : nhng s kin chnh tr mang tnh ton cu, thm ha thin
nhin hay vn chin tranh
Ri ro khng h thng (specific risks): ri ro mang tnh c th ring bit, ch nh hng
n vi loi tin, vi cp tin. V d nh cc tin tc kinh t c nh hng n 1 nc
hoc 1 vng no nh mt cuc nh cng hoc 1 s iu chnh trong li sut ca
ng CAD
hn ch ri ro khng h thng nh u t c th la chn phng thc a dng ha
u t trong danh mc u t bao gm nhiu cp tin khc nhau
-
26
Phn loi chi tit
Ri ro t gi (exchange rate risks): l ri ro thng trc, gn lin v tr thnh ri ro c
trng ca hot ng kinh doanh ngoi hi
Nguyn nhn pht sinh :
Th nht l do v th ngoi hi khng tng xng: nh kinh doanh ngoi hi ch
chu ri ro t gi khi duy tr mt trng thi ngoi hi m. V vy vn t ra trong
qun tr ri ro ngoi hi l lm th no qun l tt trng thi mua bn ngoi t ngn
nga ri ro t gi pht sinh
Th hai l do nh hng bi cc nhn t khc nh cung cu ngoi t trn th trng,
cn cn thanh ton quc t, chnh sch thu quan, nng sut lao ng, tnh hnh chnh tr
ca mi nc, li sut ng ngoi t v ni t.
Ri ro li sut (interest rate risks) : s tng gim li sut ng tin trong cp tin vo
thi gian giao dch s nh hng n lng tin li/ph c th phi tr cho nh mi gii
hng ngy duy tr lnh giao dch
Ri ro thanh khon (liquidity risks): ri ro ny pht sinh khi cng ty mi gi ti khon
giao dch khng cn kh nng thanh ton khi ch ti khon yu cu rt tin. V vy,
nh u t cn cn trng trong la chn cng ty mua gii khi tham gia giao dch kinh
doanh ngoi hi
Ri ro k thut (Technology risks): s gin on, hng hc ca cc thit b giao dch, hay
li ng truyn mng . Do tnh cht ton cu ha a phn giao dch ngoi hi u ph
thuc vo cng ngh, song y l dng ri ro m nhiu nh u t t quan tm n. V
vy hn ch nh hng xu t ri ro ny, cn phi c nhng d phng v ng
mng thay th khi cn thit, ng thi d phng my khi my tnh chnh b hng hc.
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27
4.1.3 Vn trng thi ngoi hi (exchange position)
Trng thi ca mt ngoi t l s chnh lch gia tng s mua vo v bn ra ca ngoi t
ti mt thi im nht nh
Trng thi ng (close position) : - = 0
Trng thi m (open position): - 0
Trong :
Trng thi trng (long position) - 0
Trng thi on (short position) - 0
Bng 4.1: Tng hp cc giao dch lm pht sinh trng thi ngoi hi
Trng thi trng (long position) Trng thi on (short position)
Mua ngoi t (spot, forward) Bn ngoi t (spot, forward)
Thu li cho vay bng ngoi t Tr li vay bng ngoi t
Thu ph dch v bng ngoi t Chi tr ph dch v bng ngoi t
Nhn chuyn tin ngoi t Chuyn ngoi t i.
Ngun : Tng hp t tc gi
Xc nh trng thi ngoi t
EPX,t : trng thi ngoi t X ti thi im t
LPx, t0 t : doanh s pht sinh trng thi trng ca ngoi t X trong thi k t0 t
SPX, t0 t : doanh s pht sinh trng thi on ca ngoi t X trong thi k t0 t
Trng thi ngoi t s c xc nh da vo cng thc sau:
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28
Cch 1 : EPX(t) = LPX (t0 t) SPX (t0 t)
Cch 2 : EPX(t) = EPX(t-1) +LPX (t) SPX (t)
Ngoi ra i vi mi thi k cng s c nhng qui nh v tng trng thi ngoi t ca
tt c ngoi t c qui i theo ng ni t
4.1.4 Vn qun tr ri ro trong kinh doanh ngoi hi
ngn nga v ch ng i ph vi nhng ri ro pht sinh trong kinh doanh ngoi
hi. Mt s vn chnh sau y cn c c bit ch :
Th nht l cn c s duy tr tnh cn xng v trng thi ngoi hi: qun l bng cng c
hn mc (position limit). Trong :
Nguyn tc phn b hn mc: thng da vo kinh nghim thm nin v kh
nng kinh doanh trn th trng forex ca nh u t
Hn mc theo cc ng tin kinh doanh: c ngha l i vi nhng ng tin
bin ng thp th hn mc phn b cao hn v ngc li nhng ng tin bin
ng cao s c mc hn mc thp hn
Ngoi ra cn c th thc hin thit lp hn mc cho tng loi nghip v c th.
ng thi kt hp vi vic s dng linh hot cc cng c lnh giao dch
Th hai, cn c mt s a dng ha danh mc u t hp l : trong thc hin giao
dch vi nhiu loi ngoi t khc nhau v s dng kt hp nhiu loi nghip v kinh
doanh trn th trng ngoi hi
Th ba l cn chn mc n by thch hp v mc margin requirement hp l
Th t l vic t chc hot ng kinh doanh cn c nh hng, k hoch. Trong , k
hoch cn phi m bo nhng tiu chun nht nh: (1) loi c cu thi gian s dng
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29
giao dch, (2) tm kim nhng tn hiu ch dn nhn bit xu hng, (3) tm kim tn
hiu ch dn gip xc nhn xu hng chung, (4) xc nh mc chp nhn ri ro, (5)
xc nh thi gian nhp cuc v thot khi phin giao dch, (6) t nhng qui nh cho
h thng giao dch v kim tra h thng giao dch
V cui cng cn lu rng khng c mt loi ri ro no l thch hp vi tt c cc nh
u t, mi nh u t s c kh nng sn sng chp nhn mc ri ro khc nhau. S
chp nhn ri ro ny khng phi l mt mc c nh m thay i ty thuc vo k nng
v s hiu bit ca nh u t khi tham gia th trng. Vn l cn c lng c
mc t l gia ri ro sn sng chu ng v mc ri ro c th chp nhn c nu xy ra
trong thc t . T thit lp c mt k hoch kinh doanh hp l nhm t c s
cn bng gia ri ro v li nhun tim nng.
4.2 D liu v xy dng m hnh thc nghim
Bi nghin cu s dng d liu thu nhp kinh doanh ngoi hi theo tn s hng ngy
ca 7 cp t gi c doanh s giao dch ln trn th trng forex GBP/USD, EUR/USD,
AUD/USD, CHF/ USD, NZD/USD, JPY/USD cho mu thi gian 6 nm 1/1/2006-
1/11/2012 (bao gm 2192 quan st). Thu nhp c tnh trn c s phng php logarit
Rt = ln(St/St-1) trong St v St-1 ln lt l t gi ngy th t v t-1.
Bng 4.2 : Thng k m t thu nhp ca cc cp tin t trong giai on 1/11/2006-
1/11/2012
GBP EUR CAD AUD CHF NZD JPY
Mean -7.65E-05 8.85E-06 5.43E-05 0.000135 0.000134 9.51E-05 0.000176
Median 0.000000 0.000000 0.000000 0.000100 0.000000 0.000100 0.000000
Maximum 0.031400 0.034600 0.041700 0.052900 0.038300 0.047300 0.029000
Minimum -0.039900 -0.025200 -0.038100 -0.061400 -0.045300 -0.047900 -0.032000
Std. Dev. 0.004619 0.004746 0.004945 0.007060 0.005069 0.007031 0.006005
Skewness -0.748269 0.034628 -0.222315 -0.477176 -0.220738 -0.467170 -0.147762
Kurtosis 12.36901 7.371491 9.817916 13.20338 13.67035 8.635094 6.116667
Jarque-Bera 8221.635 1745.812 4263.593 9591.800 10416.69 2979.958 895.1533
Probability 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
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30
Ngun : Theo tnh ton t tc gi
Kim nh tnh dng
Bi nghin cu s tin hnh kim nh tnh dng ca cc bin qua kim nh nghim
n v theo phng php Augmented Dickey-Fuller (ADF) test.
Bng 3.2 (xem phn Ph lc) trnh by kt qu kim nh nghim n v Augmented
Dickey-Fuller (ADF) test v tnh dng ca chui cc bin. Kt qu cho thy, v c bn
cc chui d liu ang xem xt u dng 2 mc ngha 1% v 5% trong trng hp
hi quy c chn, khng xu th v hi quy c chn c xu th.
5. KT QU THC NGHIM :
5.1 Kt qu xc nh VaR cho tng cp tin t ring l:
Bi nghin cu s dng 3 phng php tip cn : M hnh HS, m hnh RiskMetrics cho
d liu hng ngy vi nhn t phn r bng 0.94 v m hnh GARCH (1,1) tnh ton
gi tr VaR vi 2 tin cy l 99% v 95 %. T tin hnh d bo VaR cho ngy tip
theo ca chui (quan st th 2193). Kt qu d bo c trnh by trong bng 5.1 v
bng 5.2 vi cc n v tnh l phn trm v gi tr tuyt i theo n v dollar.
Bng 5.1: Kt qu tnh VaR cho tng cp tin t (n v %)
GBP EUR CAD AUD CHF NZD JPY
VaR
99%
RM Daily 0.55% 0.69% 0.60% 0.70% 0.64% 0.81% 1.11%
10 days 1.75% 2.18% 1.89% 2.20% 2.03% 2.57% 3.52%
GARCH(1,1) Daily 0.61% 0.79% 0.68% 0.84% 0.72% 1.00% 1.21%
10 days 1.91% 2.49% 2.16% 2.66% 2.28% 3.15% 3.81%
HS Daily 0.68% 0.89% 0.63% 0.93% 0.93% 1.11% 0.82%
10 days 2.15% 2.82% 1.98% 2.94% 2.93% 3.51% 2.60%
VaR
95%
RM Daily 0.39% 0.49% 0.42% 0.49% 0.45% 0.57% 0.79%
10 days 1.24% 1.54% 1.34% 1.56% 1.44% 1.81% 2.49%
GARCH(1,1) Daily 0.43% 0.56% 0.48% 0.59% 0.51% 0.71% 0.85%
Sum -0.167600 0.019400 0.119100 0.295300 0.293000 0.208400 0.386100
SumSq. Dev. 0.046742 0.049350 0.053576 0.109212 0.056291 0.108326 0.078995
Observations 2192 2192 2192 2192 2192 2192 2192
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31
10 days 1.35% 1.76% 1.53% 1.88% 1.61% 2.23% 2.69%
HS Daily 0.46% 0.56% 0.46% 0.71% 0.57% 0.71% 0.81%
10 days 1.47% 1.77% 1.44% 2.25% 1.80% 2.23% 2.55%
Ngun: Theo tnh ton t tc gi
Bng 5.2 : Kt qu tnh VaR cho tng cp tin t ring l (n v USD)
GBP EUR CAD AUD CHF NZD JPY
VaR
99%
RM
Daily $11,053 $13,727 $11,938 $13,886 $12,801 $16,158 $22,150
10
days $34,745 $43,089 $37,510 $43,580 $40,200 $50,650 $69,208
GARCH(1,1)
Daily $12,073 $15,670 $13,641 $16,742 $14,340 $19,853 $23,955
10
days $37,934 $49,134 $42,821 $52,462 $44,996 $62,107 $74,774
HS
Daily $13,576 $17,755 $12,485 $18,498 $18,425 $22,057 $16,392
10
days $42,617 $55,610 $39,216 $57,913 $57,686 $68,903 $51,382
VaR
95%
RM
Daily $7,823 $9,716 $8,448 $9,828 $9,059 $11,437 $15,686
10
days $24,629 $30,562 $26,596 $30,913 $28,509 $35,947 $49,185
GARCH(1,1)
Daily $8,546 $11,093 $9,655 $11,851 $10,150 $14,056 $16,968
10
days $26,896 $34,867 $30,373 $37,239 $31,921 $44,116 $53,165
HS Daily $9,259 $11,189 $9,119 $14,209 $11,368 $14,050 $16,075
10
days $29,110 $35,181 $28,674 $44,582 $35,727 $44,079 $50,381
Ngun: Theo tnh ton t tc gi
Hnh 5.1: Kt qu d bo VaR cho tng cp tin t ring l
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32
Ngun : Theo tnh ton t tc gi
5.2 Xc nh hn mc u t, li nhun v thua l tch ly ca danh mc da
vo gi tr VaR
T gi tr VaR, bi nghin cu s tip tc tin hnh xc nh hn mc u t ti a hng
ngy. Gi nh mi ngy nh u t c mc gii hn VaR 99% l $2000,000. m
bo mc an ton, lng u t mi ngy phi tha iu kin
$Positiont+1
V vy mc u t ti a cho mi ngy s l
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33
$Positiont+1
T ta c mc li nhun/thua l (P/L) hng ngy: (P/L)t+1 = $Positiont+1 (St+1/St -1)
Kt qu P/L tch ly hng ngy ca tng cp tin t trong danh mc s c trnh by
trong hnh 5.2
Hnh 5.2: Ktqu P/L tch ly hng ngy ca tng cp tin t
Ngun : Theo tnh ton t tc gi
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34
5.3 Kim tra m hnh Backtesting VaRs
kim tra tnh thch hp ca cc m hnh VaR xy dng, php th Backtesting s
c thc hin da trn 3 kim nh chnh nh trnh by trn l kim nh
Unconditional coverage, kim nh tnh c lp v im nh tng hp Conditional
coverage. Cc kim nh ny thc hin theo phn phi 2 vi mc ngha 10% v bc
t do 1 (cho 2 kim nh u) v 1 (cho kim nh cui cng)
Bng 5.3: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t GBP/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1655 1586 1664 1608 1655 1597
T1 36 105 27 83 36 94
T00 1622 1501 1645 1545 1622 1525
T01 33 85 19 62 33 72
T10 33 85 19 63 33 72
T11 3 20 8 21 3 22
2.13% 6.21% 1.60% 4.91% 2.13% 5.56%
2.22E-76 1.30E-171 7.16E-61 1.59E-144 2.22E-76 2.30E-158
L(p) 5.97E-80 1.15E-172 5.46E-62 1.56E-144 5.97E-80 1.34E-158
1.99% 5.36% 1.14% 3.86% 1.99% 4.51%
8.33% 19.05% 29.63% 25.30% 8.33% 23.40%
L 1.65E-75 7.30E-167 5.81E-53 2.75E-135 1.65E-75 2.11E-150
LRuc 16.443 4.851 5.149 0.030 16.443 1.075
LRind 4.013 21.868 36.423 42.549 4.013 36.669
LRcc 19.224 37.369 47.844 60.796 20.456 37.744
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
LRind Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
LRcc Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Ngun: Theo tnh ton t tc gi
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35
Bng 5.4:Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t EUR/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1656 1578 1657 1590 1657 1588
T1 35 113 34 101 34 103
T00 1624 1489 1632 1518 1627 1507
T01 32 89 25 72 30 81
T10 32 89 25 72 30 81
T11 3 24 9 29 4 22
2.07% 6.68% 2.01% 5.97% 2.01% 6.09%
1.04E-74 6.60E-181 4.98E-73 7.36E-167 4.98E-73 3.03E-169
L(p) 5.91E-78 6.78E-183 5.85E-76 1.50E-167 5.85E-76 4.16E-170
1.93% 5.64% 1.51% 4.53% 1.81% 5.10%
8.57% 21.24% 26.47% 28.71% 11.76% 21.36%
8.84E-74 8.83E-175 1.43E-65 2.39E-154 2.99E-71 7.11E-163
LRuc 14.937 9.157 13.490 3.180 13.490 3.974
LRind 4.287 28.212 34.354 57.615 8.191 29.334
LRcc 19.224 37.369 47.844 60.796 21.681 33.308
Hypothesis Testing (Chi-Square Test)
Significance level =10%
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
LRind Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
LRcc Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Ngun: Theo tnh ton t tc gi
Bng 5.5:Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t CAD/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1667 1584 1674 1612 1669 1595
T1 24 107 17 79 22 96
T00 1644 1492 1660 1553 1648 1512
T01 23 92 14 59 21 83
T10 23 92 14 59 21 83
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36
T11 1 15 3 20 1 13
1.42% 6.33% 1.01% 4.67% 1.30% 5.68%
2.00E-55 5.83E-174 4.94E-42 2.48E-139 1.05E-51 8.14E-161
L(p) 5.30E-56 3.19E-175 4.94E-42 2.04E-139 5.19E-52 3.72E-161
1.38% 5.81% 0.84% 3.66% 1.26% 5.20%
4.17% 14.02% 17.65% 25.32% 4.55% 13.54%
3.09E-55 4.84E-172 2.62E-39 4.85E-130 1.84E-51 6.75E-159
LRuc 2.657 5.809 0.000 0.392 1.414 1.567
LRind 0.873 8.841 12.548 42.788 1.122 8.836
LRcc 3.530 14.650 12.548 43.180 2.536 10.403
Ngun: Theo tnh ton t tc gi
Bng 5.6:Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t AUD/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1655 1585 1671 1605 1660 1593
T1 36 106 20 86 31 98
T00 1620 1495 1655 1540 1629 1508
T01 35 90 16 65 31 85
T10 35 90 16 65 31 85
T11 1 16 4 21 1 13
2.13% 6.27% 1.18% 5.09% 1.83% 5.80%
2.22E-76 8.67E-173 6.66E-48 2.31E-148 6.62E-68 3.01E-163
L(p) 5.97E-80 6.06E-174 5.09E-48 2.28E-148 5.68E-70 1.03E-163
2.11% 5.68% 0.96% 4.05% 1.87% 5.34%
2.78% 15.09% 20.00% 24.42% 3.13% 13.27%
2.30E-76 2.45E-170 2.73E-44 1.18E-139 1.38E-69 1.75E-161
LRuc 16.443 5.320 0.539 0.026 9.516 2.147
LRind 0.068 11.289 16.639 40.109 -7.742 8.118
LRcc 16.511 16.609 17.178 40.135 1.774 10.265
Hypothesis Testing (Chi-Square Test)
Significance level =10%
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
LRind Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
LRcc Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
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37
Ngun: Theo tnh ton t tc gi
Bng 5.7: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t CHF/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1657 1604 1660 1589 1660 1613
T1 34 87 31 102 31 78
T00 1625 1531 1634 1508 1632 1545
T01 32 73 26 81 28 68
T10 32 73 26 81 28 68
T11 2 14 5 21 3 10
2.01% 5.14% 1.83% 6.03% 1.83% 4.61%
4.98E-73 1.24E-149 6.62E-68 4.70E-168 6.62E-68 5.09E-138
L(p) 5.85E-76 1.20E-149 5.68E-70 7.90E-169 5.68E-70 3.87E-138
1.93% 4.55% 1.57% 5.10% 1.69% 4.22%
5.88% 16.09% 16.13% 20.59% 9.68% 12.82%
1.20E-72 2.52E-146 8.24E-65 3.22E-162 1.05E-66 4.15E-136
LRuc 13.490 0.074 9.516 3.567 9.516 0.548
LRind 1.768 15.229 14.252 26.871 5.522 8.802
LRcc 15.258 15.303 23.768 30.438 15.038 9.350
Ngun: Theo tnh ton t tc gi
Hypothesis Testing (Chi-Square Test)
Significance level =10%
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
LRind Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
LRcc Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
LRind Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
LRcc Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
-
38
Bng 5.8:Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t NZD/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1650 1595 1672 1614 1656 1601
T1 41 96 19 77 35 90
T00 1610 1512 1653 1551 1622 1523
T01 40 83 19 63 34 78
T10 40 83 19 63 34 78
T11 1 13 1 14 1 12
2.42% 5.68% 1.12% 4.55% 2.07% 5.32%
1.52E-84 8.14E-161 5.71E-46 1.06E-136 1.04E-74 2.10E-153
L(p) 6.28E-90 3.72E-161 5.04E-46 7.36E-137 5.91E-78 1.75E-153
2.42% 5.20% 1.14% 3.90% 2.05% 4.87%
2.44% 13.54% 5.26% 18.18% 2.86% 13.33%
1.52E-84 6.75E-159 1.33E-47 3.85E-132 1.09E-74 1.81E-151
LRuc 24.793 1.567 0.251 0.731 14.937 0.362
LRind 0.000 8.836 -7.512 21.001 0.098 8.911
LRcc 24.793 10.403 -7.261 21.731 15.035 9.274
Ngun: Theo tnh ton t tc gi
Bng 5.9: Kt qu kim tra Backtesting cho m hnh VaR ca cp tin t JPY/USD
Test Statistics
RiskMetrics Historical Simulation GARCH(1,1)
1% 5% 1% 5% 1% 5%
T0 1665 1565 1676 1661 1672 1605
T1 26 126 15 30 19 86
T00 1640 1453 1661 1633 1654 1528
T01 25 113 15 28 18 77
T10 25 112 15 28 18 77
T11 1 13 1 2 1 9
1.54% 7.45% 0.89% 1.77% 1.12% 5.09%
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
LRind Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
LRcc Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Reject
VaR model
Reject
VaR model
-
39
4.50E-59 1.87E-195 5.42E-38 3.60E-66 5.71E-46 2.31E-148
L(p) 5.40E-60 1.61E-199 4.84E-38 9.29E-77 5.04E-46 2.28E-148
1.50% 7.22% 0.89% 1.69% 1.08% 4.80%
3.85% 10.32% 6.67% 6.67% 5.26% 10.47%
6.26E-59 4.03E-195 1.47E-39 1.26E-65 1.26E-45 1.97E-147
LRuc 4.239 18.711 0.227 48.763 0.251 0.026
LRind 0.662 1.542 -7.217 2.510 1.583 4.285
LRcc 4.901 20.253 -6.991 51.273 1.833 4.311
Ngun: Theo tnh ton t tc gi
T cc kt qu chp nhn hoc bc b m hnh VaR tng hp trn ta c th a ra kt
lun v mc hot ng ca cc m hnh HS, RiskMetrics, GARCH (1,1) ti 2 mc
ngha : mc an ton 1% v mc cnh bo hn 5%. Trn c s la chn c m hnh
VaR thch hp cho vic ra quyt nh u t i vi tng cp tin t nm trong danh
mc.
Phn tip theo ca bi nghin cu s tin hnh xc nh gi tr VaR cho ton b danh
mc. Trong c tnh n t trng ca tng cp tin, tng tc gia cc bin ng v
phn tch cho thy li ch thu c t vic a dng ha u t.
5.4 Xc nh VaR cho c danh mc
i vi danh mc u t bi nghin cu la chn r tin t gm 7 cp tin c doanh s
giao dch ln nht trn th trng ngoi hi. Trong mc ri ro ca danh mc s
c tnh ton da trn ma trn VAR-COVAR
Hypothesis Testing (Chi-Square Test)
Significance level =10%
RiskMetrics Historical Simulation GARCH(1,1)
LRuc Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
LRind Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
Reject VaR
model
LRcc Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Reject
VaR model
Don't Reject
VaR model
Don't Reject
VaR model
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40
Bng 5.10 Ma trn phng sai ca cc bin
Ngun : Theo tnh ton t tc gi
Bng 5.11 Ma trn tng quan gia cc bin
GBP EUR CAD AUD CHF NZD JPY
GBP 1.000000 0.652350 0.543942 0.608540 0.439179 0.598801 -0.086342
EUR 0.652350 1.000000 0.548975 0.636670 0.724104 0.625330 0.082953
CAD 0.543942 0.548975 1.000000 0.725011 0.317643 0.669558 -0.189959
AUD 0.608540 0.636670 0.725011 1.000000 0.364527 0.858912 -0.206986
CHF 0.439179 0.724104 0.317643 0.364527 1.000000 0.382959 0.276215
NZD 0.598801 0.625330 0.669558 0.858912 0.382959 1.000000 -0.165678
JPY -0.086342 0.082953 -0.189959 -0.206986 0.276215 -0.165678 1.000000
Ngun: Theo tnh ton t tc gi
Bng 5.12 trnh by kt qu tnh VaR cho tng cp t gi ring l v cho ton b danh
mc u t. n gin, bi nghin cu gi nh t trng tng ng tin trong danh
mc ln lt l GBP (10%), EUR (15%), CAD (10%), AUD (25%), CHF (20%), NZD
(10%), JPY (10%). (trong thc t, xc nh t trng u t ti u, c th da vo
nguyn tc phn b Pareto). M hnh VaR c xy dng vi d liu t gi hng ngy
v tin cy 99%. o lng hiu ng tc ng qua li gia bin ng cc cp tin,
bi nghin cu s xc nh da trn ma trn phng sai- hip phng sai. Theo kt qu
m hnh cho thy, gi tr VaR o lng c cho ton danh mc khi c tnh n s
tng tc nh hn rt nhiu so vi tng gi tr VaR cho tng cp tin t ring l (0.8%
so vi 3.34%). iu ny cho thy tc ng rt ln ca vic a dng ha danh mc u
t, n gip gim thiu ti a cc ri ro phi h thng khi nh u t s hu mt danh mc
c a dng ha tt. ng thi kt qu trn cho thy : c 1% xc sut cho vic khon
GBP EUR CAD AUD CHF NZD JPY
GBP 2.13E-05 1.43E-05 1.24E-05 1.98E-05 1.03E-05 1.94E-05 -2.39E-06
EUR 1.43E-05 2.25E-05 1.29E-05 2.13E-05 1.74E-05 2.09E-05 2.36E-06
CAD 1.24E-05 1.29E-05 2.44E-05 2.53E-05 7.96E-06 2.33E-05 -5.64E-06
AUD 1.98E-05 2.13E-05 2.53E-05 4.98E-05 1.30E-05 4.26E-05 -8.77E-06
CHF 1.03E-05 1.74E-05 7.96E-06 1.30E-05 2.57E-05 1.36E-05 8.40E-06
NZD 1.94E-05 2.09E-05 2.33E-05 4.26E-05 1.36E-05 4.94E-05 -6.99E-06
JPY -2.39E-06 2.36E-06 -5.64E-06 -8.77E-06 8.40E-06 -6.99E-06 3.60E-05
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41
l ngy mai s vt mc 0.8% gi tr danh mc ngy hm nay. Nu gi tr danh mc
ngy hm nay l 2 triu dollar th $ Var s l :
$VaR = VPF (1- exp (-VaR)) = 2000000 (1- exp (-0.008)) = $ 15936.17
Bng 5.12 Kt qu tnh VaR cho ton danh mc
GBP
Variance 0.000021
Weight 10%
VaR 0.34%
EUR
Variance 0.000023
Weight 15%
VaR 0.43%
CAD
Variance 0.000024
Weight 10%
VaR 0.36%
AUD
Variance 0.000050
Weight 25%
VaR 0.82%
CHF
Variance 0.000026
Weight 20%
VaR 0.53%
NZD
Variance 0.000049
Weight 10%
VaR 0.52%
JPY
Variance 0.000036
Weight 10%
VaR 0.44%
Portfolio
Variance 0.000012
VaR 0.80%
Sum of individual VaRs 3.44%
6. KT LUN
Thng qua vic ng dng m hnh Value at risk trong lng ha ri ro kinh doanh ngoi
hi trn th trng Forex, bi nghin cu a ra c nhng kt qu kho st thc
nghim qui trnh ng dng VaR trong thc tin u t, gii quyt cc vn lng ha
nhng bin ng ca d liu ti chnh (chui t gi) thng qua cc m hnh d bo
phng sai tham s v phi tham s. ng thi, t vic khai thc gi tr VaR, bi nghin
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42
cu cng tin hnh xc nh mt s thng tin chi tit cho vic lp k hoch u t ,
c th l vic xc nh hn mc u t ti a v li nhun/thua l (P/L) tch ly d kin.
Cui cng l, vi nhng yu t hnh thnh m hnh nh : vn phn phi xc sut, la
chn khung thi gian v tin cy, bi nghin cu cng tin hnh thit lp v kim
nh thc t a ra kt lun v tnh thch hp v ti u ca m hnh. Nhn chung c
th thy, vic xc nh mt m hnh ph hp v cho kt qu d bo chnh xc ph thuc
phn ln vo c tnh ca chui d liu, v vy khng c mt m hnh no l chun i
vi nh u t, vic kho st thc t v lin tc c cc php th kim nh l v cng
cn thit a ra nhng iu chnh kp thi.
T nhng kt lun trn a ra mt vi im cn lu trong vic vn dng VaR trong
thc tin:
Th nht, m hnh ny s dng d liu qu kh d bo cc hnh vi trong tng lai.
Tuy nhin, v lch s khng phi lc no cng phn nh c tng lai, nht l i vi
nhng yu t khng chc chn lin quan n hnh vi con ngi. V s liu trong qu
kh kh c th phn nh c nhng s kin kiu nh "black swan" s xy ra trong
tng lai nn trong qu trnh c lng bng d liu qu kh, phi ht sc ch trng
n vic la chn d liu ph hp v nht l khng b st nhng s kin quan trng,
Th hai, m hnh c xy dng da trn cc gi nh khng phi lun thch hp trong
tt c cc iu kin. V vy, ngi dng cn ht sc cn trng i vi nhng gii hn
ca m hnh v xc nh hm cho cc tnh ton ca mnh.
Th ba, gi tr VaR d bo ch c th c s dng ra quyt nh ng khi ngi
dng c kin thc v khi nim gi tr ti ri ro cng nh qu trnh xy dng m hnh.
Cui cng, nh G.Box tng ni: "all models are wrong but some are useful".VaR l
mt phng php c nh gi cao v n p ng c c bn cc nhu cu cn thit
ca mt nh u t nh: nh gi ri ro, gii hn ri ro, thit lp cc ngng an ton
vn, phn b vn ni b. Tuy nhin, VaR vn cha phi l cu tr li hon ho cho cc
thch thc t ra trong qu trnh qun tr ri ro, nht l khi n cn bc l nhng yu
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43
im nht nh. Gii nghin cu cng nh cc nh u t vn cn kh nhiu bn khon
v hiu qu thc s ca m hnh ny. Song, c mt thc t l VaR suy cho cng cng
ch l mt con s, mt cng c khng hm ngha tuyt i. V vy, vn hiu qu s
ph thuc vo vic n nm trong tay mt ngi s dng nh th no? S xut hin
ca VaR l tm im m ra thi k nghin cu v pht trin mi trong lnh vc lng
ha v qun tr ri ro. Do , c th ni y vn l mt cng c o lng ri ro mang
nhiu ha hn trong tng lai.
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a
DANH MC TI LIU THAM KHO
Ti liu ting Anh
1. Alexander, C. (2001), Market Models: A Guide to Financial Data Analysis,
John Wiley & Sons, West Sussex.
2. Barone-Adesi and Giannopoulos (2000), VaR Modelling on Long Run
Horizons, Journal Automation and Remote Control Volume 64 Issue 7, July
2003 ,Pages 1094 - 1100
3. Brooks, C., A. D. Clare, J.W. Dalle Molle, and G. Persand (2003), A
Comparison of Extreme Value Theory Approaches for Determining Value at
Risk, Journal of Empirical Finance, Forthcoming, Cass Business School
Research Paper.
4. Caserta, S. and C. G. de Vries (2003), Extreme Value Theory and Statistics for
Heavy Tail Data, Modern Risk Management A History, Field, P. (ed.), 169-
178, RISK Books, London.
5. Christoffersen, PeterF. Elements of nancial risk management/ Peter
Christoffersen.2nd ISBN 978-0-12-374448-7
6. Cotter, J. and K. Dowd (2007), The tail risks of FX return distributions: a
comparison of the returns associated with limit orders and market orders,
MPRA Papers series at University Library of Munich, Germany.
7. Dacorogna, M. M. and P. Blum (2002), "Extreme Moves in Foreign Exchange
Rates and Risk Limit Setting," EconWPA Risk and Insurance Series, reference
0306004
8. Duffie, D. and J. Pan (1997), "An Overview of Value at Risk", Journal of
Derivatives, 7-49.
9. Embrechts, P., C. Kluppelberg, and T. Mikosch (1997), Modelling Extremal
Events for Insurance and Finance, Springer-Verlag, Berlin.
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b
10. Engel, J. and M. Gizycki (1999), Conservatism, Accuracy and Efficiency:
Comparing Value-at-Risk Models, Working Paper at Reserve Bank of
Australia, Sydney.
11. Engle (1982) AutoRegressive Conditional Heteroskedasticity, Nobel lecture
12. Gonzalo J. and J. Olmo (2004), Which Extreme Values are Really Extreme?,
Journal of Financial Econometrics, 2.3, 349-369.
13. Hendricks, D. (1996), Evaluation of Value-at-Risk Models Using Historical
Data, Economic Policy Review, 2, 39-70
14. Hols, M. A. C. B and C. G. de Vries (1991), The Limiting Distribution of
Extremal Exchange Rate Returns, Journal of Applied Econometrics, 6.3., 287-
302.
15. Huisman, R., K. Koedijk, C. Kool, and F. Palm (2001), Tail Index Estimates
in Small Samples, Journal of Business and Economic Statistics, 19, 208-216.
16. Huisman, R., K. Koedijk, C. Kool, and F. Palm (1998), The Fat-Tailedness of
FX returns, Working Paper at University of Maastricht, Department of
Economics, Center for Economic Studies and Ifo Institute for Economic
Research, Maastricht.
17. Jorion, P. (2001), Value at Risk - The New Benchmark for Managing Financial
Risk, 2nd Edition, McGraw-Hill, New York.
18. Kaplanski, G. and H. Levy (2009), Value-at-Risk Capital Requirement
Regulation, Risk Taking and Asset Allocation: A Mean-Variance Analysis,
Working Paper available at http://ssrn.com/abstract=1081288.
19. Matthys G. and J. Beirlant (2000), Adaptive Threshold Selection in Tail Index
Estimation, in P. Embrechts (ed.), Extremes and Integrated Risk Management,
37-49, RISK Books, London.
20. McNeil, A.J. (1997a), Estimating the Tails of Loss Severity Distributions
Using Extreme Value Theory, ASTIN Bulletin, 27, 117-137.
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c
21. McNeil, A.J. (1997b), The Peaks over Threshold Method for Estimating High
Quantiles of Loss Distributions, ETH preprint (www.math.ethz.ch/~mcneil).
22. McNeil, A.J. (1998), Calculating Quantile Risk Measures for Financial Return
Series Using Extreme Value Theory, ETH preprint
(www.math.ethz.ch/~mcneil).
23. Resnick, S. (2007), Heavy-Tail Phenomena Probabilistic and Statistical
Modelling, Springer, New York, 73-114.
24. Robert, C. Y., J. Segers, and C. A. T. Ferro (2008), A Sliding Block Estimator
for the Extremal Index, Working Paper at Statistics Institute, Catholic
University of Louvain, Belgium.
25. Rockafellar, R.T. and S. Uryasev (2002), Conditional Value-at-Risk for
General Loss Distribution, Journal of Banking and Finance, 26, 1443-1471.
26. Wagner, N. and T. Marsh (2003), Measuring Tail Thickness under GARCH
and an Application to Extreme Exchange Rate Changes, Working Paper at
Haas School of Business, University of California Berkeley, California.
Ti liu ting Vit
1. Nguyn Minh Kiu.(2008) Th trng ngoi hi v cc gii php phng nga
ri ro (Qun tr ri ro ti chnh) / NXB Thng K, 2008.
2. Trn Hong Ngn, Nguyn Minh Kiu (2007) Gio trnh Thanh ton quc t /
NXB Thng k, 2007.
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PH LC
Hnh 4.1 : Biu phn phi tn sut ca cc cp tin t
JPY
Ngun : Theo tnh ton t tc gi
GBP EUR CAD
AUD CHF NZD
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e
Hnh 4.2 : Bin ng t gi hng ngy ca cc cp tin t
ngun : Theo tnh ton t tc gi
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f
Bng 4.3 : Kim nh ADF test v tnh dng ca cc bin
ADF Unit Root Test
I TI GBP -30.9571(*)(**) S -30.9551(*)(**) S EUR -30.5633(*)(**) S -30.5713(*)(**) S CAD -30.4164(*)(**) S -30.4101(*)(**) S AUD -36.6483(*)(**) S -36.6399(*)(**) S CHF -30.2275(*)(**) S -30.2243(*)(**) S NZD -36.0676(*)(**) S -36.0602(*)(**) S JPY -47.8223(*)(**) S -47.8145(*)(**) S
Lu : I, TI : hi quy c chn, khng xu th v c chn, c xu th. *,** th hin c kh nng bc b gi thit Ho: chui c nghim n v mc ngha ln lt l1% v 5%. S/N dng v khng dng.
Bng 4.4: Kt qu o lng bin ng ca cc cp t gi bng m hnh
GARCH (1,1)
Dependent Variable: GBP
Method: ML ARCH
Date: 11/17/12 Time: 20:37
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 14 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob. Variance Equation
C 7.43E-08 2.35E-08 3.162019 0.0016
RESID(-1)^2 0.037617 0.004059 9.267759 0.0000
GARCH(-1) 0.958521 0.004579 209.3525 0.0000
R-squared -0.000274 Mean dependent var -7.65E-05
Adjusted R-squared -0.001188 S.D. dependent var 0.004619
S.E. of regression 0.004622 Akaike info criterion -8.267514
Sum squared resid 0.046755 Schwarz criterion -8.259724
Log likelihood 9064.196 Durbin-Watson stat 1.354166
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g
Dependent Variable: EUR
Method: ML ARCH
Date: 11/17/12 Time: 21:00
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 15 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 4.60E-08 1.59E-08 2.896032 0.0038
RESID(-1)^2 0.029049 0.003060 9.492336 0.0000
GARCH(-1) 0.969440 0.002609 371.5709 0.0000
R-squared -0.000003 Mean dependent var 8.85E-06
Adjusted R-squared -0.000917 S.D. dependent var 0.004746
S.E. of regression 0.004748 Akaike info criterion -8.071416
Sum squared resid 0.049350 Schwarz criterion -8.063625
Log likelihood 8849.272 Durbin-Watson stat 1.399958
Dependent Variable: CAD
Method: ML - ARCH
Date: 11/17/12 Time: 21:06
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 13 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 1.07E-07 3.01E-08 3.548604 0.0004
RESID(-1)^2 0.045261 0.003677 12.30889 0.0000
GARCH(-1) 0.950882 0.003923 242.3588 0.0000
R-squared -0.000121 Mean dependent var 5.43E-05
Adjusted R-squared -0.001035 S.D. dependent var 0.004945
S.E. of regression 0.004948 Akaike info criterion -8.061934
Sum squared resid 0.053582 Schwarz criterion -8.054143
Log likelihood 8838.880 Durbin-Watson stat 1.485046
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h
Dependent Variable: AUD
Method: ML - ARCH
Date: 11/17/12 Time: 21:11
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 13 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 3.38E-07 5.28E-08 6.402043 0.0000
RESID(-1)^2 0.057847 0.004896 11.81637 0.0000
GARCH(-1) 0.934688 0.005059 184.7465 0.0000
R-squared -0.000364 Mean dependent var 0.000135
Adjusted R-squared -0.001278 S.D. dependent var 0.007060
S.E. of regression 0.007065 Akaike info criterion -7.471443
Sum squared resid 0.109252 Schwarz criterion -7.463652
Log likelihood 8191.701 Durbin-Watson stat 1.519890
Dependent Variable: CHF
Method: ML - ARCH
Date: 11/17/12 Time: 21:15
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 20 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 1.04E-07 3.15E-08 3.302102 0.0010
RESID(-1)^2 0.041539 0.003752 11.07152 0.0000
GARCH(-1) 0.955365 0.004093 233.3945 0.0000
R-squared -0.000696 Mean dependent var 0.000134
Adjusted R-squared -0.001610 S.D. dependent var 0.005069
S.E. of regression 0.005073 Akaike info criterion -7.952218
Sum squared resid 0.056330 Schwarz criterion -7.944427
Log likelihood 8718.631 Durbin-Watson stat 1.370660
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i
Dependent Variable: NZD
Method: ML - ARCH
Date: 11/17/12 Time: 21:20
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 16 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 3.20E-07 6.72E-08 4.757645 0.0000
RESID(-1)^2 0.039802 0.003669 10.84727 0.0000
GARCH(-1) 0.953907 0.003806 250.6229 0.0000
R-squared -0.000183 Mean dependent var 9.51E-05
Adjusted R-squared -0.001097 S.D. dependent var 0.007031
S.E. of regression 0.007035 Akaike info criterion -7.278418
Sum squared resid 0.108346 Schwarz criterion -7.270627
Log likelihood 7980.147 Durbin-Watson stat 1.489828
Dependent Variable: JPY
Method: ML - ARCH
Date: 11/17/12 Time: 21:17
Sample (adjusted): 11/02/2006 11/01/2012
Included observations: 2192 after adjustments
Convergence achieved after 17 iterations
Variance backcast: ON
GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) Coefficient Std. Error z-Statistic Prob.
C 1.09E-06 1.31E-07 8.362190 0.0000
RESID(-1)^2 0.047718 0.004875 9.787827 0.0000
GARCH(-1) 0.921728 0.007483 123.1766 0.0000
R-squared -0.000861 Mean dependent var 0.000176
Adjusted R-squared -0.001775 S.D. dependent var 0.006005
S.E. of regression 0.006010 Akaike info criterion -7.466621
Sum squared resid 0.079063 Schwarz criterion -7.458830
Log likelihood 8186.416 Durbin-Watson stat 2.038624
Ngun: Theo tnh ton t tc gi
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j