 t cc tr  ng d  
ng ri ro 

c Th

ng i hc Khoa hc T 
Luc
: 60 46 15
ng dn: TS.Trn Tr
o v: 2011 Abstract: 
(1943) v c trm v min hp dn ci,
 Q--c tr.
ng dt cc tr ng r
ng ri ro.

Keywords: ng; R   ;  t; Th  
hc

Content
Lung:
Chng 1: Tp trung l r c kt qu ch ca l thuyt cc tr. 
  qu cho phn ng dng chng 2. i cc tr, xp x
i vt ngc tr cho khi cc u kin c
 mm trong min hp dn ci G.
1 . Chi ting Fisher and Tippet (1928), Gnedenko (1943))
c tr.
2 Min hp dn ca mt phn phi G.
3 H phn phi vt ngng

2.2
u t c t chc) nm gi mt danh mc. t i
m hin ti, (t+1) m cui ca k u t (thm trong tng lai), V
t
, V
t+1

  ca danh mc t

c th

m t, t+1 tng  V
t
t, V
t+1
cha
bin ngm gi danh mu t s i mt vi ri ro:
u t s b thua l, tn tht nu V
t+1
< V
t
c thua l: X = V
t+1
- V
t
n
ngV 
    t th       i ro), mt ch  nh
lng va th hin m ri ro ca danh mc (mc thua l)  bt k ngun gc
ng ca th trng, t t, v n va thun tin cho


(X). Trong qun tr xem

(X) nh
khon d n th chp,
 i ro

(X) gĐộ đo rủi ro chặt chẽ nu thu ki)
sau:
 T1: Bt binh tin:
Vi mi XX, a

:

(X+a) =

(Xa
 T2: C di:
Vi mi X
1
, X
2
X  :

(X
1
+X
2
) 


)
 gii t nh sau:
 T1: Vi danh m ri ro

(X), khi b n phi r a 
m ri ro ca danh mc gi

(Xa.
 T2: Ri ro ca danh mc tng hp (ng vi X
1
+ X
2
n ln tng ri ro ca
anh mp v Đa dạng hóa đầu
tư.
 T3: Danh mn.
 T4: Danh mc thua l tim 
Nh vy tt c i v u h p vi
thc tin.
 i ro ca danh mp ct t
n tr r  nguồn gốc của rủi ro   th.
Kt qu sau s cung c  i ro c th  
ri ro cht ch 

2.2u di

i ro cht ch
(pu gi
1
0

(xem [10]):
 t ch  khi (p)A.
Vc biu din (2.1) c i ro cht ch  
 th p vi ngun gc ch(p
gt quan trng ri ro. 2.3  ri ro (Value At Risk)
2.3.1 Ngun gn
Thut ng  ri ro (Value at Risk  

c s dng r
c s tr t



m quan trng trong khoa hc kinh t t sau s kin th
trng ch 
Ngp c 
 la chn danh mu t 
trn hip phng sai li su n phi u danh mu t.
Trong nhu thy ban Chi h
K (SEC -   bu
cu v vn l   tin cy 95% trong
khong th  i li su c s dng
 n l ting thn
khai s dng mt h th vu t c
Trong thi gian cui thu tht s t chc hin
 h tr cho vi vu t n ch ri ro ca th trng.
Nhng s kiu nhy rt nhip

mn trong mt chu k k n v thi gian) vi m tin cy nhnh.
 2.1: Mu t quyu t mt khon tin lt danh mc c
phia r danh mu t m xung 50000USD.
Sau khi khn nhn st gim li nhun, anh ta mun bit
m tn tht t li ngay lp t mt
ht khon tiu t, nh lp vi thc t t
trng hp thit hi lm khi x ln ti
s ki c bi  n tht t     ng hp s   
4000USD i m ca VaR.
Trong qun tr r s dng r ri ro
m tn tht danh mnh. Cho mt danh m
sung thnh n m ngng sao cho
 tn tht danh mc trong khong thi gian nh
t 

cho trc.

2.3
2.3.3.1 Tip c
Gi s rng mu t quynu t mt danh mn P. Ti thi
 ca danh mu t 
t
V
. Sau mt khong thi gian
t
, ti thi
m
k t t  
 ca danh mu t 
k


: Biu di n sau khong thi gian
t

 V
k
n ngn ngi F
k

 t c


 x

gPhân vị mức α F
k
. V 


P&L(k) < 0 t   u t trng v s b tn th    x

  
Pr(P&L(k)  x

) = 1 - 

) = 1 -  
u t n v s b tn tht.

V

) = 1 - P(
)(kV


) = 1 -  u t chu
mc tn thc x

(x

- 
 hai v th u tu t chu tn tht t
danh mc st gi  hai trng hc cho nh 
mc tn th  
vy VaR ca mt danh mc vi chu k  tin cy (1- 
 F
k
(x). i l 
Nh v
)(kV


 , 

t u t
nm gi danh mc P  sau mt chu k k, v tin cy (1- u t 
 tn tht mt khon s bng
VaR(k, α)
u kin hong.
 2.2: : VaR(1
u USD. Nh vy vt 5%, trong m thng ca

YEuEYEYE
.
 vng ca
t
Y
i. Vi gi thii ta tin
r t thu .
 tr  n nht thit ph 
 Thi gian c nh: Gi thit khong thi gian
u khong thi gian. Chng hn, nu cho khong thi gian
mt tu m rng cho m
 i chun: Trong mt s ph thit li su
si chun, ch tr mt s php cn VaR
phi tham s nh Monte Carlo.

2.3


t l







n, 











a li

t
r
.

2.3i sun
Gi thit chui li sut cn
t
r
i d chun. Vi gi thit
 cn s dng hai tham s k vng (

 lch chun (

) (hoc s
dc lng c  VaR.
T gi thit
),(~
2

Nr
t



. Vi m
 = 5% VaR ca li sut :
-1,64 0,03 = -0,0492.
Suy ra VaR ca danh mc:

t
, 5%) = VaR
Li sut

t
= (- 0,0492)*100 = - 4,92.
Vy sau mt 5%, kh u t  l u.

2.3c
Cho danh mc P: (w
1
, w
2
, , w
N
) vi li su n trong danh mc 
 

n: r
i

2
( , )



y li sut ca danh mc r
P

2
( , )
PP
Nr

. T ng t nh i vn
c VaR ca danh mc:
ppr
NngàyVaR
p

)(%)100)1(,1(
1

. (2.3)
: Nc P di d: P: x = (x
1
, x
2

N
) vi x
i
 khon
tiu t n i  

1
; '
N
P L i i P L
i
x r x Vx




. 
- )100% ) = 
P&L
+ N
-1
()
P&L
= 
P&L
+ N
-1
(x)
1/2
(2.4)
Vi chu k i lng 
P&L
 c t  b 
th 
- )100% ) = N
-1




 . 


 ta 

 ng ph

 i cho c lng VaR gn vi  tn tht
trong thc t nht.

2.3.3.5 n ch c i ro VaR
VaR ca danh mn th hin m tn th xi vi danh
m n trong mt khong thi gian nhnh vi m tin cy nh nh. Tuy
,    VaR 

i 





, VaR mi ch
 mt tn l 
VaR  lt phn nh i (1% hay
ng xu-ng vi nhng din bin bt thng ca th trng), khi xy ra tn
tht, mc tn th d  i ro ES d cho
 li.


  
. (2.6)
Nh mt s t u vit hn VaR, vic s d i ro ES th hin vi
lng r hg VaR.

2.4.2 Mt s t ca ES




ch





sau (xem [10]):
  i ro cht ch ca danh mc.
 M i ro cht ch a danh m biu din nh mt t
hp li ca ES v   (X).
Nh vy via danh mc va thay th VaR 
ng r hn va ch i ro u vit.

2.4.3 Phc nghim c lng ES
 thuc lc
l X ca danh m   i sut (loga li sut) ca danh mc  nh bi:
( 1)
ln
t

i:n

th t th i ca mu, t
1:n
 X
2:n
 
i:n
 X
n:n
. Gi k n
a n

t p = n

- k. Nu n

 p 
mu c t t n k:
1: 2: :
:

n n k n
kn
X X X
X
k
  

(2.7)



(2.9)
 2.4: Trong  , ta c lng thc nghim ES cho th trng ch
Vi hu a
c thu thp trong khong thi gian t n 6/2010 t ngun
VnDirect. c 

m, ng





 








c (xem [10]): n =1116,

n

= 11,6 
ra k
1

VaR
VnIndex_tun
(1%) = 10,294 (%); VaR
VnIndex_tun
(5%) = 8,242 (%)
ES

(1%) = 14,96 (%); ES

(5%) = 13,43 (%)

2.4.4 
Tn tht k vng ca danh mc v tin cy (1- ).100%, n th


vt ngng
VaR

:
( / )ES E X X VaR


.
Mc tn tht k vng (ES) ca danh mc g xu i ro b
sung cho VaR nhm quan trng cn tr ri r
rDo cc tp h c lng ES c
phc bi cp ti danh mc tp nh 
danh mc ca t chng.

References

udiger Frey, Alexander J. McNeil, VaR an d expected shortfall in portfo-
lios of dependent credit risks: Conceptual and practical insights, Journal of
Banking & Finance 26 (2002) 1317–1334p.
14. R D. Reiss & M. Thomas, Statistics Analysis of Extreme Values, with Ap-
plications to Insurance, Finance, Hydrology a nd Other Fields
15. Yasuhiro Yamai, Toshinao Yoshiba, Value-at-risk versus expected shortfall:
A practical perspective, Journal of Banking & Finance 29 (200 5) 997 –
1015p.
65