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srtc.org.vn PT10/2007 1

PHN TCH V U T TRI PHIU (Bi 2)

ThS. Nguyn Thy HonTel: (84 4) 553 5876Email: [email protected]

TRUNG TM NGHIN CU V O TO CHNG KHON

PT10/2007 2srtc.org.vn

NI DUNG (bi 1):

Gii thiu tng quan v th trng tri phiu

Kin thc c bn

Li ch v Ri ro trong u t tri phiu

Li sut tri phiu, ng cong li sut/cutrc k hn

nh gi tri phiu


NI DUNG (bi 2):

nh gi tri phiu chuyn i

o lng tnh bin ng gi ca tri phiu(s dng thc o: Duration v Convexity)

Chin lc trung ha ri ro li sut trongu t tri phiu

Bi tp ng dng


E NH GI TRI PHIU (tt)2 NH GI TRI PHIU CHUYN I

Khi nim T l chuyn i Gi chuyn i Gi tr chuyn i


E NH GI TRI PHIU (tt) T l chuyn i:= S lng c phiu/TP khi tri phiu c chuyn i

Gi chuyn i:= Mnh gi TP/T l chuyn i

Gi tr chuyn i:= T l chuyn iTh gi c phiu


E NH GI TRI PHIU (tt) Gi tr tri phiu khng thc hin chuyn i:= Gi tri phiu thng thng (khng chuyn i)

T l chnh lch chuyn i:= [(Th gi TP- Gi tr chuyn i)/Gi tr chuyn i]

Gi tr li ch chuyn i= Max (gi tr chuyn i, gi tr TP khng thc

hin chuyn i)


E NH GI TRI PHIU (tt) Gi s, cui nm 2005, mt cng ty XYZ pht

hnh mt loi tri phiu chuyn i vi li coupon 2,5%/nm, mnh gi 1triu ng, o hn ngy1/1/2011. Coupon c tr vo u mi nm, btu t nm 2007. T l chuyn i l 1Tp:10cp. Vo 1/1/2006, c phiu cng ty ny c giaodch vi gi 81.000 vi mc li sut yu cu 5%/nm.

Nh u t c nn thc hin quyn chuyn ivo ngy 1/1/2006 khng?


E NH GI TRI PHIU (tt)

Gi trthc

Gi trTP

Gi tr cng ty

Gi TP thngthng

Gi trchuyn i

Gi tr quyn chuyn i


F O LNG TNH BIN NG GI CA TRI PHIUDng cc thc o:

Thi gian o hn bnh qun(Duration)

Thi gian o hn bnh qun iuchnh (Modified Duration)

li (Convexity)



Duration l thi gian o hn bnh qun giaquyn ca cc dng tin ca tri phiu.

Cng thc tnh:

P)y(nM

)y(tCD

)CF(PVtP

tP

)CF(PVD

n

n

tt

t

n

tt

n

t

t

111

1

1

11

+++=

==

=

==


Thi gian o hn bnh qun iuchnh (Modified Duration - MD) Cng thc tnh

)y(DMD += 1

1


li (Convexity)

Cng thc tnh

P1

)y1(M)1n(n

)y1(C)1t(t

P1

yPConvexity 2n

n

1t2tt

2

2

++++

+== +

=+


Thay i gi tri phiu khi li sutthay i

y2 y0 y1

P2

P2

P0

P1P1

2

0

1

Do tc ng caDuration thay i

Do tc ng ca lithay i



Thay i gi tri phiu do Duration

Thay i gi tri phiu do Convexity

P do Duration

= - MD Gi triphiu

y

P do Convexity

= 1/2 Gi triphiu

Convexity (y)2



Kt hp

P = P do Duration + P do Convexity


V d 1:

Mt tri phiu c mnh gi l 100.000 VND, thi gian o hn l 3 nm, li sut o hn l 7%/nm, li sut Coupon l 8%/nm, tr litheo nm.

Tnh thi gian o hn bnh qun v li(convexity) ca tri phiu ?

D kin do nh hng chung ca li sut trn thtrng, li sut o hn tng 0,5%/nm. Hy d bomc thay i gi tri phiu?


Gi tri phiu (P0)

+++= = n

n

1tt

t

)y1(M

)y1(CP

102624.32P =

88160.1710800036987.51800027476.6480001

PVCFt @ 7%CFtNm



P)y(nM

)y(tCD n

n

tt

t 1111

+++= =

2.79285932.17102624.32P264480.5188160.171080003

13975.026987.5180002

7476.647476.6480001

Durationt PVCFt @

7%PVCFt @ 7%CFtNm


li (Convexity)

P1

)y1(M)1n(n

)y1(C)1t(t

P1

yPConvexity 2n

n

1t2tt

2

2

++++

+== +

=+

9.49973709.82285932.17102624.32P

924030.09264480.5188160.171080003

36618.9713975.026987.5180002

13060.777476.647476.6480001

Convexityt(t+1)CFt/(1.07)^(t+2)t PVCFt @ 7%PVCFt @ 7%CFtNm


Thi gian o hn bnh qun iuchnh (Modified Duration - MD)

60720717921

1 ,),/(,)y(

DMD ==+=


Thay i gi tri phiu khi li sutthay iThay i gi tri phiu do Duration

Thay i gi tri phiu do Convexity

P do Duration

= - MD Gi triphiu

y

P do Convexity

= 1/2 Gi triphiu

Convexity (y)2

12.17P do C-1336.13P do D

2.60MD2.79D



Kt hp

P = P do Duration + P do Convexity

-1323.96P =12.17P do C

-1336.13P do D


Trung ha ri ro li sut

Chin lc trung ha ri ro li sut trong ut tri phiu

Bc 1: Xc nh thi gian o hn bnhqun ca tng loi tri phiu

Bc 2: Khp thi gian o hn bnh qunca ton b cc tri phiu trong danh mcvi k u t


V d 2:Gi s cu trc li sut l phng, vi mc li sut 10%/nm. Bn mun thit k mt DMT c k ut 2,5 nm gm 2 loi tri phiu sau:

TP A c li Coupon 8%/nm, thi gian o hn 2 nm.

TP B c li Coupon 12%/nm, thi gian o hn 3 nm.C hai loi tri phiu trn u c MG 1000 USD, trli theo nmNu bn u t 5 triu USD vo DMT th bn phimua mi loi l bao nhiu trung ho ri ro lisut?


V d 2:

Gi tri phiu:PA= 80. PVA1(2,10%) +1000. PV1(2,10%)

= 80. 1,736 +1000. 0,826= 138,88 + 826 = 964,88 USD

PB= 120. PVA1(3,10%)+ 1000. PV1(3,10%)= 120. 2,487 + 1000. 0,751= 298,44 + 751 = 1049,44 USD


V d 2:Thi gian o hn bnh qun (Duration):

702441049

1

101

10003

101

1203

101

1202101

1201

93188964

1

101

10002

101

802101

801

1

11

332

22

1

,,),(

.

),(

.

),(

.

),(

.

,,),(

.

),(

.

),(

.

.)(

.

)(

.

=

++

++

+++=

=

++

+++=

+

++

= =

B

A

n

tnt

t

D

D

Py

Mn

y

CtD


V d 2:Gi XA l t l u t vo tri phiu AXB=1-XA l t l u t vo tri phiu B

trung ho ri ro: Duration c danh mc = K u t

DP= 2,5 nm.DP= XA. DA+(1- XA)DB

2,5=XA.1,93+(1-XA).2,70 XA= 0,26XB= 0,74


V d 2:Vy u t vo tri phiu A:

0,26 . 5000000 = 1.300.000 USD

hay: TP A

u t vo tri phiu B:0,74 . 5000000 = 3.700.000 USD

hay: TP B

134888,964000.300.1

352544,1049000.700.3


Ph lc

dxdh

dxdg

dxdf)x(h)x(g)x(f

dx)x(g.a

dxdf)x(g.a)x(f

nxdxdfx

x)x(f )n(nn

+=+=

==

=== + 11


o lng tnh bin ng gi catri phiu

==+

==+

==

++

+=++=

++=+=

+=

+++=

n

tt

tn

t)t(t

n

tt

tn

t)t(

t

n

tt

tn

n

tt

t

)y(CF)t(t

)y()y(CF)t(t

yP

)y(tCF

)y()y(tCF

yP

)y(CF

)y(M

)y(CP

12

122

2

111

11

11

11

11

111

1

111



P1

)y1(tCF

)y1(1dy

P1

yP

PdP

dyyPdP

)y1(tCF

)y1(1

)y1(tCF

yP

n

1tt

t

n

1tt

tn

1t1t

t

++==

=

++=+=

=

==+



2n

1t2t

t22

22

22

22

)dy(P1

)y1(CF)1t(t)dy(

P1

yP

PPd

)dy(yPPd

++=

=

=

=

+



Khai trin Taylor

2

22

2

)y(Convexity21y.MD

PP

)dy(P1

yP

21dy

P1

yP

PdP

+=

++

=


Xin cm n!

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