DANH MC HIU QU KHNG BN KHNGTNH TON GI TR CHU RI RO

10.1 DANH MC HIU QU KHNG BN KHNGnh 1 trong chng 9 cho php tm c mt danh mc u t hiu qu bng cch tm kim mt danh mc tip tuyn vi ng bin tp hp cc danh mc nm trong vng kh thi. Gii php cho bi ton ti u ny l phi cho php t trng vn u t c gi tr m; Khi xi

10.1 DANH MC HIU QU KHNG BN KHNGBi ton danh mc hiu qu khi khng bn khng:

Sao cho

xi 0, i =1,N

Vi : v

10.1 DANH MC HIU QU KHNG BN KHNGBi ton danh mc hiu qu khi khng bn khng: c th gii quyt bng cng c Solver ca Excel (chng 3).

10.1 DANH MC HIU QU KHNG BN KHNG

10.1 DANH MC HIU QU KHNG BN KHNGKhi thay i gi tr ca hng s c, ta s c c mt danh mc khc. Khng phi tt c cc gi tr c u cho ra danh mc m rng buc bn khng l c tc dng. Khi c c gi tr qu thp hoc qu cao th rng buc v bn khng s c tc dng.

10.1 DANH MC HIU QU KHNG BN KHNGng bin hiu qu khi khng c bn khng:

Page 201-204, 207

Khng c bn khngRESULTS

Ma trn phng sai - hip phng saiTSSLcSigmaMeanx1x2x3x4

0.10.03-0.080.058%Ctrl+A works the VBA program-0.03520.24%8.70%0.6050.0890.3070.000

0.030.20.020.039%which calculates efficient-0.0320.25%8.70%0.6040.0890.3070.000

-0.080.020.30.210%portfolios for no-short sales.-0.02520.25%8.70%0.6030.0890.3070.000

0.050.030.20.911%This program iteratively-0.0220.25%8.71%0.6030.0890.3080.000

substitutes a constant ranging-0.01520.25%8.71%0.6020.0900.3090.000

hng s c11.0%from -3.5% 'till 16% (1/2%-0.0120.26%8.71%0.6010.0900.3090.000

jumps) and calculates the-0.00520.26%8.71%0.5990.0910.3100.000

T trng ti uoptimal portfolio.020.27%8.71%0.5980.0910.3110.000

x10.00000.00520.27%8.71%0.5970.0920.3110.000

x20.00000.0120.28%8.72%0.5950.0930.3120.000

x30.00000.01520.29%8.72%0.5930.0930.3130.000

x41.00000.0220.30%8.72%0.5910.0940.3150.000

Tng100.02520.31%8.73%0.5890.0950.3160.000

0.0320.32%8.73%0.5860.0970.3180.000

TSSL trung bnh ca danh mc11.00%

10.2 GI TR CHU RI RO VaRGi tr chu ri ro VaR (Value-at-Risk) o lng khon l mong i xu nht c th xy ra trong mt khong thi gian xc nh, vi mt mc tin cy cho trc. Var tr li cho cu hi: nh u t c th b l bao nhiu vi mc xc sut xy ra l x% trong khong thi gian trong tng lai c xc nh trc. Hai thng s c bn (1) khon thi gian T v (2) gi tr t c ca bin s X ti mt mc xc xut cho trc l nhng thng s ch yu nn c la chn s dng nh l mt phng php thch hp o lng ri ro ca mt mc tiu chung no .

10.2 GI TR CHU RI RO VaRKhung tnh hung:Mt nh qun l c mt danh mc ch bao gm mt chng khon, t sut sinh li ca chng khon ny tun theo quy lut phn phi chun v c t sut sinh li trung bnh l 20% v lch chun l 30%. Gi tr ca danh mc ny thi im hin ti l 100 triu$. Gi tr ca danh mc ny vo cui nm l bao nhiu?Xc sut xy ra khon l ln hn 20 triu$ vo cui nm (v d l xc sut gi tr ca danh mc ny vo cui nm thp hn 80 triu$) l bao nhiu?Vi xc sut 1% th khon l ln nht vo cui nm l bao nhiu? Cu hi ny cn c ngha l chng ta hy tnh VaR ti mc xc sut l 1%.

10.2 GI TR CHU RI RO VaRHm Normdist c th a ra cc gi tr phn phi chun tch ly (trong v d ny l cc gi tr danh mc c th t c) v cc mc xc sut xy ra tng ng.

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaRGi tr danh mc vo cui nm ng vi mc xc sut xy ra 1% l bao nhiu? Ta c th s dng hm Solver tm cu tr li: Vi xc sut 1% th gi tr danh mc vo cui nm thp hn 50,20865, t suy ra VaR l 100 50,20865 = 49,79135.

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaRChng ta c th s dng cng c Solver tm cc gi tr Quantile ng vi bt k loi phn phi no. Chng ta s dng hai phn phi: phn phi chun (normal distribution) v phn phi Loganormal (lognormal distribuition) tm VaR, v Excel c nhng hm tng ng gip chng ta tm Quantile l hm Norminv( ) v hm Loginv( ). Hm Normsinv v hm Loginv gip tm gi tr chuyn i (t mt mc xc sut cho trc tm gi tr t c ca bin s) ca phn phi chun (normal), phn phi chun tc (Standard normal) v phn phi lognormal.

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaRPhn phi Lognormal s l mt phn phi hp l hn so vi phn phi chun khi kho st bin ng gi ca cc chng khon (i lng ny khng bao gi m). Gi nh rng t sut sinh li ca danh mc tun theo quy lut phn phi chun vi gi tr trung bnh hng nm l v lch chun hng nm l , gi tr hin ti ca danh mc c cho trc l V0.

Ln VT~Phn phi chun

10.2 GI TR CHU RI RO VaRTrng hp danh mc u t vi 3 ti sn:Vic c lng cc thng s trong phn phi t sut sinh li ca mt ti sn no . Trong th gii thc, c th tnh ton VaR th chng ta phi c c cc c lng v gi tr trung bnh, phng sai v s tng quan ca cc gi tr t sut sinh li. Nhng tnh ton thc t khi quy m giao dch ln.

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaRM phng d liu:Gi nh rng 10/01/1997 mt cng ty ang xem xt u t vo 2 ti sn:Mua hai chng ch qu u t. Gi th trng ca mt chng ch qu u t ny l 293$ v vy vn u t l = 2*293$ = 586$.Bn mt tri phiu nc ngoi (bng ng Franc Thy s CHF). T gi hi oi l 3.5. Tri phiu zero-coupon ny c mnh gi l l 100 CHF v thi im o hn l vo ngy 08/05/2000. Nu li sut ng CHF hin ti l 5,3% th khi gi tr tri phiu bng ng CHF vo ngy 10/01/1997 l:100*exp[5,3%*(08/05/2000 10/01/1997)/365] = 84,2166Gi tr tri phiu tnh bng ng USD l 84,2166*3,40 = 286,3365, v vy gi tr danh mc rng l = 586 286,3365 = 299,66.

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaR

10.2 GI TR CHU RI RO VaRChng ta mun s dng nhng d liu ny lm nn tng tnh ton cc gi tr t sut sinh li ngu nhin t c t danh mc u t ny. Chng ta s s dng mt k thut c gi l xo bi (xem ph lc ca chng ny) theo chng ta s thay i ngu nhin cc d liu. th trong bng tnh trn cho thy phn phi t sut sinh li khc rt nhiu so vi phn phi chun. T ct L, M, v N ta c th ni rng VaR ti 5% l khong 47% hay vi xc xut l 5%, cng ty c th b l 47% trn vn u t ca mnh.