Chuong3-Chuong8-ToiUuPhiTuyen

TI U HA PHI TUYNCHNG 3

3.1 GiI THIU M HNH PHI TUYNTrn thc t c nhiu vn trong kinh t v trong cc hot ng kinh doanh c nhng mi lin h vi nhau khng phi l mi quan h tuyn tnh m l phi tuyn. S tn ti cc mi quan h khng theo t l ( doanh s t c khng theo t l vi gi bn v gi bn c th tng v doanh s c th gim.S tn ti cc mi quan h khng mang tnh cng b sung (ri ro ca danh mc s khc vi bnh qun gia quyn ca 2 chng khon trong danh mc ny.S hiu qu v khng hiu qu theo quy m (khi sn lng tiu th vt qu mt mc gii hn no th tng nh ph v bin ph n v s thay i)

3.1 GiI THIU M HNH PHI TUYNBt c gi tr no ca x m ti o hm ring = 0 gi l im dng.Ti gi tr ti u a phng (ti thiu hoc ti a) tt c cc o hm ring phi = 0. im ti u cc i hoc cc tiu lun l im dng.Vic thit lp cc o hm ring cp 1 bng 0 trong mt hm n bin s to ra n h phng trnh. Ngoi tr trng hp h phng trnh l tuyn tnh, th i vi trng hp hm phi tuyn (v d hm s gc l hm bc 3) khng d dng tm li gii v s khng kh thi khi gii bng tay. iu kin th 2 kh phc tp, yu cu phi tnh ton cc nh thc ca cc ma trn o hm ring cp 2. Trn thc t, ngay c trong trng hp hm f ch c mt hay hai bin s nhng qu phc tp th dng nh chng ta vn khng c kh nng gii bng th cng bi ton ti u ny.

3.2 TI U HA PHI TUYN QUA TH


Gii php ti u ca m hnh phi tuyn khng phi lun lun ti gc nh ca m hnh tuyn tnh


Gii php ti u trong m hnh danh mc u t

3.2 TI U HA PHI TUYN QUA THTrong phng php The hillclimbing m Solver p dng cho bi ton tm gi tr cc i, mt im dng u tin s c chn, sau hng th tng dn c thc hin bng cch phng chng cc mc thay i ban u dc theo ng gi tr ti u (Optimal Value OV) tng dn, ti im cao nht c th t c ca ng ny. Phng php ny s kt thc khi cc mc thay i phng chng theo tt c cc hng (o hm ring cp 1) tin dn v 0 (iu kin th nht c tha mn). Nhng im ny khi s lun l im cc tr a phng hoc im ti u a phng. Nhng im ti u khc c tip tc tm kim bng cch khi ng li chng trnh ti u ha, bt u ti mt im khi s khc cho gi tr ban u cc bin s ca m hnh.

3.2 TI U HA PHI TUYN QUA THS so snh gia LP v NLPC mt vi im tng ng gia LP v NLP. V d:Mt s gia tng (hay gim) RHS ca bt phng trnh rng buc () s ni lng iu kin rng buc. iu ny khng lm co li v c th m rng vng kh thi. Vic ni lng iu kin rng buc khng lm tn hi v c th gip gia tng gi tr mc tiu ti u.Vic tht cht iu kin rng buc khng gip ch v c th gy tn hi gi tr mc tiu ti u.

3.2 TI U HA PHI TUYN QUA THGi tr ti u a phng (cc tr a phng) so vi gi tr ti u ton cc (cc tr ton cc) Trong m hnh LP cc tr a phng cng l cc tr ton ccTrong m hnh NLP c th va c cc tr a phng v va c ca tr ton cc. Gi tr cc i ton cc l im cc i theo rng buc ton cc bi v gi tr ca hm mc tiu ti im ny l ln nht so vi tt c cc im kh thi khc. Trong m hnh NLP tm ra cc tr ton cc t cc cc tr a phng cn phi b sung cc iu kin cc iu kin li v iu kin lm. Nhng iu kin ny phi c tha mn m bo rng gi tr ti u ha a phng cng s l gi tr ti u ha ton cc.

3.3 S DNG SOLVER CHO M HNH PHI TUYN

Trong m hnh LP, Solver s dng phng php di chuyn t gc ny sang gc khc trong cc vng kh thi. Trong m hnh NLP, Solver s dng phng php leo dc da trn tin trnh tm kim dc c gim thiu chung v phng php ny cn c gi l GRG. Cc bc ca tin trnh ny c thc hin nh sau: S dng cc gi tr ban u ca cc bin s quyt nh tnh ton mt hng i c sao cho ci thin nhanh nht gi tr ca hm mc tiu.Solver li th mt hng tnh ton mi t mt im khi s mi, tin trnh trn c lp li cho n khi gi tr OV khng cn c ci thin tt hn trn bt k mt hng mi no th tin trnh tm kim gi tr ti u kt thc.

3.4 M HNH QUN L HNG TN KHO EOQKin thc nn ti chnh

Cc chi ph lin quan n tn kho Ti cng mt thi im khi mt doanh nghip c hng nhng li ch t vic s dng hng tn kho th cc chi ph c lin quan cng pht sinh tng ng, bao gm:Chi ph t hng (Ordering costs)Chi ph tn tr (Carrying costs)Chi ph thit hi do kho khng c hng (Stockout costs)

3.4 M HNH QUN L HNG TN KHO EOQKin thc nn ti chnh

Chi ph t hngChi ph t hng bao gm cc chi ph giao dch, chi ph vn chuyn v chi ph giao nhn hng. Chi ph t hng c tnh bng n v tin t cho mi ln t hng. Chi ph tn trChi ph tn tr bao gm tt c cc chi ph lu gi hng trong kho. Chi ph tn tr c tnh bng n v tin t trn mi n v hng lu kho hoc c tnh bng t l phn trm trn gi tr hng lu kho trong mt thi k. Chi ph thit hi khi khng c hng (hng tn kho ht)Chi ph thit hi do hng tn kho ht (Stockout costs) xy ra bt c khi no doanh nghip khng c kh nng giao hng bi v nhu cu hng ln hn s lng hng sn c trong kho.

3.4 M HNH QUN L HNG TN KHO EOQKin thc nn ti chnhGi Q l lng hng tn kho cho mi ln t hng. Ti thi im u k, lng hng tn kho l Q v thi im cui k l 0 nn s lng tn kho bnh qun trong k l:

Gi C l chi ph lu gi cho mi n v hng tn kho th tng chi ph lu gi hng tn kho trong k l:

3.4 M HNH QUN L HNG TN KHO EOQKin thc nn ti chnhGi S l lng hng tiu th trong k nn s ln t hng trong k l

Gi O l chi ph cho mi ln t hng th tng chi ph t hng trong k l:

Gi TC l tng chi ph th:

3.4 M HNH QUN L HNG TN KHO EOQ

3.4 M HNH QUN L HNG TN KHO EOQV d:Cng ty bn s Steco c nhu cu hng ha mi thng duy tr mc n nh l vo khong 5.000 sn phm (60.000 sn phm/nm).Gi nh chi ph cho mt ln t hng ca cng ty Steco l 25$. Chi ph lu gi tnh trn mi sn phm tn kho bao gm chi ph c hi ca vn l 20% trn gi mua vo v chi ph tn tr l 4% trn gi mua vo mi sn phm. Vy chi ph lu gi cho mi n v hng tn kho l 24% x 8,00$ = 1,92$.

3.6 M HNH QUN L HNG TN KHO EOQBi ton ti u ha ca cng ty Steco

Hm mc tiu:

Bin s ra quyt nhQRng buc:Q >= 1

YU CUChuyn m hnh ti u ha trn vo bng tnhDng Solver gii quyt v so snh kt qu ca Cng thc tn kho ti u:

Thc hnh vi m hnh EOQ chit khu theo s lng t hng

3.5 NG DNG M HNH PHI TUYNM hnh danh mc (portfolio)Khung tnh hung:Cc nh qun l danh mc u t lun tm kim ri ro thp v t sut sinh li cao nn c gng tt a ha t sut sinh li (ng vi ri ro cho php) hoc ti thiu ha ri ro (vi gii hn v ri ro).Nh u t cn xc nh t trng ti u vo cc loi chng khon trong danh mc.Tp hp cc quyt nh kh thi phi tha mn cc rng buc.Tng t trng u t = 1 (gii hn chnh sch u t ht)T trng mi loi phi cao hn hoc thp hn 1 con s cho php (gii hn chnh sch a dng ha)T trng phi >=0 (gii hn chnh sch khng bn khng).Tng vn u t nh hn ngun vn c sn (gii hn t nhin)Ri ro thp hn 1 mc no hoc TSSL phi cao hn mc cho php.

3.5 M HNH PORTFOLIOBi ton ti u haHm mc tiu:TSSL danh mc -> MaxHoc RR danh mc -> MinBin s ra quyt nh:T trng u t vo cc chng khon (xi)Rng buc:Rng buc v vn u t.Rng buc v u t ht.Gii hn v trn ri ro hoc sn TSSL.Rng buc v bn khng v a dng ha.

3.5 M HNH PORTFOLIOKin thc nn ti chnhxi l t trng u t vo c phiu i. i2 = phng sai ca chng khon th i12 = hip phng sai gia t sut sinh li c phiu 1 v 2ri = t sut sinh li mong i hng nm ca c phiu ib = t sut sinh li ti thiu mong i hng nm t tng s tin u t vo danh mcSi = mc u t ti a vo c phiu th i ; i = 1,2

3.5 M HNH PORTFOLIOBi ton ti u haHm mc tiu:12x12 + 212x1x2 + 22x22 > MinBin s ra quyt nh:x1, x2Rng bucx1 + x2 = 1 (tt c s tin phi c u t ht)x1r1 + x2r2 b (t sut sinh li mong i ti thiu ca danh mc)x1 S1 (mc u t ti a vo c phiu 1)x2 S2 (mc u t ti a vo c phiu 2)x1, x2 0 (khng c bn khng c phiu)

YU CUChuyn bi ton ti u ha trn vo bng tnhS dng Solver gii quytSo snh vi kt qu ha trong schThc hnh vi danh mc gm 3 chng khon.

BI TP LN:S dng s liu thc t lp v gii quyt m hnh Portfolio trong thc t (S lng chng khon trong danh mc l 5)

M HNH PORTFOLIOCHNG 8

8.1 TNG QUANKhung tnh hungHm mc tiu:TSSL danh mc -> MaxHoc RR danh mc -> MinBin s ra quyt nh:T trng u t vo cc chng khon (xi)Rng buc:Rng buc v vn u t.Rng buc v u t ht.Gii hn v trn ri ro hoc sn TSSL.Rng buc v bn khng v a dng ha.

8.2 CC K HIUE(ri) l t sut sinh li mong i ca ti sn i Var(ri) phng sai ca t sut sinh li ti sn i Cov(ri;rj) l hip phng sai ca gia ti sn i v ti sn j. Cov(ri;rj) l ij Var(ri) l ii

8.3 M HNH 2 CHNG KHONT s liu gi ng ca vo cui mi thng (tun, ngy) ca mi c phiu, chng ta tnh ton t sut sinh li hng thng (tun, ngy) ca mi c phiu.

y l cng thc tnh theo k ghp li lin tc, trong trng hp c c tc, chng ta c th tnh:

8.3 M HNH 2 CHNG KHONGi nh rng cc d liu t sut sinh li trong 12 thng qua th hin phn phi t sut sinh li ca c phiu ny trong nhng thng (tun, ngy) sp ti. Tnh TSSL mong i nh sau:

Tnh phng sai ca TSSL:

Tnh hip phng sai gia 2 chng khon A,B

8.3 M HNH 2 CHNG KHONS dng cc hm Average( ), Varp( ), v Stdevp( ) v COVAR() trong Excel tnh TSSL mong i, Phng sai, lch chun v hip phng sai.Tnh ton h s tng quan gia chng khon:

Hoc dng hm Correl () trong ExcelH s tng quan lun lun nm gia +1v 1 hay 1 AB+1Nu h s tng quan l +1, khi t sut sinh li gia 2 chng khon c tng quan xc nh hon ton.Nu h s tng quan l 1, khi t sut sinh li gia 2 chng khon s c tng quan ph nh hon ton.

8.3 M HNH 2 CHNG KHON

Gi tr trung bnh t sut sinh li ca danh mc l bnh qun gia quyn vi trng s l t l vn u t vo mi c phiu thnh phn. Gi xA l t trng vn u t vo c phiu A, ta c:E(rp) = xAE(rA) + (1xA)E(rB)Phng sai danh mc khng phi l bnh qun gia quyn ca cc phng sai (v c mi tng quan trong bin ng TSSL ca cc c phiu)Var(rp) = xA2 Var(rA) + (1 xA)2 Var(rB) + 2 xA(1xA)Cov(rA,rB)

p2 = xA2 A2 + (1 xA)2 B2 + 2 xA(1xA)ABAB

8.3 M HNH 2 CHNG KHONng hiu qu danh mc:

Page 131-133

Gi c phiu

ThngC phiu AC phiu B

025.0045.00

124.1244.85

223.3746.88

324.7545.25

426.6250.87

526.5053.25

628.0053.25

728.8862.75

829.7565.50

931.3866.87

1036.2578.50

1137.1378.00

1236.8868.23

Tnh ton t sut sinh li

C phiu AC phiu B

ThngGi CPTSSLGi CPTSSL

025.0045.00

124.12-3.58%44.85-0.33%

223.37-3.16%46.884.43%

8.3 M HNH 2 CHNG KHONCU HI:Gi nh th trng ch c 2 loi chng khon A v B, ng hiu qu danh mc trn c phi l ng bin hiu qu ca th trng khng?YU CU:C PH LC 2 SCH M HNH TI CHNH

8.4 M HNH NHIU CHNG KHONTrong trng hp tng qut vi N chng khon (hay N ti sn), gi nh rng t l vn u t vo chng khon i trong danh mc l xi, nh vy ta c ma trn ct X cc t trng vn u t vo danh mc nh sau:

Chng ta c th vit XT nh l ma trn o ca ma trn ct X:XT = [x1, x2, x3, .xn]

8.4 M HNH NHIU CHNG KHONBy gi ta vit E(r) nh l ma trn ct ca t sut sinh li cc chng khon

E(r)T nh l ma trn hng ca t sut sinh li cc chng khon:E(r)T = [E(r1), E(r2), E(r3), .E(rn)]

8.4 M HNH NHIU CHNG KHONT sut sinh li mong i ca danh mc di dng cng thc ma trn nh sau:

Hoc c th dng hm SUMPRODUCT () ca 2 vector hng hoc 2 vector ct.

8.4 M HNH NHIU CHNG KHONPhng sai danh mc:Gi ma trn c ij trong hng th i v ct th j l ma trn phng sai hip phng sai:

Phng sai ca danh mc l Var(rp) = XTSX

8.4 M HNH NHIU CHNG KHONHip phng sai ca 2 danh mc:Nu chng ta gi ma trn X = [x1, x2, x3,..,xN] l t trng vn u t vo danh mc 1 Ma trn Y = [y1, y2, y3,..,yN] l t trng vn u t vo danh mc 2, Hip phng sai ca 2 danh mc l Cov(1,2) = X S YT.YU CU:Xy dng ng bin hiu qu ca 1 th trng gm 5 chng khon (s dng s liu thc tin).

8.5 TNH TON MA TRN HIP PHNG SAICch 1:Da trn cng thc thng k v cc hm ca Excel, chng ta c th tnh ma trn phng sai hip phng sai:A l ma trn chnh lch t sut sinh li cc chng khon

8.5 TNH TON MA TRN HIP PHNG SAIMa trn chuyn v ca ma trn A:

Ma trn phng sai hip phng sai c tnh nh sau:

8.5 TNH TON MA TRN HIP PHNG SAIS dng hm COVAR kt hp vi hm Offset

Hm Covar(array1;array2): dng tnh hip phng sai ca 2 mng d liu (2 chui TSSL quan st)

Hm Offset(initial cells, rows, columns) s tham chiu khi cc tng ng v hnh dng vi cc gc ban u nhng thay i v tr sang cc hng v ct khc.

8.5 TNH TON MA TRN HIP PHNG SAIM hnh ch s nGi nh ca m hnh l t sut sinh li ca mi mt ti sn c th c hi quy tuyn tnh t cc ch s ca th trng:

T , chng ta c 2 lp lun: lp lun th nht ging m hnh CAPM v lp lun th 2 dng tnh ma trn phng sai hip phng sai:

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Chuong3-Chuong8-ToiUuPhiTuyen