Ubumenyi bwa Data kuri Portfolio Optimisation: Markowitz Hagati-Ibitekerezo

Inshingano zishoramari ni ikusanyirizo ryumutungo wimari, nkibigega, ingwate, cyangwa amafaranga, aho umuntu ashora imari. Ishoramari rigaragazwa ahanini ningaruka zaryo (uburyo agaciro gahindagurika) ninyungu zayo (ninyungu ziteganijwe). Abashoramari bafite intego yo kubaka portfolio igabanya ingaruka mugihe bagaruye inyungu.

Kubera ko ishoramari ryose ari ugusobanukirwa imibare, abacuruzi b'inzobere bakoresha tekinoroji yubumenyi nicyitegererezo kugirango batezimbere ingamba zabo zishoramari. Imwe muri ubwo buryo ni Moderi igezweho ya Portfolio (MPT), izwi kandi nka Markowitz Hagati-Itandukaniro. Icyitegererezo gitanga uburyo bwiza bwo gushora imari ukoresheje isuzuma ryibyago kandi bikagaruka cyane kubashoramari.

Reka twumve uruhare rwa siyanse yubumenyi mugushora imari neza, turebe ibitekerezo bya portfolio bigezweho, kandi tuganire kubitekerezo hamwe ningaruka zijyanye na siyanse yubumenyi.

Ibindi Kuri Markowitz Hagati-Itandukaniro

The Markowitz Mean-Variance Theory yasohowe bwa mbere na Harry Markowitz mu 1952. Igitekerezo cyerekana icyitegererezo gishingiye ku makuru asesengura imigendekere y’imari yo kugereranya ingaruka n’inyungu. Nkuko bisanzwe bigenda, ishoramari ryashyizwe mubikorwa nkibyago bike, kugaruka-bike, hamwe ningaruka nyinshi, kugaruka cyane. Mu magambo yoroshye, ishyiraho ko ishoramari rifite ingaruka nyinshi zitwara ibihembo byinshi naho ubundi.

MPT itanga amahitamo meza yishoramari iringaniza ingaruka zigihembo. Guhitamo kwanyuma kwishoramari nu mugabane wabo muri portfolio byerekana ingamba nziza zishoramari zishingiye kumibare yamakuru.

Siyanse Yihishe inyuma ya Theory Portfolio

Reka twumve imibare iri inyuma ya MPT. Ariko, ubanza, tugomba kumva amagambo yingenzi atuma imibare yimibare ishoboka.

• Ibiteganijwe kugaruka: Iyi ni ijanisha ryinyungu ziteganijwe kubushoramari. Irashobora kubarwa ukoresheje isesengura mibare yimiterere yamateka.

• Gutandukana bisanzwe: Ibi bigereranya ihindagurika ryumutungo runaka wimari. Ni igipimo cyibyago bijyana nishoramari, ni ukuvuga, umutungo utandukanye utwara ibyago byinshi nibihembo byinshi. Iragereranijwe kandi ukoresheje isesengura mibare yimibare yamakuru.

• Covariance: Ibi bigereranya isano iri hagati yumutungo utandukanye. Covariance ifasha mugukwirakwiza portfolio muguhindura uburemere bwumutungo bitewe na covariances.

Uhaye imigabane itatu, A, B, na C, reka twubake portfolio. Umushoramari afite intego yo kumenya umubare w'amafaranga yagenerwa imigabane. Kububiko bwatanzwe, reka dufate ko buri kigega gifite ibintu bikurikira.

Niba amafaranga yose yishoramari ari $ 1000, $ 200 ni kuri Stock A, $ 300 kuri B, na $ 500 kuri C. Urebye kugabana, kugaruka kwa portfolio biva hanze.

Ijanisha ryijanisha naryo rifatwa nkuburemere bwumwirondoro mugihe bagena umubare wishoramari rijya mumitungo.

Ikintu cya kabiri cyingenzi tugomba gusuzuma hano ni itandukaniro rya portfolio cyangwa Risk. Ibyago bya portfolio biragoye kubara kuko urebye kubana kumitungo itandukanye. Inshingano nziza munsi ya Markowitz ikubiyemo umutungo ufite isano ribi. Niba umutungo runaka ugabanutse, undi uzazamuka kandi uhangane nigihombo cyacyo, bigabanye ingaruka rusange.

Inzira ya portfolio itandukanye iba

Covariance igomba kubarwa kuri buri mutungo hamwe muri portfolio. Reka dufate ko umutungo wacu ufite matrisa ikurikira.

Urebye indangagaciro zifitanye isano no gutandukana bisanzwe, turashobora kubara covariances dukoresheje formula ikurikira:

Matrix ya covariance iba

Ukoresheje ibiciro byavuzwe haruguru, portfolio co-variance iba

Imipaka ikora neza

Urugero ruvuzwe haruguru rugaragaza uburyo bumwe bwo gushora imari. Igitekerezo cya Markowitz kirema ibintu byinshi nkibyo ukoresheje indangagaciro zitandukanye (uburemere). Inshingano zitandukanye zerekana urwego rutandukanye rwo kugaruka kubiciro byatanzwe (variance). Izi nshingano zitandukanye zigaragara ku mbonerahamwe yitwa Imipaka ikora neza.

Gukata byerekana ingaruka-ibihembo byubucuruzi aho abashoramari bashishikajwe nibintu byose biri hejuru yumurongo. Ikindi kintu gishimishije cyiyi mbonerahamwe ni umurongo wo kugabura Umurwa mukuru (CAL) uva ahantu hatagira ingaruka (Zero Standard-Deviation) kandi ugakora tangent kuruhande. Ingingo ifatika ifite ibihembo byinshi-byagereranijwe kandi ni byiza gushoboka gushora imari.

Ibyingenzi

Inshingano zishoramari zigizwe numutungo utandukanye nkimigabane na bonds. Buri mushoramari atangirana nigishoro gihamye kandi agahitamo amafaranga yo gushora muri buri mutungo. Ubuhanga bwa siyansi yamakuru nka Markowitz bisobanura-gutandukanya ibitekerezo bifasha kumenya kugabana umugabane mwiza kugirango wubake portfolio nziza.

Igitekerezo cyerekana imibare kugirango ihindure umutungo wagenewe kugirango ubone inyungu nini kurwego runaka. Isesengura umutungo wimari itandukanye kandi ikareba igipimo cy’inyungu n’impamvu zishobora guterwa, ukurikije amateka yabo. Igipimo cyo kugaruka nikigereranyo cyinyungu inyungu umutungo uzabyara mugihe runaka. Impamvu zishobora kugereranywa hakoreshejwe gutandukana bisanzwe agaciro k'umutungo. Gutandukana cyane byerekana umutungo uhindagurika, bityo, ibyago byinshi.

Garuka ningaruka zagaciro zibarwa kubintu bitandukanye bya portfolio kandi bigaragarira kumurongo ugaragara neza. Umurongo ufasha abashoramari kumenya inyungu nyinshi bahuye ningaruka bahisemo.