Data Sayenzi yePortfolio Optimization: Markowitz Mean-Variance Theory

Mari yekudyara muunganidzwa wezvinhu zvemari, zvakaita semasheya, mabhondi, kana cryptocurrency, umo munhu anodyara. Mari yekudyara inonyanya kuzivikanwa nenjodzi yayo (kuderera kwakadii kukosha) uye kudzoka kwayo (chii chinotarisirwa kuwana). Vagadziri vemari vanovavarira kuvaka portfolio inoderedza njodzi uku vachiwedzera kudzoka.

Sezvo kudyara kuri kwese kwekunzwisisa huwandu, vatengesi vane hunyanzvi vanoshandisa data sainzi matekiniki uye modhi kuti vakwanise hurongwa hwavo hwekudyara. Imwe mhando yakadai ndeye Modern Portfolio Theory (MPT), inozivikanwawo seMarkowitz Mean-Variance Theory. Iyo modhi inopa yakakwana yekudyara portfolio uchishandisa njodzi yekuongorora uye inowedzera kudzoka kune investor.

Ngatinzwisisei basa resainzi yedata mukuita mari yakanaka, titarise dzidziso yemazuva ano yepotfolio, uye tikurukure fungidziro nenjodzi dzine chekuita nemhando dzesainzi yedata.

Zvimwe Pamusoro peMarkowitz Mean-Variance Theory

The Markowitz Mean-Variance Theory yakatanga kubudiswa naHarry Markowitz muna 1952. Dzidziso inopa data-based model iyo inoongorora maitiro emari kuti ienzanise ngozi nekudzoka. Sekutonga kwechigunwe, mari yekudyara inoiswa muchikamu seyakaderera-njodzi, yakaderera-kudzoka, uye yakanyanya-njodzi, yakakwirira-kudzoka. Mumashoko akareruka, inosimbisa kuti mari yekudyara ine njodzi yepamusoro inotakura mubairo wepamusoro uye zvinopesana.

MPT inopa sarudzo yakakwana yekudyara inoyera kunze kwengozi yemubairo. Kusarudzwa kwekupedzisira kwekudyara uye mugove wavo mupodfolio inomiririra yakanakira nzira yekudyara yakavakirwa pane data maitiro.

Sayenzi Kuseri Kwemazuva Ano Portfolio Theory

Ngatinzwisisei masvomhu ari kumashure kweMPT. Nekudaro, chekutanga, isu tinofanirwa kunzwisisa mashoma akakosha mazwi anoita kuti iyo masvomhu modhi igoneke.

• Zvinotarisirwa Kudzoka: Iyi ndiyo chiyero chekudzoka chinotarisirwa kubva mukudyara. Inogona kuverengwa uchishandisa nhamba yekuongorora yezvakaitika kare.

• Standard Deviation: Izvi zvinoyera kusagadzikana kwechimwe chinhu chemari. Ndiyo chiyero chenjodzi inosanganisirwa nekudyara, kureva kuti, yakakwira mutsauko asset inotakura njodzi huru uye mubairo mukuru. Inofungidzirwawo kushandisa nhamba yekuongorora maitiro e data.

• Covariance: Izvi zvinofungidzira hukama pakati pezvinhu zvakasiyana. Covariance inobatsira kukwirisa kugovaniswa kwepodfolio nekushandura huremu hweasset zvichienderana necovariances.

Tichipihwa masheya matatu, A, B, uye C, ngativake portfolio. An investor ane chinangwa chekuona kuti ingani mari yekugovera kune chero stock. Pamastock akapihwa, ngatifungei kuti stock yega yega ine zvinotevera maficha.

Kana mari yese yekudyara iri $1000, $200 ndeyeStock A, $300 yeB, uye $500 yeC. Zvichipa kugoverwa, iyo inorehwa portfolio yekudzoka inobuda.

Mapeji ekugoverwa anotariswawo huremu hweprofile sezvo ivo vachiona kuti imarii mari inopinda mune ipi asset.

Chechipiri chakakosha chekutarisa pano musiyano wepodfolio kana Njodzi. Portfolio ngozi ine tricker kuverenga sezvo ichifunga covariance yezvinhu zvakasiyana. Iyo yakakwana portfolio pasi peiyo Markowitz modhi inosanganisira midziyo ine isina kunaka kuwirirana. Kana imwe asset yadzikira, imwe inosimuka yopikisa kurasikirwa kwayo, zvichideredza njodzi yeportfolio yese.

Iyo fomula yekusiyana kwepodfolio inova

Iyo covariance inoda kuverengerwa kune yega yega asset pair mune portfolio. Ngatifungei kuti midziyo yedu ine inotevera correlation matrix.

Tichifunga nezve kukosha kwekubatanidza uye nepamusoro chiyero kutsauka, tinogona kuverenga iyo covariances tichishandisa inotevera fomula:

Iyo covariance matrix inova

Uchishandisa izvo zvakaverengerwa pamusoro, yedu portfolio co-variance inova

Inoshanda Frontier

Muenzaniso uri pamusoro unoratidza mukana mumwe chete wekudyara portfolio. Dzidziso yaMarkowitz inogadzira misanganiswa yakawanda yemapotifoliyo akadaro uchishandisa magovero akasiyana (maremu). Iwo akasiyana mapotifolio anoratidza akasiyana mazinga ekudzoka kune yakapihwa njodzi kukosha (kusiyana). Aya mapotfolio akasiyana anoonekwa pachati inonzi Efficient Frontier.

Iyo curve inomiririra njodzi-mubairo kutengeserana-kure uko vanoisa mari vanofarira mune zvese zviri pamusoro pemutsara. Chimwe chinonakidza chechati iyi mutsara weCapital Allocation (CAL) unomhanya kubva panzvimbo isina njodzi (Zero Standard-Deviation) uye inoumba tangent kuyambuka curve. Iyo tangent poindi ine mubairo wepamusoro-kune-njodzi reshiyo uye ndiyo yakanakisa portfolio yekudyara.

Key Takeaways

Imari yekudyara inosanganisira zvinhu zvakasiyana siyana semasheya nemabhondi. Wese investor anotanga neyakagadziriswa mari yekudyara uye anosarudza kuti yakawanda sei yekudyara mune imwe neimwe asset. Maitiro esainzi yedata senge Markowitz zvinoreva-mutsauko dzidziso inobatsira kuona iyo yakakwana yekugovaniswa yekuvaka iyo yakakwana portfolio.

Dzidziso inogadzira modhi yemasvomhu kuti ikwidze kugovewa kwezvinhu kuti uwane kudzoka kwakanyanya kune yakapihwa nhanho. Inoongorora hupfumi hwakasiyana-siyana uye inotarisa chiyero chavo chekudzoka uye nengozi zvinhu, zvichipiwa maitiro avo ezvakaitika kare. Mutengo wekudzoka ndeye fungidziro yekuti yakawanda sei purofiti iyo asset ichaunza pane imwe nguva yakatarwa. Iyo njodzi inoverengerwa uchishandisa chiyero kutsauka kweiyo asset kukosha. Kutsauka kwepamusoro kunomiririra chinhu chinoshanduka uye, nekudaro, njodzi yakanyanya.

Kudzosa uye kukosha kwengozi kunoverengerwa kune akasiyana mapotifolio misanganiswa uye inomiririrwa painoshanda miganhu curve. Iyo curve inobatsira vanoisa mari kuona iyo yakanyanya kudzoserwa panjodzi yavo yakasarudzwa.