ISayensi yeDatha yoLungiso lwePotfoliyo: Ithiyori ye-Markowitz Mean-Variance

Ipotfoliyo yotyalo-mali yingqokelela yempahla yezemali, enjengezitokhwe, iibhondi, okanye i-cryptocurrency, apho umntu atyala imali. Utyalo-mali luchongwa ngumngcipheko walo (ubungakanani bexabiso eliguqukayo) kunye nembuyekezo yalo (ithini inzuzo elindelekileyo). Abatyali-mali bajonge ukwakha ipotifoliyo enciphisa umngcipheko ngelixa besandisa imbuyekezo.

Ekubeni utyalo-mali lumalunga nokuqonda amanani, abarhwebi abaziingcali basebenzisa ubuchule besayensi yedatha kunye neemodeli zokwandisa isicwangciso sabo sotyalo-mali. Enye imodeli enjalo yiTheory yePotfoliyo yanamhlanje (MPT), ekwabizwa ngokuba yiMarkowitz Mean-Variance Theory. Imodeli ibonelela ngeyona potfoliyo yotyalo-mali igqwesileyo kusetyenziswa uvavanyo lomngcipheko kwaye yandisa imbuyekezo kumtyali-mali.

Masiqonde indima yenzululwazi yedatha ekwenzeni utyalo-mali olusebenzayo, sijonge ithiyori yepotfoliyo yale mihla ngokweenkcukacha, kwaye sixoxe ngeengqikelelo kunye neengozi ezinxulumene neemodeli zesayensi yedatha.

Ngakumbi kwi-Markowitz Mean-Variance Theory

I-Markowitz Mean-Variance Theory yaqala ukupapashwa nguHarry Markowitz kwi-1952. Ithiyori ibonisa imodeli esekelwe kwidatha ehlalutya iindlela zemali ukuqikelela umngcipheko kunye nokubuyisela. Njengomgaqo wesithupha, utyalo-mali luhlelwa njengomngcipheko ophantsi, imbuyekezo ephantsi, kunye nomngcipheko ophezulu, imbuyekezo ephezulu. Ngamagama alula, imisela ukuba utyalo-mali olunomngcipheko ophezulu wokufumana umvuzo ophezulu kwaye ngokuphambeneyo.

I-MPT ibonelela ngokhetho olulolona lufanelekileyo lotyalo-mali olulinganisa umngcipheko womvuzo. Ukhetho lokugqibela lotyalo-mali kunye nesabelo salo kwipotfoliyo imele isicwangciso sotyalo-mali esifanelekileyo esisekwe kwiintsingiselo zedatha.

INzululwazi eNgemva kweTheory yePotfoliyo yanamhlanje

Masiqonde imathematika emva kweMPT. Nangona kunjalo, okokuqala, kufuneka siqonde amagama ambalwa abalulekileyo enza ukuba imodeli yemathematika ibe nokwenzeka.

• Imbuyekezo elindelekileyo: Le yipesenti yembuyekezo elindelekileyo kutyalo-mali. Inokubalwa kusetyenziswa uhlalutyo lwamanani lweentsingiselo zembali.

• Ukutenxa eMgangathweni: Oku kulinganisa ukuguquguquka kwempahla ethile eyimali. Ngumlinganiselo womngcipheko onxulumene notyalo-mali, oko kukuthi, i-asethi ephezulu yomahluko inomngcipheko omkhulu kunye nomvuzo ophezulu. Kwakhona kuqikelelwa kusetyenziswa uhlalutyo lweenkcukacha-manani kwiintsingiselo zedatha.

• I-Covariance: Oku kuqikelela ubudlelwane phakathi kwee-asethi ezahlukeneyo. I-Covariance inceda ukwandisa ukuhanjiswa kweepotfoliyo ngokuguqula ubunzima be-asethi ngokuxhomekeke kwii-covariances.

Sinikwe izitokhwe ezintathu, A, B, kunye no-C, masenze ipotfoliyo. Umtyali-mali ujonge ukufumanisa ukuba zingaphi iimali eziya kwabela nasiphi na isitokhwe. Kwizitokhwe ezinikiweyo, masicinge ukuba isitokhwe ngasinye siphethe ezi mpawu zilandelayo.

Ukuba isixa-mali esipheleleyo sotyalo-mali yi-$ 1000, i-$ 200 ye-Stock A, i-$ 300 ye-B, kunye ne-$ 500 ye-C. Ukunikezelwa kokusasazwa, imbuyekezo yepotfoliyo ephakathi ivela.

Iipesenti zolwabiwo nazo zikwajongwa njengobunzima beprofayili njengoko zimisela ukuba lungakanani utyalo-mali olungena kweyiphi i-asethi.

Into yesibini ebalulekileyo ekufuneka iqwalaselwe apha kukwahluka kwepotfoliyo okanye uMngcipheko. Umngcipheko wepotfoliyo unzima ukubala njengoko uqwalasela i-covariance yee-asethi ezahlukeneyo. Ipotfoliyo efanelekileyo phantsi kwemodeli ye-Markowitz ibandakanya i-asethi ene-negative correlation. Ukuba i-asethi ethile iyehla, enye iya kunyuka kwaye ithintele ilahleko yayo, inciphisa umngcipheko wepotfoliyo iyonke.

Ifomula yomahluko wepotfoliyo iba

I-covariance kufuneka ibalwe ngesibini ngasinye se-asethi kwipotfoliyo. Masicinge ukuba ii-asethi zethu zinale matrix yolungelelwaniso ilandelayo.

Ukuqwalasela amaxabiso olungelelaniso kunye nokutenxa komgangatho ongentla, sinokubala i-covariances sisebenzisa le fomula ilandelayo:

I-covariance matrix iba

Ngokusebenzisa la maxabiso abalwe ngasentla, ukwahluka kwepotfoliyo yethu kuba

Umda osebenzayo

Lo mzekelo ungasentla ubonisa ukuba nokwenzeka kwepotfoliyo yotyalo-mali. Ithiyori kaMarkowitz idala imidibaniso emininzi yeepotfoliyo ezinjalo kusetyenziswa amaxabiso ahlukeneyo olwabiwo (ubunzima). Iipotifoliyo ezahlukeneyo zibonisa amanqanaba ahlukeneyo embuyekezo ngexabiso elinikiweyo lomngcipheko (umahluko). Ezi potfoliyo zahlukeneyo zibonwa kwitshati ebizwa ngokuba yi-Efficient Frontier.

Ijika libonisa ukurhweba ngomngcipheko apho abatyali-mali banomdla kuyo yonke into engaphezulu komgca. Enye into enomdla yale tshati ngumgca we-Capital Allocation (CAL) osuka kwindawo engenamngcipheko (i-Zero Standard-Deviation) kwaye yenza i-tangent ngaphesheya kwegophe. Indawo ye-tangent inowona mlinganiselo uphezulu womvuzo-kumngcipheko kwaye yeyona potfoliyo inokwenzeka kutyalo-mali.

Izinto eziphambili zokuThatha

Ipotfoliyo yotyalo-mali iquka ii-asethi ezahlukeneyo ezifana nezitokhwe kunye neebhondi. Umtyali-mali ngamnye uqala ngenkunzi yotyalo-mali esisigxina kwaye enze isigqibo sokuba yimalini oza kuyityala kwi-asethi nganye. Ubuchule benzululwazi yedatha obufana nethiyori yentsingiselo-yantlukwano yeMarkowitz inceda ukumisela elona sabelo silungileyo solwabiwo ukwakha ipotifoliyo eyiyeyona.

Ithiyori iqulunqa imodeli yemathematika yokwandisa ulwabiwo lwee-asethi ukufumana eyona nzuzo iphezulu kwinqanaba lomngcipheko onikiweyo. Ihlalutya ii-asethi zemali ezahlukeneyo kwaye ithathela ingqalelo ireyithi yembuyekezo kunye nemiba yomngcipheko, ngenxa yeendlela zazo zembali. Umlinganiselo wembuyekezo luqikelelo lwenzuzo engakanani i-asethi eya kuyenza ngexesha elithile. Umngcipheko ubalwa kusetyenziswa ukutenxa okusemgangathweni kwexabiso le-asethi. Ukutenxa okuphezulu kubonisa i-asethi eguquguqukayo kwaye, ngenxa yoko, umngcipheko ophezulu.

Amaxabiso embuyekezo kunye nomngcipheko abalwa kwiiphothifoliyo ezahlukeneyo zendibaniselwano kwaye zimelwe kumda osebenzayo wegophe. Igophe linceda abatyali-mali ukuba babone imbuyekezo ephezulu ngokuchasene nomngcipheko abawukhethileyo.