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.    Le yipesenti yembuyekezo elindelekileyo kutyalo-mali. Inokubalwa kusetyenziswa uhlalutyo lwamanani lweentsingiselo zembali. Imbuyekezo elindelekileyo:    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. Ukutenxa eMgangathweni:    Oku kuqikelela ubudlelwane phakathi kwee-asethi ezahlukeneyo. I-Covariance inceda ukwandisa ukuhanjiswa kweepotfoliyo ngokuguqula ubunzima be-asethi ngokuxhomekeke kwii-covariances. I-Covariance:     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.

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