Isayensi Yedatha Yokuthuthukisa Iphothifoliyo: I-Markowitz Mean-Variance Theory

Iphothifoliyo yokutshala imali iqoqo lezimpahla zezezimali, njengezitoko, amabhondi, noma i-cryptocurrency, lapho umuntu etshala khona imali. I-investimenti ibonakala kakhulu ngengozi yayo (ukuthi inani lishintshashintsha kangakanani) kanye nembuyiselo yalo (iyini inzuzo elindelekile). Abatshalizimali bahlose ukwakha iphothifoliyo enciphisa ubungozi kuyilapho andisa imbuyiselo.

Njengoba ukutshalwa kwezimali kumayelana nokuqonda izinombolo, abathengisi abangongoti basebenzisa amasu esayensi yedatha namamodeli ukuze bathuthukise isu labo lokutshala imali. Enye imodeli enjalo i-Modern Portfolio Theory (MPT), eyaziwa nangokuthi i-Markowitz Mean-Variance Theory. Imodeli ihlinzeka ngephothifoliyo yokutshalwa kwezimali efanelekile isebenzisa ukuhlolwa kobungozi futhi yandise imbuyiselo kubatshalizimali.

Masiqonde indima yesayensi yedatha ekwenzeni ukutshalwa kwezimali okuphumelelayo, sibheke ithiyori yephothifoliyo yesimanje ngokuningiliziwe, futhi sixoxe ngokuqagela nezingozi ezihlobene namamodeli esayensi yedatha.

Okuningi ku-Markowitz Mean-Variance Theory

I-Markowitz Mean-Variance Theory yanyatheliswa okokuqala ngu-Harry Markowitz ngo-1952. Ithiyori iveza imodeli esekelwe kudatha ehlaziya izitayela zezimali ukuze kulinganiswe ubungozi kanye nembuyiselo. Njengomthetho wesithupha, ukutshalwa kwezimali kuhlukaniswa njengengcuphe ephansi, inzuzo encane, kanye nengcuphe ephezulu, imbuyiselo ephezulu. Ngamagama alula, ithola ukuthi ukutshalwa kwezimali okunobungozi obuphezulu kunomvuzo ophezulu futhi okuphambene nalokho.

I-MPT ihlinzeka ngokukhetha okuphelele kokutshalwa kwezimali okulinganisa ubungozi bokuthola umvuzo. Ukukhethwa kokugcina kwezimali ezitshaliwe kanye nesabelo sazo kuphothifoliyo kumelela isu elihle lokutshala imali elisuselwe kumathrendi edatha.

I-Science Behind the Modern Portfolio Theory

Masiqonde izibalo ezingemuva kwe-MPT. Kodwa-ke, okokuqala, kufanele siqonde amagama ambalwa ayisihluthulelo enza imodeli yezibalo yenzeke.

• Okulindelekile Imbuyiselo: Lena iphesenti lembuyiselo elindeleke ku-investimenti. Ingabalwa kusetshenziswa ukuhlaziya kwezibalo kwamathrendi omlando.

• Ukuchezuka Okujwayelekile: Lokhu kulinganisa ukuntengantenga kwempahla ethile yezezimali. Kuyisilinganiso sengozi ehlotshaniswa nokutshalwa kwezimali, okungukuthi, impahla ehlukile ephezulu inengcuphe ephezulu kanye nomvuzo omkhulu. Kuphinde kulinganiswe kusetshenziswa ukuhlaziya kwezibalo kwamathrendi edatha.

• I-Covariance: Lokhu kulinganisa ubuhlobo phakathi kwempahla ehlukene. I-Covariance isiza ukuthuthukisa ukusatshalaliswa kwephothifoliyo ngokushintsha izisindo zempahla kuye ngama-covariances.

Njengoba kunikezwe izitoko ezintathu, A, B, no-C, ake sakhe iphothifoliyo. Umtshali-zimali uhlose ukuthola ukuthi zingaki izimali ezizokwabela noma yisiphi isitoko. Ezitokweni ezinikeziwe, ake sicabange ukuthi isitoko ngasinye siphethe izici ezilandelayo.

Uma isamba senani lokutshalwa kwezimali lingu-$1000, i-$200 eyesitoko A, i-$300 ye-B, kanye ne-$500 ka-C. Uma kubhekwa ukusatshalaliswa, imbuyiselo yephothifoliyo emaphakathi ivela.

Amaphesenti okunikezwa nawo abhekwa njengezisindo zephrofayela njengoba enquma ukuthi ingakanani utshalomali olungena kuyiphi impahla.

Isici sesibili esibalulekile okufanele sicatshangelwe lapha ukwehluka kwephothifoliyo noma Ubungozi. Kunzima ukubala ubungozi bephothifoliyo njengoba kucutshungulwa ukuhambisana kwezimpahla ezahlukene. Iphothifoliyo efanelekile ngaphansi kwemodeli ye-Markowitz ihlanganisa amafa anokuxhumana okungekuhle. Uma impahla ethile yehla, enye izokhuphuka futhi ibhekane nokulahlekelwa kwayo, inciphise ubungozi bephothifoliyo iyonke.

Ifomula yokuhluka kwephothifoliyo iba

I-covariance idinga ukubalwa kupheya ngayinye yempahla kuphothifoliyo. Ake sicabange ukuthi izimpahla zethu zine-matrix yokuhlobana elandelayo.

Ngokucabangela amanani okuxhumana kanye nokuchezuka okujwayelekile okungenhla, singabala ama-covariances sisebenzisa ifomula elandelayo:

I-covariance matrix iba

Ngokusebenzisa amanani abalwe ngenhla, ukuhluka ngokubambisana kwephothifoliyo yethu kuba

I-Frontier Ephumelelayo

Isibonelo esingenhla sibonisa ukuthi kungenzeka kube nephothifoliyo yokutshala imali. Ithiyori kaMarkowitz idala izinhlanganisela eziningi zamaphothifoliyo anjalo kusetshenziswa amanani ahlukene okwabiwa (izisindo). Amaphothifoliyo ahlukene abonisa amazinga ahlukahlukene ezimbuyiselo yenani elithile lengozi (ukwehluka). Lawa maphothifoliyo ahlukene aboniswa eshadini elibizwa ngokuthi i-Efficient Frontier.

Ijika limele ukuhwebelana komvuzo lapho abatshalizimali benentshisekelo kukho konke okungaphezulu komugqa. Enye into ethokozisayo yaleli shadi ulayini Wokwabiwa Kwemali (CAL) osuka endaweni engenazo ubungozi (Zero Standard-Deviation) bese wenza i-tangent ngaphesheya kwejika. Iphoyinti le-tangent linesilinganiso esiphakeme kakhulu somvuzo ukuya engcupheni futhi iphothifoliyo engcono kakhulu yokutshalwa kwezimali.

Okuthathwayo Okubalulekile

Iphothifoliyo yokutshalwa kwezimali ihlanganisa izimpahla ezihlukahlukene njengezitoko namabhondi. Wonke umtshali-zimali uqala nge-investimenti yemali engaguquki futhi anqume ukuthi uzotshala malini kumpahla ngayinye. Amasu esayensi yedatha afana nethiyori ye-Markowitz mean-variance asiza ukunquma isabelo esilungile sokwabelana ukuze kwakhiwe iphothifoliyo elungile.

Itiyori ibumba imodeli yezibalo ukuze ithuthukise ukwabiwa kwempahla ukuze ithole imbuyiselo ephezulu yeleveli yobungozi ethile. Ihlaziya izimpahla zezezimali ezihlukene futhi icabangele izinga lazo lembuyiselo nezici zobungozi, uma kubhekwa amathrendi azo omlando. Izinga lembuyiselo liwukulinganiselwa kokuthi yimalini inzuzo ezotholwa yimpahla esikhathini esithile. Isici sobungozi silinganiswa kusetshenziswa ukuchezuka okujwayelekile kwevelu yempahla. Ukuchezuka okuphezulu kumelela impahla eguquguqukayo, ngakho-ke, ingozi ephezulu.

Imbuyiselo kanye namanani engozi abalwa ezinhlanganisela ezihlukahlukene zephothifoliyo futhi amelelwa ejikeni elisebenza kahle lomngcele. Ijika lisiza abatshalizimali ukuthi banqume imbuyiselo ephezulu uma beqhathaniswa nengcuphe abayikhethile.