Upravljanje razpršenosti portfeljev : delo diplomskega seminarja

Pirnovar, Andraž (author), Košir, Tomaž (mentor)

Razpršenost portfelja je pomemben dejavnik pri upravljanju z njim. Lahko jo predstavimo na veliko različnih načinov, v tem diplomskem delu pa se bomo osredotočili na razpršenost v odvisnosti od nekoreliranih virov tveganja, predstavljenimi z glavnimi portfelji. Ko imamo med sabo nekorelirane glavne portfelje, lahko na njihovi podlagi predstavimo razpršenost portfelja. To naredimo z eksponentom entropije razpršenostne porazdelitve, ki predstavlja približno število nekoreliranih virov tveganja. Na podlagi te vrednosti lahko izvedemo maksimizacijo z omejitvami, kjer omejitve predstavljajo portfeljske omejitve. Ko večkrat glede na investitorjeve preference tveganja zgradimo optimalni portfelj, te portfelje združimo v razpršenostno mejo. To metodo uporabimo na primeru kriptovalut, ki so med seboj zelo korelirane. Z njeno pomočjo najdemo glavne portfelje in razpršenostno mejo za uporabljene kriptovalute, hkrati pa primerjamo razpršenost glede na to metodo z razpršenostjo, ki temelji na optimalnem Sharpovem razmerju.

• Language: Slovenian
• Keywords: razpršenost portfelja, razpršenostna porazdelitev, glavni portfelj, meja povprečje-razpršenost, kriptovaluta
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-103667
• UDC: 519.8
• COBISS.SI-ID: 18478681
• Publication date in RUL: 21.09.2018

Secondary language

• Language: English
• Title: Managing Portfolio diversification

Abstract

Portfolio diversification plays a crucial role in portfolio management. It can be presented in various ways, but in this thesis, the focus will be on diversification based on uncorrelated sources of risk, presented with principal portfolios. Once we have found uncorrelated principal portfolios, we can use them to present the portfolio's diversification. This can be achieved by using the exponential of the diversification distribution's entropy, which represents an approximate number of uncorrelated sources of risk. On the basis of this value, a maximization can be carried out, with restrictions representing portfolio constraints. Depending on the investor's risk preference, we build multiple optimal portfolios, which we then join into a diversification frontier. This method is then used in the example of cryptocurrencies, which are highly correlated. With its help, we find the diversification frontier for the cryptocurrencies used. At the same time, we are comparing the diversification according to this method with the one based on optimal Sharpe ratio.

• Keywords: portfolio diversification, diversification distribution, principal portfolio, mean-diversification efficient frontier, cryptocurrency