Optimizacija portfeljev za vrednostne papirje s težkimi repi
delo diplomskega seminarja
Abstract
Precej časa so znanstveniki domnevali, da so donosi vrednostnih papirjev porazdeljeni normalno, zaradi česar veliko modelov za optimizacijo portfelja temelji na normalni porazdelitvi. Eden najbolj popularnih je Markowitzev model optimizacije portfelja. Leta, ki so sledila po finančni krizi leta 2008, so pokazala, da sta tehnični napredek finančnih trgov in njihova globalizacija prinesla tudi nekaj novih izzivov oziroma vprašanj. Eden od teh je potreba po strategijah diverzifikacije, ki upoštevajo velike izgube in naraščajočo odvisnost od donosov sredstev v kriznih obdobjih. To je tudi povečalo pomen ne-Gaussovih modelov in odvisnosti od repa pri optimizaciji portfelja.
Zaradi empiričnih dokazov, ki temeljijo na različnih podatkih, je med strokovnjaki danes splošno sprejeto, da vrednosti finančnih instrumentov nakazujejo na težkorepo porazdelitev. Cilj tega dela diplomskega seminarja je tako opisati optimizacijo portfeljev, katerih vrednosti so slučajne spremenljivke s težkimi repi. Podrobneje bom opisala klasičen Markowitzev model, enako utežen portfelj in pristop z indeksom ekstremnih tveganj. Zadnja metoda izvira iz teorije ekstremnih vrednosti in je še posebej močna v primeru težkih repov, za katere je ta metoda tudi zasnovana. Zmanjšuje verjetnost velikih izgub in zato lahko pripomore k boljši vrednosti portfelja tudi v času visokega tveganja na trgih.
Na koncu bom raziskala kakšen potencial imajo opisane optimizacijske metode v praksi, pri čemer bo primerjava temeljila na testiranju za nazaj, kjer bom za podatke vzela dnevne cene delnic, ki sestavljajo indeks EURO STOXX 50 v obdobju od leta 2001 do leta 2011.
Keywords
finančna matematika;indeks ekstremnih tveganj;Markowitzev model;optimizacija portfelja;repno tveganje;teorija ekstremnih vrednosti;testiranje za nazaj;težkorepe porazdelitve;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2021 |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UL EF - Faculty of Economics |
| Publisher: | [E. Babnik] |
| UDC: | 519.2 |
| COBISS: |
76686851
|
| Views: | 1184 |
| Downloads: | 71 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Portfolio optimization for heavy-tailed assets |
| Secondary abstract: | It has been assumed for quite some time that assets returns are normally distributed, making many portfolio optimization models based on normal distributions. One of the most popular is Markowitz’s portfolio optimization model. The years following the 2008 financial crisis have shown that the technical progress of financial markets and their globalization have also brought up some new challenges as well as some issues. One of these is the need for a diversification strategy that takes into account large losses and the growing dependence of returns on assets in crisis periods. This also increased the importance of non-Gaussian models and tail dependence in portfolio optimization. Due to empirical evidence based on various data, it has been generally accepted today by the experts that the values of financial assets indicate a heavy-tailed distribution. The aim of this diploma thesis is to describe the optimization of portfolios, whose values are random variables with heavy tails. I will present in more detail the classic Markowitz model, the equally weighted portfolio and the optimization strategy based on the extreme risk index. The last method comes from extreme value theory and is especially strong in the case of heavy tails, for which this method is designed. It reduces the likelihood of large losses and can therefore contribute to improved portfolio values, even in times of high market risk. Finally, I will explore the potential of described optimization methods in practice with the comparison based on backtesting, where I will take the daily share prices of the components of the EURO STOXX 50 index for the period 2001-2011. |
| Secondary keywords: | extreme risk index;Markowitz model;portfolio optimization;tail risk;extreme value theory;backtesting;heavy-tailed distributions; |
| Type (COBISS): | Final seminar paper |
| Study programme: | 0 |
| Thesis comment: | Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja |
| Pages: | 28 str. |
| ID: | 13424976 |
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