Modificirani algoritem hierarhične paritete tveganja : magistrsko delo

Čampa, Gašper (author), Košir, Tomaž (mentor), Jerovšek, Jure (co-mentor)

Leta 2016 je Marcos López de Prado objavil model hierarhične paritete tveganja (angl. hierarchical risk parity (HRP)). Model sloni na hierarhičnem rojenju (angl. clustering) kovariančne matrike pričakovanih donosov in uravnoteženmu razporejanju uteži po rojih. HRP model je numerično stabilnejši kot modeli povprečje-varianca, saj tekom konstruiranja optimalnega portfelja ne potrebuje inverza kovariančne matrike. V magistrskem delu bom razširil HRP algoritem z vpeljavo investitorjevih ocenah o pričakovanih donosih ter z algoritmom mej, ki prilagodi predlagani optimalni portfelj z uporabniškimi omejitvami uteži po naložbah. Na podlagi narejenih primerjav med optimizacijskimi metodami, bomo videli, da HRP algoritem optimizira portfelj podobno kot alokacija sredstev, izbrana na učinkoviti meji z najmanjšim standardnim odklonom. Za investitorje, ki želijo imeti konzervativen portfelj, je to zelo dobrodošlo, saj HRP algoritem zmore optimizirati portfelj tudi na podlagi singularne kovariančne matrike (česar večina optimizacijskih metod ne zmore). Poleg doseganja podobnih rezultatov je bil s HRP algoritmom optimiziran portfelj bolj razpršen. Tudi modificiran HRP algoritem se na podlagi narejenih primerjav izkaže za konkurenčno optimizacijsko metodo. Modificiran algoritem uspešno alocira uteži tudi na podlagi pričakovanih donosnosti, kar omogoča vpeljavo investitorjevih ocen.

• Language: Slovenian
• Keywords: strojno učenje, optimizacija portfelja, Black-Litterman model, učinkovita meja, hierarhična pariteta tveganja
• Work type: Master's thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-108169
• UDC: 519.8
• COBISS.SI-ID: 18660185
• Publication date in RUL: 20.06.2019

Secondary language

• Language: English
• Title: Modified hierarchical risk parity algorithm

Abstract

In 2016 Marcos López de Prado published a Hierarchial Risk Parity (HRP) model. The model clusters covariance matrix of expected returns and allocates portfolio weights among clusters. Compared to traditional mean-variance models the HRP model is numerically more stable, because it does not need to compute the inverse of covariance matrix. In my thesis I will expand the HRP model by incorporating investors views on expected returns and by introducing algorithm of constraints, which modifies suggested optimal portfolio with users assets allocations constraints. Based on comparisons between optimization methods I have made, we shall see that HRP algorithm optimizes portfolio similar as selecting minimum variance portfolio on efficient frontier. For investors, wishing to have a conservative portfolio, is this very welcoming, because the HRP algorithm can optimize the portfolio even on singular covariance matrix (which a lot of optimization methods can not do). Besides achieving similar results the portfolio optimized with HRP algorithm was also more disperse. Based on made comparisons it turns out the modified HRP algorithm is also competitive optimization method. The modified algorithm successfully allocates portfolio weights based on expected returns, which allows for incorporating investors views.

• Keywords: machine learning, portfolio optimization, Black-Litterman model, efficient frontier, hierarchical risk parity