Model Black-Litterman in optimizacija donosa portfelja : delo diplomskega seminarja

Resnik, Tim (author), Košir, Tomaž (mentor)

V delu so najprej predstavljene osnove portfeljske teorije, kamor sodijo pojmi kot so vektor donosa, tržni portfelj, učinkovita meja, itd. Brez izpeljav je povzet CAPM model, na katerega se močno navezuje celoten model Black-Litterman. Na podlagi Markowitzevega problema alokacije sredstev, privatnih informacij in tržnega ravnovesja je vpeljan tradicionalen Black-Litterman model. Delo se nadaljuje s predstavo Black-Litterman modela v novi luči s pomočjo inverzne optimizacije. Naveden je tudi pomemben primer za preizkuševanje na koncu naloge, imenovan PV-IO. Inverzno optimizacijo modela se nadgradi in obenem poveča njeno uporabnost z vpeljavo drugačnih mer tveganja (npr.Var in CVaR). Podan je pomemben primer za testiranje, imenovan RPV-IO. V zadnjem delu naloge se novo vpeljane optimizacijske probleme in pripadajoče portfelje preizkusi najprej na simulacijah, nato pa še na zgodovinskih podatkih. V zaključku so podana mnenja o prednostih in slabostih novih modelov ter možnih nadaljnjih poteh raziskovanja.

• Language: Slovenian
• Keywords: portfeljska teorija, model Black-Litterman, inverzna optimizacija, mere tveganja
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-117587
• UDC: 519.8
• COBISS.SI-ID: 58161411
• Publication date in RUL: 17.07.2020

Secondary language

• Language: English
• Title: Black-Litterman model and portfolio return optimization

Abstract

The basics of the portfolio theory are presented in the beginning of the diploma, where the main concepts include vector of mean asset returns, market portfolio, efficient frontier, etc. Then, the CAPM model is presented because of the close relationship between it and the Black-Litterman model. Based on the Markowitz portfolio allocation problem, private informations and market equilibrium, the traditional Black-Litterman model is introduced. The paper continues with the reinterpretation of the Black-Litterman model with the help of the inverse optimization. At the end of the section, an important example in the form of PV-IO is presented. The general applicability of the model is broadened through alternative measures of risk (e.g. VaR and CVaR). An important example is again provided, this time in the form of RPV-IO. The last part of the diploma is concerned with testing the newly introduced optimization problems through simulations, and later on through backtesting. The main advantages and disadvantages are highlighted in the conclusion of the paper, along with propositions for further research.

• Keywords: portfolio theory, Black-Litterman model, inverse optimization, risk measures