| Title |
From markowitz's mean-variance portfolio optimization to conditional value-at-risk / |
| Translation of Title |
Nuo Markowitz vidurkio-dispersijos portfelio optimizavimo iki sąlyginės vertės pokyčio rizikos. |
| Authors |
Marcinkevičiūtė, Agnė |
| Full Text |
|
| Pages |
28 |
| Keywords [eng] |
mean-variance, CVaR, efficient frontier, Bitcoin, copula, non-parametric, vidurkis–dispersija, CVaR, efektyvumo frontas, Bitkoinas, kopula, neparametrinis modelis. |
| Abstract [eng] |
This master’s thesis explores methods of portfolio optimization. Starting from the meanvariance approach Sharpe ratio is calculated and the efficient frontier is plotted to minimize the variance for different returns. To assess the tail risk of the return distribution Conditional Valueat- Risk (CVaR) is estimated. Data includes stock and Bitcoin closing prices and is obtained from Yahoo Finance [12]. The code for the empirical analysis is produced using Matlab programming language [6]. As Bitcoin price is highly volatile and might behave asymmetrically to traditional assets non-parametric methods are used to estimate CVaR. The usage of copulas allows to estimate the distribution of return vectors by modeling marginals individually. To estimate the copula density the kernel density is used. Simulated returns from the estimation are used to optimize CVaR. The contribution to the research lies in the utilization of non-parametric methods to analyze Bitcoin expected return and risk trade-off. Therefore, in this analysis risk perception of investors is analyzed in highly volatile market conditions. The aim of this thesis is to compare both optimization methods for a portfolio consisting of both traditional and non-traditional assets. Results indicate that CVaR creates a more diversified portfolio than mean-variance model. Also, CVaR allocates at least 10% of funds to Bitcoin for all portfolios, as it is viewed as a non-linear return driver. Mean-variance model increases allocation to Bitcoin with the growth of portfolio risk, because it sees volatility directly as risk. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Master thesis |
| Language |
English |
| Publication date |
2025 |
