Optimizing Bond Portfolios Using Yield Curve Analysis

Erik Pitoňák

Master's thesis

Abstract:

This diploma thesis examines optimization for a maximum Sharpe Ratio (SR) portfolio of Czech government bonds using principal component analysis (PCA) complemented with Monte Carlo simulation. The study begins by analyzing the term structure of interest rates, reviewing PCA's effectiveness in modeling term structures, and examining portfolio optimization strategies. In the empirical section, PCA is applied to historical data on Czech government bond indices to extract principal components. These components are then used in Monte Carlo simulations to generate future yield curve scenarios and possible portfolio returns. The PCA method effectively reconstructs the yield curve in a reduced dimension, capturing significant variance, as supported by existing literature. While some limitations are present related to the type of data or initial output, the optimization results demonstrate effective weight adjustments that can enhance portfolio performance, validating the applicability of combining PCA and Monte Carlo simulation methods.

Abstract:

This diploma thesis examines optimization for a maximum Sharpe Ratio (SR) portfolio of Czech government bonds using principal component analysis (PCA) complemented with Monte Carlo simulation. The study begins by analyzing the term structure of interest rates, reviewing PCA's effectiveness in modeling term structures, and examining portfolio optimization strategies. In the empirical section, PCA is applied to historical data on Czech government bond indices to extract principal components. These components are then used in Monte Carlo simulations to generate future yield curve scenarios and possible portfolio returns. The PCA method effectively reconstructs the yield curve in a reduced dimension, capturing significant variance, as supported by existing literature. While some limitations are present related to the type of data or initial output, the optimization results demonstrate effective weight adjustments that can enhance portfolio performance, validating the applicability of combining PCA and Monte Carlo simulation methods.

Keywords

Fixed income portfolio, Principal Component Analysis (PCA), Sharpe Ratio (SR), Monte Carlo Simulation, Optimization methods

Keywords

Fixed income portfolio, Principal Component Analysis (PCA), Sharpe Ratio (SR), Monte Carlo Simulation, Optimization methods

Language used: English

Date on which the thesis was submitted / produced: 15. 6. 2024

Thesis defence

• Date of defence: 11. 9. 2024
• Supervisor: Jiří Witzany
• Reader: Martin Babušík

Vysoká škola ekonomická v Praze

Master programme:
Finance and Accounting