Optimizing Bond Portfolios Using Yield Curve Analysis

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.