Bayesian Optimization and Monte Carlo Simulation in Technology Sector Portfolio Allocation: A Comparative Analysis Using the Sharpe Ratio

Abstract

In the dynamic landscape of financial markets, the pivotal role of adept portfolio construction is more prominent than ever. By enabling investors to form combinations of assets, it not only aids in accomplishing specified investment objectives but also in diversifying potential risks. This process employs a systematic investment approach, fostering informed and judicious decision-making strategies in the financial domain. This research seeks to explore the application of Bayesian statistics in parameter estimation and portfolio optimization, particularly focusing on the volatility of the technology sector. Utilizing a conjugate prior to obtaining the posterior and employing Maximum Likelihood Estimation (MLE) to calculate the expected return and covariance matrix, the study constructed portfolio weights based on Mean-Variance Optimization. This portfolio was then compared with weights derived from historical data analysis and a Monte Carlo simulation optimized by the Sharpe ratio. Remarkably, upon empirical testing on an out-of-sample dataset, the Bayesian approach exhibited a superior performance, showcasing robust resilience to potential risks. The study also acknowledges several limitations, suggesting directions for future research to refine the precision and reliability of portfolio optimization in the face of market volatility.