A Comparative Study of Portfolio Optimization and Asset Allocation Models Using the R Programming Language.

Financial markets today are characterized by uncertainty and volatility, making portfolio optimization both essential and complex. This thesis examines three prominent portfolio optimization frameworks — Markowitz, CAPM, and Black–Litterman — with the guiding question: Which model performs better in constructing optimal portfolios under real market conditions? Using data from 50 selected S&P 500 stocks, each model is implemented in R to generate optimal portfolios, evaluated based on returns, variance, and Sharpe ratios. The thesis is organized into three chapters: the first reviews the theoretical foundations of each model, the second details their practical implementation, and the third provides an empirical comparison of their performance. Results show that Markowitz optimization achieves the highest in-sample returns and Sharpe ratios, particularly for the tangency portfolio, but at the cost of extreme and unstable allocations prone to overfitting. By contrast, the Black–Litterman model produces more conservative, diversified, and robust portfolios, offering greater stability and making it better suited to long-term or risk-averse investors. CAPM and the market portfolio serve as useful benchmarks, though their restrictive assumptions limit the overall practical effectiveness. Overall, the study underscores the trade-off between efficiency and stability in portfolio optimization and recommends aligning the choice of model with the investor’s risk tolerance and investment horizon. Future research could explore alternative risk measures and broader data sources to enhance portfolio robustness.