Modern Portfolio Theory – A Theoretical Framework for Portfolio Optimization and Risk Management

This short study demonstrates the foundational ideas of Modern Portfolio Theory (MPT), showing how diversification, optimization, and risk measurement work in practice. It begins with the core mathematical principles — expected return, portfolio volatility, and the Sharpe ratio — then builds up to the efficient frontier, the tangency portfolio, and the Capital Market Line (CML) using real market data. The report also visualizes key risk metrics such as Value at Risk (VaR) and Expected Shortfall (ES), comparing empirical and parametric estimates to highlight the limitations of assuming normality in financial returns.

Highlights

• Derivation and explanation of MPT fundamentals (Markowitz 1952)
• Efficient frontier and capital market line visualizations
• Implementation of global minimum variance and tangency portfolios
• Empirical illustration of diversification and risk-return trade-offs
• Practical computation and visualization of VaR and Conditional VaR (ES)

Visual Insights

• Efficient Frontier Plot: shows the transition from single risky assets to optimized portfolios.
• VaR & ES Plot: illustrates how tail-risk measures quantify downside exposure.

References

Markowitz (1952), Sharpe (1966), Jorion (2007)