How Modern Portfolio Theory Helps Investors Manage Risk in Volatile Markets

Value-at-Risk (VaR) is a widely used risk management tool in financial markets to quantify potential portfolio losses at a given confidence level. Traditional VaR estimation methods, such as Variance-Covariance, Historical Simulation, and Monte Carlo Simulation, are not efficient when markets exhibit fat tails, volatility clustering, or structural breaks leading to continuous evolution in VaR estimation. This study adopted a mixed-methods design, combining a critical literature review on the transformation in Modern Portfolio Theory (MPT) with quantitative empirical analysis implemented in R. The reviewed empirical studies demonstrate a shift in MPT modelling algorithms toward adaptive ML and hybrid models, which improve VaR estimation, highlighting the growing need to address dynamic market risks in the stock market. Empirically, the study investigates four national equity indices: S&P 500 (United States), FTSE 100 (United Kingdom), Shanghai Composite (China), and Nikkei 225 (Japan). Daily data from January 2022 to October 2025 were analyzed. Risk exposures were assessed using 95% VaR, CVaR, HVaR, and Monte Carlo CVaR. CVaR captured large tail risks of 2.0–3.1%. Monte Carlo CVaR produced far smaller values, ranging from approximately 0.03% to 0.06% losses. FTSE appeared most stable, while Nikkei 225 and S&P 500 were highly vulnerable. Shanghai Composite displayed episodic but severe volatility. Overall, the findings confirm that modern downside risk metrics and adaptive estimation techniques strengthen MPT frameworks, enabling investors to mitigate losses and allocate capital prudently.