Mathematical Framework for Dynamic Downside-Minimizing Portfolio with Exotic Option Overlay

This study develops and evaluates a dynamic downside-minimizing portfolio through five stages. Starting with a 4-asset universe of equity, bonds, gold, and a volatility instrument, the portfolio is expanded to 13 and then 21 assets while incorporating mean-semivariance optimization, Asian arithmetic-average puts, American puts valued with Longstaff–Schwartz Least-Squares Monte Carlo, covered calls, momentum tilts, and regime-aware rebalancing. The final stage targets a 15% expected return. Portfolio performance is evaluated using correlated Geometric Brownian Motion with 20,000 Monte Carlo paths over a one-year horizon. The four-asset semivariance-optimized portfolio has a Sortino ratio of 2.04 and a maximum simulated loss of −23.7%, compared with 1.20 and −45.9% for SPY. Adding Asian and American puts increases the Sortino ratio to 2.26 and reduces maximum simulated loss to −8.8%. The 13-asset buy-and-hold portfolio reaches a mean Sortino ratio of 5.81. Among the rebalancing strategies tested, calendar rebalancing produced the highest mean Sortino ratio of 9.62. The 21-asset portfolio with a 15% return target has a Sortino ratio of 4.06 and maximum simulated loss of −28.8%; the full option overlay reduces the latter to −9.1%. These results characterize the tradeoffs among diversification, downside protection, return targets, and adaptive rebalancing within the simulated framework.