Precise risk management is crucial in options trading, especially in strategies with limited risk and capped profit potential. The Short Iron Condor is a widely adopted strategy due to its structured risk-reward profile. It provides traders with controlled exposure in low-volatility markets while maintaining defined profit and loss parameters. This paper deals with developing an optimization framework using a mixed-integer programming model to evaluate key factors influencing return efficiency, including maximum loss limits, price confidence intervals, and holding periods. Using 2023 options data for 14 U.S. equities and 9 ETFs, filtered and selected using Out of the Money Strategy (OTM), 324 option contracts from as many snapshots as possible, the study analyzes 324 trading scenarios with maturities ranging from 5 to 20 days. Results indicate that increasing the maximum loss limit raises total return but reduces return efficiency. A $100 loss limit generates an average return of $30 with a 40.7% return on investment, while a $900 limit increases returns to $131 but lowers return on investment to 18.8%. These findings demonstrate that higher risk exposure does not always enhance return efficiency in capped-risk strategies. The proposed framework provides actionable insights for traders aiming to refine strategy selection within well-defined risk constraints. Risk managers can utilize these findings to sustain stable investment portfolios, while algorithmic trading systems may integrate this optimization model for automated strategy refinements and real-time adjustments. This study enhances decision-making in options trading, portfolio risk management, and financial strategy development.

The core principle of investment posits a direct correlation between risk and return. In the language of finance, "risk" refers to the degree of uncertainty or the likelihood of financial loss associated with an investment choice. Conventional wisdom holds that as investment risk escalates, investors expect higher returns as compensation for the increased risk they undertake. Yet, the interplay between risk and return is not always linear or predictable. This study utilized optimization modeling in the options market to investigate the risk-return relationship, focusing on how returns change with different risk levels. Concentrating on the short iron condor strategy, with its capped risk and return, the research aimed to maximize returns within various loss scenarios. This method clarified return levels at different risk thresholds and emphasized the short iron condor strategy's role in delineating the risk-return dynamics. Using 2023 data, research on the 14 most traded US equity and 9 ETF options, with maturities ranging from 5 to 20 days, identified a clear relationship between risk, measured by both maximum loss levels and price fluctuations, and potential returns in short iron condor strategies. While higher maximum loss limits led to larger potential returns, the risk-adjusted returns, expressed as the return-to-risk ratio, declined as risk increased. However, with increased price fluctuations, the potential return actually decreased due to the capped profit potential of the strategy, showing a different dynamic compared to maximum loss risk. Furthermore, longer time to maturity further reduced this ratio, highlighting that both the level of risk and the duration of the position play critical roles in determining returns. These findings emphasize the complex balance between risk and return, and the diminishing marginal benefits of increasing risk and holding periods in short iron condor strategies.