Abstract
A stochastic-arbitrage opportunity is present in the equity index options market when a feasible option-enhanced indexed portfolio dominates passive index investment by stochastic dominance under an estimated physical distribution, observed bid–ask prices, and explicit portfolio constraints. We develop and empirically implement the direct use of lower partial co-moment conditions as computationally scalable linear restrictions for constructing such portfolios. While these conditions appear in earlier work as analytical necessary first-order conditions, we show that they provide an exact necessary and sufficient characterization of the stochastic-arbitrage portfolio problem under co-monotonicity of the option-enhanced payoff and the index value, which is induced by an established position limit allowing at most one option position per unit of index exposure. This exact characterization substantially reduces problem size and computation time, allowing fine discretization, large-scale backtesting, and extensive robustness analysis without specialized computing resources. Using this framework, we test for stochastic-arbitrage opportunities in one-month S&P 500 index options. Out-of-sample tests indicate such opportunities in high-volatility regimes, predominantly in the form of call front spreads, when portfolio construction accounts for time variation in the market risk premium and negative conditional skewness of index returns. The qualitative findings are robust across alternative density forecasts, data treatments, and optimization specifications, while no comparable evidence is found in low- or medium-volatility regimes.