Despite their remarkable performance across various time periods and numerous asset classes, cross-sectional momentum strategies, that hold long positions in portfolios of past winners and short positions in portfolios of past losers, occasionally produce dramatically negative rates of return. The occurrence of these momentum crashes is mostly due to the uncertainty of the stock market recovery from bear market periods, when past losers unexpectedly stop being losers. To account for the uncertainty neglected in the formulation of the cross-sectional momentum strategy, this research exploits the flexibility of stochastic programming based on scenarios of past winner and loser portfolio returns. To generate scenarios, heuristic and exact optimization approaches for moment-matching are applied to capture the first four central moments as well as the correlation of winner and loser portfolio returns. The reliability of scenarios is evaluated using the mass transportation rank histogram and verified by Cramér-von Mises hypothesis testing. Backtesting over nearly a century using total returns of NYSE, NASDAQ and AMEX equities shows that the proposed approach generates reliable scenarios of past winner and loser portfolio monthly returns.