Explain how scenario analysis and Monte Carlo simulation are used to stress-test an asset allocation's robustness

Mean–variance analysis is single-period, but real investors face multi-period paths with contributions, withdrawals, rebalancing, taxes and fees. Monte Carlo simulation generates thousands of return paths from assumed distributions, applies the cash flows and rules to each, and reports the distribution of terminal wealth and the probability of meeting spending or funding goals. It captures path dependence, such as the damage of large losses early in retirement, and can use non-normal returns. Scenario analysis and stress testing instead apply specific historical or hypothetical shocks, such as a stagflation episode or a liquidity crisis, to see how the allocation and the investor's obligations respond. The trap is trusting simulated probabilities without questioning the input assumptions, which drive the output entirely.