The traditional way by which rich countries assure old-age income security is through mandatory, publicly financed pensions. Most national systems provide defined-benefit pensions in which a worker's benefit is calculated based on years of coverage under the program and average wages while contributing to the system. Traditional systems are designed to replace a predictable and stable percentage of workers' average earnings over their later careers. Excessive pension commitments have pushed many pay-as-you-go pension programs toward insolvency, however. One reform option is to scale back traditional pensions gradually and replace them with pensions financed out of individual investment accounts. A presidential commission recently outlined three reform plans to reduce benefits under the U.S. Social Security system and replace them with annuities financed out of retirement savings accounts (President's Commission to Strengthen Social Security, 2002). This paper examines evidence on the likely success of individual accounts in providing retirement income. I use historical and simulated data on financial-market performance to evaluate the market risks facing contributors to a system that is based on individual investment accounts. The paper estimates the hypothetical pensions that workers in five industrialized countries could have obtained based on historical data. The empirical magnitude of retirement income risks is shown to be quite large, almost certainly larger than would be tolerated in most rich democracies.