We use stochastic dominance to test whether investors should prefer riskier securities as the investment horizon lengthens. Simulated return distributions for stocks, bonds, and U.S. Treasury bills are generated for holding periods of one to 20 years and stochastic dominance tests are run to establish preferences among the alternative portfolios. With independent returns, we find no evidence that high-risk securities (stocks) dominate low-risk securities (bonds) as the investment horizon lengthens. Under the assumption that security returns are correlated across time, we find that common stocks dominate corporate bonds and U.S. Treasury bills for sufficiently long investment horizons.