Revisiting U.S. Stock Market Returns: Individual Retirement Accounts

Numerous studies have estimated U.S. stock market returns measured by various indexes such as the S&P 500 Index over certain periods. The purpose of this paper is twofold: first we calculate, under certain scenarios, the final total accumulation of a representative individual who invests a certain amount of funds per month during a long investment horizon of say 30 or 40 years. Second, we evaluate the performance of such an investment plan of defined monthly contributions. This evaluation is based on a benefit target and working backwards we compute the necessary monthly contributions. In our calculations we use actual monthly returns of the S&P 500 Index instead of averages obtained from a large sample. We calculate that accumulations of gradual investments over 30 or 40 years are skewed to the right and we also compute the probability that a given percentage of contributions will be sufficient to finance certain retirement benefits.