Evaluating the Long-Term Risk of Equity Investments in a Portfolio Insurance Framework

The impact of the time horizon upon the risk of equity investments is still a controversial issue. In this paper, we analyse long-term risk in a portfolio insurance framework based on option pricing theory. The insurance strategies are implemented alternatively with a portfolio of stocks and put options or bonds and call options. The risk of stock holdings is measured by the permissible relative stock position in the replicating portfolio for an exogenous floor function. Our findings indicate that there is no general conclusion as to the long-term risk of stocks; the risk can only be determined for specific floor functions. Because the utility function is implicit in any floor specification, we argue that the assumption of preference-free determination of risk with the help of option-pricing theory, as recently suggested in the literature, is a fallacy. Moreover, the popular belief that a longer time horizon reduces the risk of equity investments and therefore makes it optimal to invest a greater fraction of one's wealth in stocks may not be justified.