Maximizing Long Term Return

This paper is motivated by the attempt to answer the following question: For an investor with an extremely long time horizon, what is the optimum portfolio, and can one improve upon the traditional answer of "100% in equities"? In the process of answering the above question, the paper provides a much needed clarification of the meaning of the phrase "expected long term return" from the viewpoint of long term investors such as pension funds, insurance companies, and charities. "Mean" returns turn out to be "meaningless" for practical purposes. Particular care is needed in asset liability modeling work, where presentation of outcomes in terms of means and standard deviations is very misleading. The author calculates the "expected long term return" for various portfolios, including those containing equities, bonds, and European equity options, for the geometric Brownian stochastic model. In particular, the author demonstrates that the long term returns to be expected from two strategies currently popular in the retail market, namely guaranteed capital and enhanced income strategies (via put purchases and call sales, respectively), are likely to disappoint those who subscribe to them. In addition, the author demonstrates what may be termed "portfolio synergy" effects arising from rebalancing, namely that the "expected long term return" for a portfolio does not equal the linear combination of "expected long term returns" for the portfolio constituents. This is true whether the portfolio is rebalanced periodically or continuously. Finally, the author attempts to answer the original question, subject to various constraints as to whether short asset positions are allowed, and concludes that "100% in equities" can frequently be improved upon.