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This chapter analyzes two types of investment strategies for an investor with a savings plan for retirement. In one, the investor sets an upper target which his wealth should not go above. In the other, the investor adds a lower target which his wealth should not go below. The analysis is done in a Black-Scholes model with one risky stock and one risk-free bond, with the restriction that the investor cannot invest more than his current wealth in the risky stock. We illustrate the results by describing a 30-year horizon. We use quantiles of the terminal wealth distribution or the level of accumulated wealth obtained by a given percentage of investors who follow the recommended strategy. The embedded guarantee and freedom to choose the upper and lower bounds represent the main appeal of this approach. We discuss the connection between expected return, affordable risk, and transparent fees for funds management.
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All findings, interpretations, and conclusions of this paper represent the views of the authors and not those of the Wharton School or the Pension Research Council. © 2015 Pension Research Council of the Wharton School of the University of Pennsylvania. All rights reserved.
Date Posted: 12 March 2019