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Dynamic investment strategies and their risk-return measures

The two classic objectives of investment are to reduce variability, and to protect the portfolio from shortfalls. There is a profound contradiction between these two objectives. We have shown that the dynamic efficient frontier (DEF) with minimal standard deviation for a given expected profit leads to a contrarian trading strategy. The Black-Jones-Perold constant proportion portfolio insurance (CPPI) corresponds to an opposing strategy. Both DEF and CPPI could be replaced by power options with correspondingly negative and positive powers. These findings provide a motivation to analyze the short-term and long-term implications of popular, static risk-return guidelines for portfolio management, including the efficient frontier, CPPI-controlled downside, Value-at-Risk among others. We find that there is also a contradiction between optimal static short-term and long-term measures for dynamic investments that can be assessed by introducing coupled dynamic risk-return measures, along with a quantitative analysis of various joint profit and loss distributions. This discussion paper represents an extended summary of the results obtained by the authors earlier in Ref 1.