Equity portfolio insurance against a benchmark: Setting, replication and optimality

- Characterization of equity benchmark-driven portfolio insurance (BDPI).
- BDPI is replicable with perpetual American exchange options.
- Optimal exposure to the alternative asset increases with the impatience to consume.
- It increases only with information ratios offsetting the impatience to consume.
- Optimal consumption decreases with the information ratio.

This paper undertakes the issue of portfolio insurance from the perspective of a risk-averse agent requiring his financial wealth to grow at a floored rate in excess of an equity benchmark. The suggested solution is a generalization of the CPPI approach within a two-equity asset framework. The paper examines some features of this extension related to its dynamic, its relative risk-reward profile and its static replication. It focuses more specifically on the optimal design of this portfolio strategy in the sense of consumption-investment decision making.