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.