Constant Proportion Portfolio Insurance: Discrete-time Trading and Gap Risk Coverage

Posted: 30 Nov 2009 Last revised: 6 Feb 2014

Cathrine Jessen

Copenhagen Business School - Department of Finance

Date Written: December 8, 2010


A practical implementation of constant proportion portfolio insurance (CPPI) strategies must inevitably take market frictions into account. I study a CPPI in a setting with trading costs, fees and borrowing restrictions, and relax the assumption of continuous portfolio rebalancing. The main goals are to cover issuer's gap risk and to maximize CPPI performance according to investor's preferences over possible multipliers: the proportionality factor that determines the risky exposure of a CPPI. Investment objectives are described by the Sortino ratio and alternatively by an S-shaped utility function known from behavioral finance. Investors with either objective will choose a lower multiplier than if CPPI performance is measured by the expected return. Discrete-time trading requires a portfolio rebalancing rule, which affects both performance and gap risk. Two commonly applied strategies, rebalancing at equidistant time steps and rebalancing based on fixed market moves, are compared to a new rule, which takes trading costs into account. While the new and the market-based rules deliver similar CPPI performance, the new rebalancing rule achieves this by fewer trading interventions. Issuer's gap risk can be covered by a fee charge, by hedging or by an artificial floor. A new approach to determine the artificial floor is introduced. All three methods reduce losses from gap events effectively at only a small cost to the investor.

Keywords: CPPI, gap risk, discrete portfolio rebalancing, Sortino ratio, kinked CRRA utility

JEL Classification: G11

Suggested Citation

Jessen, Cathrine, Constant Proportion Portfolio Insurance: Discrete-time Trading and Gap Risk Coverage (December 8, 2010). 23rd Australasian Finance and Banking Conference 2010 Paper. Available at SSRN: or

Cathrine Jessen (Contact Author)

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000

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