Equity Hybrid Derivatives

CHAPTER 5

Constant Proportion Portfolio Insurance

5.1 INTRODUCTION TO PORTFOLIO INSURANCE

Portfolio insurance is a family of investment strategies designed to give the investor the possibility to limit downside risk while benefiting from rallying markets. These strategies protect the investor from falling markets and allow him to recover his initial capital or less commonly a percentage of it. One well-known portfolio insurance strategy is constant proportion portfolio insurance (CPPI). This was introduced by Perold in 1986 for fixed income instruments and by Black and Jones in 1987 for equity instruments.

In this chapter, we will introduce CPPI and discuss options on CPPI portfolios. CPPI is a trading strategy intended to keep a constant proportional exposure to a certain risky asset while guaranteeing a minimum value of the portfolio throughout its life. Let us define a strategy as a pair of evolving weights (a(t), b(t)). The portfolio consists of a risky fund denoted RF(t) and a floor denoted Floor(t). The value of the strategy denoted CPPI(t)¹ is then given by

The risky asset could be an equity, commodity, or any other risky underlying. The floor is almost always a bond, either a coupon-bearing bond or a zero bond.

Let us first introduce some standard key words that are commonly used when dealing with CPPIs. Note that this section is essential to the understanding of the rest ...