# Constant proportion portfolio insurance

CPPI portfolios move more portfolio value to the risky asset as the distance between the portfolio value and the floor increases. As the total value of the portfolio decreases, less of the portfolio is allocated to the risky asset. Leverage may be employed by the investor depending on the multiplier value and the total portfolio value.

Constant proportion portfolio investment (CPPI) is a trading strategy that allows an investor to maintain an exposure to the upside potential of a risky asset while providing a capital guarantee against downside risk. The outcome of the CPPI strategy is somewhat similar to that of buying a call option, but does not use option contracts. Thus CPPI is sometimes referred to as a convex strategy, as opposed to a "concave strategy" like constant mix.

CPPI products on a variety of risky assets have been sold by financial institutions, including equity indices and credit default swap indices. Constant proportion portfolio insurance (CPPI) was first studied by Perold (1986)[1] for fixed-income instruments and by Black and Jones (1987),[2] Black and Rouhani (1989),[3] and Black and Perold for equity instruments.[4]

In order to guarantee the capital invested, the seller of portfolio insurance maintains a position in a treasury bonds or liquid monetary instruments, together with a leveraged position in an "active asset", which constitutes the performance engine. Examples of risky assets are a basket of equity shares or a basket of mutual funds across various asset classes. While in the case of a bond+call, the client would only get the remaining proceeds (or initial cushion) invested in an option, bought once and for all, the CPPI provides leverage through a multiplier. This multiplier is set to 100 divided by the crash size (as a percentage) that is being insured against.

## References

### Articles

1. ^ André F. Perold (August 1986). "Constant Proportion Portfolio Insurance", Harvard Business School.
2. ^ a b Fischer Black; Robert W. Jones (Fall 1987). "Simplifying Portfolio Insurance". The Journal of Portfolio Management. 14 (1): 48–51. doi:10.3905/jpm.1987.409131.
3. ^ a b Fischer Black and Ramine Rouhani (1989). "Constant Proportion Portfolio Insurance and the Synthetic Put Option: A Comparison", Institutional Investor focus on Investment Management.
4. ^ Fischer Black and André F. Perold (1992), "Theory of Constant Proportion Portfolio Insurance", Journal of Economic Dynamics and Control, 16(3-4): 403-426.
5. ^ Rama Cont and Peter Tankov (July 2009), "Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices", Mathematical Finance 19(3): 379–401. doi:10.1111/j.1467-9965.2009.00377.x
6. ^ Zagst, Rudi; Kraus, Julia (2011-05-01). "Stochastic dominance of portfolio insurance strategies". Annals of Operations Research. 185 (1): 75–103. doi:10.1007/s10479-009-0549-9. ISSN 1572-9338.