 What is CPPI (Constant Proportion Portfolio Insurance)?

CPPI or Constant Proportion Portfolio Insurance is a dynamic management technique that ensures a minimum guaranteed amount to an investor at the time of maturity

Article also available in : English | français A CPPI fund is a fund where the manager allocates dynamically and regularly exposure to risky assets (underlying such as equities or stock indices) and non-risky assets (bonds, money market funds) in order to ensure the preservation of invested capital.

To achieve his goal, the manager defines the "cushion" or the percentage of the fund’s assets that may be put at risk without any effect on the level of protection.

The "cushion" is estimated by the difference between the initial value of the product and the present value minimum necessary to provide the capital guarantee at maturity.

Using quantitative models, the manager will then compute a level of indexing (or multiplier) to apply to the "cushion" to get the portfolio’s exposure to the risky underlying.

The adjustment of indexing level will depend on the dynamic changes of the risky underlying.

The more risky assets perform, the stronger indexing level will be, and the more the manager will increase exposure to risky assets.

On the other hand, the less risky assets perform, the weaker indexing level will be, and the more the manager will decrease exposure to risky assets The indexing level may exceed 100% in case of initial good performances of risky assets, and generate a better overall return for the fund. Risk of monetization (the level of exposure to the risky assets becomes zero) if the risky assets underperform at launch

### EXAMPLE

Let’s define the floor by the current value of the zero-coupon bond that will pay the amount originally promised to the investor at the time of maturity

The portfolio NPV is given by :
NPV = Cushion + Floor = Risky asset + non-risky assets

The asset allocations are given by:
Risky asset = multiplier * Cushion / NPV
Non-risky asset = NPV - Risky asset Let’s take a CPPI fund with a maturity equals to 1 year. Risky asset : CAC 40 Guarantee : The investor is guaranteed to receive 80% of the highest monthly value achieved by the fund during the investment term multiplier: 4 For simplicity, the interest rate is constant at 4.5% during the course of product life To reduce management expenses, we believe that the manager does change its allocation only when the absolute value of underlying changes is above 5%

At the beginning

NPV0 = 100%
Guarantee0 = 80%
Floor0 = 80% *1/(1+4.5%) = 76.56%
Cushion0 = 100% - 76.56% = 23.44%

RISKY-ASSETS0 = 4 * Cushion0 / NPV0 = 93.78%
NON-RISKY-ASSETS0 = 100% - Risky-Assets0 = 6.22%

First month, CAC 40 returns is 5%

NPV1 = Risky-Assets0*(1+5%) + Non-Risky-Assets0*(1+4.5%/12)
NPV1 = 93.78% * (1+5%) + 6.22% * (1+4.5%/12)= 104.71%
Guarantee1 = 80%*Max(100% ; 104.71%) = 83.77%

New allocations :
Floor1 = Guarantee1*1/(1+4.5%)^(1-1/12) = 80.46%
Cushion1 = NPV1 - Floor1 = 24.26%

RISKY-ASSETS1 = 4 * Cushion1/ NPV1 = 4*24.26%/104.71%=92.65%
NON-RISKY-ASSETS1 = NPV1 - Risky-Assets1 = 12.06%

Second month, CAC 40 is unchanged: allocations are unchanged

RISKY-ASSETS2 = Risky-Assets1
NON-RISKY-ASSETS2 = Alloc-Actifs-Sans-Risque1

Third month, 1st case: CAC 40 posted positive 5% returns

NPV3 = Risky-Assets1*(1+5%) + Non-Risky-Assets1*(1+2*4.5%/12)
Guarantee3 = Max[Guarantee1; 80%*109.44%]
Soit NPV3 = 109.44% et Guarantee3 = 87.55%

New allocations :
Floor3 = Guarantee3*1/(1+4.5%)^(1-3/12) = 84.71%
Cushion3= NPV3- Floor3 = 24.73%

RISKY-ASSETS3 = 4 * Cushion3 / NPV3 = 4*24.73%/109.44%=90.39%
NON-RISKY-ASSETS3 = NPV3 - Risky-Assets3 = 19.04%

Third month, 2nd case: CAC 40 posted negative 5% returns

NPV3 = Risky-Assets1*(1-5%)+Non-Risky-Assets1*(1+2*4.5%/12)
Guarantee3 = Max[Guarantee1 ; 80%*100.17%]
Soit NPV3 = 100.17% et Guarantee3 = 83.77%

New allocations :
Floor3 = Guarantee3*1/(1+4.5%)^(1-3/12) = 81.05%
Cushion3 = NPV3- Floor3 = 19.12%

RISKY-ASSETS3 = 4 * Cushion3 / NPV3 = 4*19.12%/100.17%= 76.35%
NON-RISKY-ASSETS3 = NPV3 - Risky-Assets3 = 23.82%

January 2008

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