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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 nonrisky 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
Advantages:
The indexing level may exceed 100% in case of initial good performances of risky assets, and generate a better overall return for the fund.
Disadvantages:
Risk of monetization (the level of exposure to the risky assets becomes zero) if the risky assets underperform at launch
Let’s define the floor by the current value of the zerocoupon 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 + nonrisky assets
The asset allocations are given by:
Risky asset = multiplier * Cushion / NPV
Nonrisky 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
NPV_{0} = 100%
Guarantee_{0} = 80%
Floor_{0} = 80% *1/(1+4.5%) = 76.56%
Cushion_{0} = 100%  76.56% = 23.44%
RISKYASSETS_{0} = 4 * Cushion_{0} / NPV_{0} = 93.78%
NONRISKYASSETS_{0} = 100%  RiskyAssets_{0} = 6.22%
First month, CAC 40 returns is 5%
NPV_{1} = RiskyAssets_{0}*(1+5%) + NonRiskyAssets_{0}*(1+4.5%/12)
NPV_{1} = 93.78% * (1+5%) + 6.22% * (1+4.5%/12)= 104.71%
Guarantee_{1} = 80%*Max(100% ; 104.71%) = 83.77%
New allocations :
Floor_{1} = Guarantee_{1}*1/(1+4.5%)^{^(11/12)} = 80.46%
Cushion_{1} = NPV_{1}  Floor_{1} = 24.26%
RISKYASSETS_{1} = 4 * Cushion_{1}/ NPV_{1} = 4*24.26%/104.71%=92.65%
NONRISKYASSETS_{1} = NPV_{1}  RiskyAssets_{1} = 12.06%
Second month, CAC 40 is unchanged: allocations are unchanged
RISKYASSETS_{2} = RiskyAssets_{1}
NONRISKYASSETS_{2} = AllocActifsSansRisque_{1}
Third month, 1st case: CAC 40 posted positive 5% returns
NPV_{3} = RiskyAssets_{1}*(1+5%) + NonRiskyAssets_{1}*(1+2*4.5%/12)
Guarantee_{3} = Max[Guarantee_{1}; 80%*109.44%]
Soit NPV_{3} = 109.44% et Guarantee_{3} = 87.55%
New allocations :
Floor_{3} = Guarantee_{3}*1/(1+4.5%)^{^(13/12)} = 84.71%
Cushion_{3}= NPV_{3} Floor_{3} = 24.73%
RISKYASSETS_{3} = 4 * Cushion_{3} / NPV_{3} = 4*24.73%/109.44%=90.39%
NONRISKYASSETS_{3} = NPV_{3}  RiskyAssets_{3} = 19.04%
Third month, 2nd case: CAC 40 posted negative 5% returns
NPV_{3} = RiskyAssets_{1}*(15%)+NonRiskyAssets_{1}*(1+2*4.5%/12)
Guarantee_{3} = Max[Guarantee_{1} ; 80%*100.17%]
Soit NPV_{3} = 100.17% et Guarantee_{3} = 83.77%
New allocations :
Floor_{3} = Guarantee_{3}*1/(1+4.5%)^{^(13/12)} = 81.05%
Cushion_{3} = NPV_{3} Floor_{3} = 19.12%
RISKYASSETS_{3} = 4 * Cushion_{3} / NPV_{3} = 4*19.12%/100.17%= 76.35%
NONRISKYASSETS_{3} = NPV_{3}  RiskyAssets_{3} = 23.82%
Next Finance , January 2008
Article also available in : English  français
The approach initiated by Ossiam’s research and management team intends to obtain an optimized portfolio that includes a selection of stocks where volatility is among the lowest in the investment universe
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