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<\/p>\n
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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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
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.<\/p>\n
The adjustment of indexing level will depend on the dynamic changes of the risky underlying.<\/p>\n
The more risky assets perform, the stronger indexing level will be, and the more the manager will increase exposure to risky assets.<\/p>\n
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<\/p>\n
Advantages:
\n– The indexing level may exceed 100% in case of initial good performances of risky assets, and generate a better overall return for the fund.<\/p>\n
Disadvantages:
\n– Risk of monetization (the level of exposure to the risky assets becomes zero) if the risky assets underperform at launch<\/p>\n
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<\/p>\n
The portfolio NPV is given by :
\n
NPV = Cushion + Floor = Risky asset + non-risky assets<\/p>\n
The asset allocations are given by:
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Risky asset = multiplier * Cushion \/ NPV
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Non-risky asset = NPV – Risky asset<\/p>\n
– Let’s take a CPPI fund with a maturity equals to 1 year<\/strong>. At the beginning<\/strong><\/p>\n NPV0<\/sub> = 100% RISKY-ASSETS0<\/sub><\/em> = 4 * Cushion0<\/sub> \/ NPV0<\/sub> = 93.78% First month, CAC 40 returns is 5%<\/strong><\/p>\n NPV1<\/sub> = Risky-Assets0<\/sub>*(1+5%) + Non-Risky-Assets0<\/sub>*(1+4.5%\/12) New allocations : RISKY-ASSETS1<\/sub><\/em> = 4 * Cushion1<\/sub>\/ NPV1<\/sub> = 4*24.26%\/104.71%=92.65% Second month, CAC 40 is unchanged: allocations are unchanged<\/strong><\/p>\n RISKY-ASSETS2<\/sub><\/em> = Risky-Assets1<\/sub> Third month, 1st case: CAC 40 posted positive 5% returns<\/strong><\/p>\n NPV3<\/sub> = Risky-Assets1<\/sub>*(1+5%) + Non-Risky-Assets1<\/sub>*(1+2*4.5%\/12) New allocations : RISKY-ASSETS3<\/sub><\/em> = 4 * Cushion3<\/sub> \/ NPV3<\/sub> = 4*24.73%\/109.44%=90.39% Third month, 2nd case: CAC 40 posted negative 5% returns<\/strong> <\/p>\n NPV3<\/sub> = Risky-Assets1<\/sub>*(1-5%)+Non-Risky-Assets1<\/sub>*(1+2*4.5%\/12) New allocations : RISKY-ASSETS3<\/sub><\/em> = 4 * Cushion3<\/sub> \/ NPV3<\/sub> = 4*19.12%\/100.17%= 76.35% 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<\/p>\n","protected":false},"author":20,"featured_media":17482,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1485],"tags":[1656,1655,1658,1673,1671,1719,1674,1651,1437,1807,1649,1692],"_links":{"self":[{"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/posts\/17484"}],"collection":[{"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/comments?post=17484"}],"version-history":[{"count":0,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/posts\/17484\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/media\/17482"}],"wp:attachment":[{"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/media?parent=17484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/categories?post=17484"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/beta.next-finance.net\/en\/wp-json\/wp\/v2\/tags?post=17484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n– Risky asset : CAC 40
\n– Guarantee : The investor is guaranteed to receive 80%<\/strong> of the highest monthly value achieved by the fund during the investment term
\n– multiplier: 4<\/strong>
\n– For simplicity, the interest rate is constant at 4.5%<\/strong> during the course of product life
\n– To reduce management expenses, we believe that the manager does change its allocation only when the absolute value of underlying changes is above 5%<\/strong><\/p>\n
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Guarantee0<\/sub> = 80%
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Floor0<\/sub> = 80% *1\/(1+4.5%) = 76.56%
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Cushion0<\/sub> = 100% – 76.56% = 23.44%<\/p>\n
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NON-RISKY-ASSETS0<\/sub><\/em> = 100% – Risky-Assets0<\/sub> = 6.22%<\/p>\n
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NPV1<\/sub> = 93.78% * (1+5%) + 6.22% * (1+4.5%\/12)= 104.71%
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Guarantee1<\/sub> = 80%*Max(100% ; 104.71%) = 83.77%<\/p>\n
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Floor1<\/sub> = Guarantee1<\/sub>*1\/(1+4.5%)^(1-1\/12)<\/sup> = 80.46%
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Cushion1<\/sub> = NPV1<\/sub> – Floor1<\/sub> = 24.26%<\/p>\n
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NON-RISKY-ASSETS1<\/sub><\/em> = NPV1<\/sub> – Risky-Assets1<\/sub> = 12.06%<\/p>\n
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NON-RISKY-ASSETS2<\/sub><\/em> = Alloc-Actifs-Sans-Risque1<\/sub><\/p>\n
\n
Guarantee3<\/sub> = Max[Guarantee1<\/sub>; 80%*109.44%]\n
Soit NPV3<\/sub> = 109.44% et Guarantee3<\/sub> = 87.55%<\/p>\n
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Floor3<\/sub> = Guarantee3<\/sub>*1\/(1+4.5%)^(1-3\/12)<\/sup> = 84.71%
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Cushion3<\/sub>= NPV3<\/sub>– Floor3<\/sub> = 24.73%<\/p>\n
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NON-RISKY-ASSETS3<\/sub><\/em> = NPV3<\/sub> – Risky-Assets3<\/sub> = 19.04%<\/p>\n
\n
Guarantee3<\/sub> = Max[Guarantee1<\/sub> ; 80%*100.17%]\n
Soit NPV3<\/sub> = 100.17% et Guarantee3<\/sub> = 83.77%<\/p>\n
\n
Floor3<\/sub> = Guarantee3<\/sub>*1\/(1+4.5%)^(1-3\/12)<\/sup> = 81.05%
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Cushion3<\/sub> = NPV3<\/sub>– Floor3<\/sub> = 19.12%<\/p>\n
\n
NON-RISKY-ASSETS3<\/sub><\/em> = NPV3<\/sub> – Risky-Assets3<\/sub> = 23.82%<\/p>\n","protected":false},"excerpt":{"rendered":"