贾永婕孩子:Constant proportion portfolio insurance - Wikipedia, the free encyclopedia

Constant proportion portfolio insurance (CPPI) is a capital guarantee derivative security that embeds a dynamic trading strategy in order to provide participation to the performance of a certain underlying. See also dynamic asset allocation. The intuition behind CPPI was adopted from the interest rate universe.

In order to be able to guarantee the capital invested, the option writer (option seller) needs to buy a zero-coupon bond and use the proceeds to get the exposure he wants. 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.

For example, say an investor has a $100 portfolio, a floor of $90(price of the bond to guarantee his $100 at maturity) and a multiplierof 5 (ensuring protection against a drop of at most 20% beforerebalancing the portfolio). Then on day 1, the writer will allocate (5 *($100 – $90)) = $50 to the risky asset and the remaining $50 to theriskless asset (the bond). The exposure will be revised as the portfoliovalue changes, i.e. when the risky asset performs and with leveragemultiplies by 5 the performance (or vice versa). Same with the bond.These rules are predefined and agreed once and for all during the lifeof the product.

Contents

• 1 Some definitions
• 2 Dynamic trading strategy
• 3 Practical CPPI
• 4 References
  • 4.1 Articles
  • 4.2 Internet

[edit] Some definitions

• Bond floor

Being a capital guarantee product, the CPPI embeds a bond. The bondfloor is the value below which the CPPI value should never fall in orderto be able to ensure the payment of all future due cash flows(including notional guarantee at maturity)

• Multiplier

Unlike a regular bond + call strategy which only allocates theremaining dollar amount on top of the bond value (say the bond to pay100 is worth 80, the remaining cash value is 20), the CPPI leverages thecash amount. The multiplier is usually 4 or 5, meaning you do notinvest 80 in the bond and 20 in the equity, rather m*(100-bond) in theequity and the remainder in the zero coupon bond,.

• Gap

A measure of the proportion of the equity part compared to the cushion :(CPPI-bond floor)/equity. Theoretically, this should equal 1/multiplierand the investor uses periodic rebalancing of the portfolio to attemptto maintain this.

• Trading rules

The CPPI being a dynamic trading strategy, on certain anniversarydates (or depending on the liquidity some trading days, say quarterlyfor a hedge fund), the weights are rebalanced so as to ensure perfectmatching of the multiplier rules and/or making sure the product stillguarantees the notional at maturity. This last rule is set up so as tomaintain the gap between two barriers, the releverage and deleveragetriggers.

[edit] Dynamic trading strategy

• Rules

If the gap remains between an upper and a lower trigger band (resp.releverage and deleverage triggers), the strategy does not trade. Iteffectively reduces transaction costs, but the drawback is that whenevera trade event to reallocate the weights to the theoretical valueshappen, the prices have either shifted quite a bit high or low,resulting in the CPPI effectively buying (due to releverage) high, andselling low.

• Risks

As dynamic trading strategies assume that capital markets trade in acontinuous fashion, gap risk is the main concern of CPPI writer, since asudden drop in the risky underlying trading instrument(s) could reducethe overall CPPI net asset value below the value of the bond floorneeded to guarantee the capital at maturity. It results in animpossibility to shift assets from the risky one to the bond, leadingthe structure to a state where it is impossible to guarantee principalat maturity. With this feature being ensured by contract with the buyer,the writer has to put up money of his own to cover for the difference(the issuer has effectively written a put option on the structure NAV).Banks generally charge a small 'protection' or 'gap' fee to cover thisrisk, usually as a function of the notional leveraged exposure.

[edit] Practical CPPI

In some CPPI structured products, the multipliers are constant. Sayfor a 3 asset CPPI, we have a ratio of x:y:100%-x-y as the third assetis the safe & riskless equivalent asset like cash or bonds. At theend of each period, the exposure is rebalanced. Say we have a note of$1million, and the initial allocations are 100k, 200k, and 700k. Afterperiod one, the market value changes to 120k:80k:600k. We now rebalanceto increase exposure on the outperforming asset and reduce exposure tothe worst performing asset. Asset A is the best performer, so itsrebalanced to be left at 120k, B is the worst performer, to itsrebalanced to 60k , and C is the remaining, 800k-120k-60k=620k. We arenow back to the original fixed weights of 120:60:620 or ratio-wise2:1:remaining.

[edit] References

[edit] Articles

• A.F. Perold, "Constant Proportion Portfolio Insurance," Harvard Business School (August 1986)
• F. Black and R. Jones, "Simplifying Portfolio Insurance," Journal of Portfolio Management(Fall 1987)
• Pricing of equity linked life insurance policies with an asset value guarantee (Michael Brennan, Eduardo Schwartz, 1976).
• F. Black and A.F. Perold, "Theory of constant proportion portfolio insurance", Journal of Economic Dynamics and Control,1992.
• AF Perold, WF Sharpe, "Dynamic strategies for asset allocation" Financial Analysts Journal, 1995.
• Constant proportion portfolio insurance and the synthetic put option : a comparison, in Institutional Investor focus on Investment Management, Black, F., & Rouhani, R. (1989).
• Expected performance and risk of various Portfolio insurance strategies. Boulier and Kanniganti.
• Portfolio Insurance: the extreme value approach to the CPPI method, Bertrand.[1]

[edit] Internet

• http://www.tstm.eu/index.php?option=com_content&view=article&id=1&Itemid=7
• http://homepages.nyu.edu/~yr366/CPPI.doc - Summary of the pricing and basic principles of CPPI on HF
• http://www.productinnovations.co.uk/knowledge/CPPI.pdf - Overview of retail examples and mechanics of CPPI