Constant proportion portfolio insurance
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
asset. 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 multiplier of 5 (ensuring protection against a drop of at most 20% before rebalancing the portfolio). Then on day 1, the writer will allocate (5 * ($100 – $90)) = $50 to the risky asset and the remaining $50 to the riskless asset (the bond). The exposure will be revised as the portfolio value changes, i.e. when the risky asset performs and with leverage multiplies by 5 the performance (or vice versa). Same with the bond. These rules are predefined and agreed once and for all during the life of the product.
Being a capital guarantee product, the CPPI embeds a bond. The bond floor is the value below which the CPPI value should never fall in order to be able to ensure the payment of all future due cash flows (including notional guarantee at maturity)
Unlike a regular bond + call strategy which only allocates the remaining dollar amount on top of the bond value (say the bond to pay 100 is worth 80, the remaining cash value is 20), the CPPI leverages the cash amount. The multiplier is usually 4 or 5, meaning you do not invest 80 in the bond and 20 in the equity, rather m*(100-bond) in the equity and the remainder in the zero coupon bond,.
A measure of the proportion of the equity part compared to the cushion : (CPPI-bond floor)/equity. Theoretically, this should equal 1/multiplier and the investor uses periodic rebalancing of the portfolio to attempt to maintain this.
The CPPI being a dynamic trading strategy, on certain anniversary dates (or depending on the liquidity some trading days, say quarterly for a hedge fund), the weights are rebalanced so as to ensure perfect matching of the multiplier rules and/or making sure the product still guarantees the notional at maturity. This last rule is set up so as to maintain the gap between two barriers, the releverage and deleverage triggers.
If the gap remains between an upper and a lower trigger band (resp. releverage and deleverage triggers), the strategy does not trade. It effectively reduces transaction costs, but the drawback is that whenever a trade event to reallocate the weights to the theoretical values happen, the prices have either shifted quite a bit high or low, resulting in the CPPI effectively buying (due to releverage) high, and selling low.
As dynamic trading strategies assume that capital markets trade in a continuous fashion, gap risk is the main concern of CPPI writer, since a sudden drop in the risky underlying trading instrument(s) could reduce the overall CPPI net asset value below the value of the bond floor needed to guarantee the capital at maturity. It results in an impossibility to shift assets from the risky one to the bond, leading the structure to a state where it is impossible to guarantee principal at 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 this risk, usually as a function of the notional leveraged exposure.
Capital guarantee
A capital guarantee product means that when an investor buys, or "enters", this specific derivative security he is guaranteed to get back at maturity a part or the totality of the money he invested on day one. Examples of capital guarantees include bond plus option, usually bond plus call, and...
derivative security that embeds a dynamic trading strategy
Trading strategy
In finance, a trading strategy is a predefined set of rules for making trading decisions.Traders, investment firms and fund managers use a trading strategy to help make wiser investment decisions and help eliminate the emotional aspect of trading. A trading strategy is governed by a set of rules...
in order to provide participation to the performance of a certain underlying
Underlying
In finance, the underlying of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the derivative depend on the value of this underlying...
asset. See also dynamic asset allocation
Dynamic Asset Allocation
Dynamic asset allocation is a strategy used by investment products such as hedge funds, mutual funds, credit derivatives, index funds, principal protected notes and other structured investment products to achieve exposure to various investment opportunities and provide 100% principal...
. 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
Bond plus option
In finance, a Bond+Option is a capital guarantee product that provides an investor with a fixed, predetermined participation to an option. Buying the zero-coupon bond ensures the guarantee of the capital, and the remaining proceeds are used to buy an option.----As an example, we can consider a...
, 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 multiplier of 5 (ensuring protection against a drop of at most 20% before rebalancing the portfolio). Then on day 1, the writer will allocate (5 * ($100 – $90)) = $50 to the risky asset and the remaining $50 to the riskless asset (the bond). The exposure will be revised as the portfolio value changes, i.e. when the risky asset performs and with leverage multiplies by 5 the performance (or vice versa). Same with the bond. These rules are predefined and agreed once and for all during the life of the product.
Some definitions
- Bond floor
Being a capital guarantee product, the CPPI embeds a bond. The bond floor is the value below which the CPPI value should never fall in order to 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 the remaining dollar amount on top of the bond value (say the bond to pay 100 is worth 80, the remaining cash value is 20), the CPPI leverages the cash amount. The multiplier is usually 4 or 5, meaning you do not invest 80 in the bond and 20 in the equity, rather m*(100-bond) in the equity 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/multiplier and the investor uses periodic rebalancing of the portfolio to attempt to maintain this.
- Trading rules
The CPPI being a dynamic trading strategy, on certain anniversary dates (or depending on the liquidity some trading days, say quarterly for a hedge fund), the weights are rebalanced so as to ensure perfect matching of the multiplier rules and/or making sure the product still guarantees the notional at maturity. This last rule is set up so as to maintain the gap between two barriers, the releverage and deleverage triggers.
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. It effectively reduces transaction costs, but the drawback is that whenever a trade event to reallocate the weights to the theoretical values happen, the prices have either shifted quite a bit high or low, resulting in the CPPI effectively buying (due to releverage) high, and selling low.
- Risks
As dynamic trading strategies assume that capital markets trade in a continuous fashion, gap risk is the main concern of CPPI writer, since a sudden drop in the risky underlying trading instrument(s) could reduce the overall CPPI net asset value below the value of the bond floor needed to guarantee the capital at maturity. It results in an impossibility to shift assets from the risky one to the bond, leading the structure to a state where it is impossible to guarantee principal at 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 this risk, usually as a function of the notional leveraged exposure.
Practical CPPI
In some CPPI structured products, the multipliers are constant. Say for a 3 asset CPPI, we have a ratio of x:y:100%-x-y as the third asset is the safe & riskless equivalent asset like cash or bonds. At the end of each period, the exposure is rebalanced. Say we have a note of $1million, and the initial allocations are 100k, 200k, and 700k. After period one, the market value changes to 120k:80k:600k. We now rebalance to increase exposure on the outperforming asset and reduce exposure to the worst performing asset. Asset A is the best performer, so its rebalanced to be left at 120k, B is the worst performer, to its rebalanced to 60k , and C is the remaining, 800k-120k-60k=620k. We are now back to the original fixed weights of 120:60:620 or ratio-wise 2:1:remaining.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 SchwartzEduardo SchwartzEduardo Saul Schwartz is a professor of finance at the Anderson School of Management, University of California, Los Angeles, where he holds the California Chair in Real Estate & Land Economics...
, 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.http://greqam.univ-mrs.fr/pdf/working_papers/2001/01a13.pdf
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