Constant proportion portfolio insurance


Constant proportion portfolio insurance

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.

Contents

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.

References

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]

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