Constant proportion portfolio insurance has been around for a long time but the iTraxx index has been around for less than a year. By combining the two, we can structure a trade based on a liquid and transparent credit index with both Aaa principal protection and an attractive expected yield.
CPPI is a principal protection technique that gives a higher participation in the underlying asset than you get from traditional capital protection. In basic terms, it works by dynamically moving capital between a so-called safe asset and a risky asset, depending on the performance of the risky asset. Given that C stands for constant, you could say CPPI should only be used to describe a structure which has constant leverage and Dynamic PPI is a more appropriate name when the leverage can change.
This article assumes the reader already understands both CPPI and the iTraxx Index. If not, then for CPPI please read a previous Learning Curve titled, 'CFOs: How they Work' (DW, 3/7/04).
In theory, combining CPPI and iTraxx is quite simple. Here are the steps:
1) Receive cash of USD100, for example, from the investor;
2) Calculate the difference between par and the cost of a zero coupon bond;
3) Multiply that difference by a leverage factor;
4) Take that leveraged amount from the USD100 total cash and invest it in an asset, in this case the 0-3% equity tranche of the iTraxx Index. Call it the risky asset. Keep the remaining cash in reserve and call it the reserve cash; and
5) As the price of the iTraxx equity tranche goes up and down adjust the allocation between risky asset and reserve cash to keep the leverage in the trade constant.
That's about it...in theory.
Let's look at an example. Note that the equity tranche of the iTraxx European Index is quoted as an upfront cash amount plus 500 basis points paid quarterly. The upfront is currently around 30% of the notional.
For this example we will assume a zero coupon costs USD70, the upfront is at 20% of notional and the leverage factor is two.
1) USD100 comes in
2) USD100 USD70 = USD30
3) USD30 x 2 = USD60 and this is the amount of cash we allocate to the risky asset
4) The iTraxx equity tranche pays an upfront cash amount of 20% x notional. Therefore, if we want to take USD60 exposure, the amount of notional we can buy is USD60 / (1 - 20%) = USD75. To look at this another way, a notional of USD75 means an uncovered exposure of USD75 less USD15 received upfront = USD60. Put the remaining USD40 in reserve cash.
To buy the iTraxx equity tranche means entering a swap. The cash we allocated to the risky asset plus the upfront cash is held as collateral for that swap.
Moving Leverage
We arranged the trade to have a leverage of two. Let's check it.
There is USD60 of risky asset and USD40 reserve cash. The zero coupon bond is USD70. The total portfolio value so far is USD100, being the sum of the risky asset value and the reserve cash:
Leverage = risky asset / (portfolio value zero coupon bond) = USD60 / (USD100 USD70) = 2
Clearly, if the value of the risky asset goes up or down the leverage is going to change. For example, let's say things are looking good in the iTraxx portfolio and the index tightens. All things being equal, the price of the equity tranche is likely to fall, reflecting lower perceived risk. In practice this means a smaller upfront premium will be paid on the tranche, say 17%. It is an increase in the value of the iTraxx equity tranche and, therefore, an increase in the value of our risky assets. It is reflected in the structure as follows:
Risky asset value = notional x (1 upfront) = USD75 x (1 17%) = USD62
It has gone up by two due to unrealized gains. Leverage is now:
USD62 / (USD102 USD70) = 1.9
To get the leverage back to two we reallocate the resources. We have risky assets with a value of USD62 and reserve cash with a value of USD40. For a leverage of two, we need risky assets of USD64 so we reallocate USD2 from reserve cash to risky assets. Reserve cash goes down by USD2 and risky assets go up USD2 to USD64. Using the new allocated cash we can buy some more iTraxx equity tranche. The current upfront is 17% so with our USD2 we can buy a notional of:
2 / (1 - 17%) = 2.4, receiving a cash upfront of USD0.4.
Check the leverage:
USD64 / (USD102 USD70) = 2
Check the cash collateralizing the notional amount of equity tranche, 77.4:
Risky asset cash USD62 + upfront cash USD15 + upfront cash USD0.4 = 77.4
Everything is in balance and we can continue. Note the difference between the value of the risky assets (USD64) and the cash allocated to risky assets (USD62) is USD2 of unrealised gains in the equity tranche (see chart 2).
The opposite process would occur if the iTraxx equity tranche value fell. Changes in the price of the zero coupon bond will also shift the leverage, as will income flows.
Note that in practice we would not reallocate the deal to account for small changes in leverage, as that would result in needless bid-offer spread expenses.
Switching Out Of CPPI Into A Zero Coupon Trade
Let's go back to the original example. We received USD100 from the investor of which USD40 went into reserve cash and USD60 we invested in the iTraxx equity tranche. The tranche notional is USD75 and is collateralized by the USD60 plus the upfront received of USD15.
Consider the unlikely situation where every name in the iTraxx portfolio defaults overnight with no recovery. The iTraxx equity tranche would be worth zero. The structuring bank is protecting principal at maturity and so would be left with a substantial loss. Principal protection costs USD70. We also have to pay out USD75 to the tranche counterparty so our total liabilities are USD145. On the other hand, we have the cash allocated to risky assets of USD60, the reserve cash of USD40 and a cash upfront of USD15. Total assets are therefore USD115 and the result is a loss of USD30.
In order to avoid that situation, there is a trigger in the trade that causes a switch from the CPPI structure into a zero coupon bond if the value of the portfolio gets very close to the cost of that zero coupon bond (see chart 3).
Things To Consider
This has been a short article on a product that has depth. It is impossible to cover all aspects of it and the reader should think more about the following issues;
* What is the impact of a continuous income stream?
* Are there any safety features to help prevent a switch into a zero coupon?
* What happens on a roll?
* What happens in a default?
* What happens when all the cash has been allocated to the risky asset?
* Who chooses the leverage factor?
This week's Learning Curve was written by Brett Clancy, director in credit structuring at IXIS Capital Marketsin Tokyo.
