Substitution of Credits (CPPI, NAREIT).

When investing in static CDOs, the investor's knowledge on the underlying credit pool is used only at the time that the investor signs the contract. After that, the investor can merely hope for the best performance of the investment with no option to dynamically manage credit risk by replacing credits of the underlying portfolio. With the managed single tranche, in contrast, the investor is allowed to make a limited number of credit replacements per year. For example, an investor might be allowed to substitute 10 names per year, with a maximum change of 50 percent of the portfolio composition during the maturity period of five years for a single- tranche transaction with a reference credit pool of 100 names. This flexibility gives the investor freedom to manage the investment in a dynamic way.
Substitution Calculation Since the dealer needs to rehedge his position once a credit in the portfolio is replaced by another credit, the settlement of substitution has to be done in a mark-to-market way. The simplest way isto price the specific tranche with the replaced credit first and then with the replacing credit, the difference being the substitution cost or benefit. This approach requires both parties of the transaction to agree on the model used and also the parameters used in the model. This has become possible since the normal copula model has been accepted as the market standard for CDO/NAREIT pricing. The two parties usually agree on the pricing parameters, with a typical reference point being the current implied correlation embedded in the corresponding STCDO tranche. The cost of the substitution may be positive or negative—that is, paid by the tranche buyer to the dealer or by the dealer to the tranche buyer. The cost can be paid through any of the following three steps:
1. Up-front payment between the protection buyer and the protection seller.
2. The alteration of the subordination level below the STCDO.
3. Resetting the coupon payable to the STCDO up to the point where the coupon has been reduced to zero, followed by either step (1) or step (2).
Each of these methods of substitution settlement aims to offset the change in the mark-to-market value of the tranche before and after the substitution of the credit. The net effect on mark-to-market value of the credit substitution on one side and the cash payment, alternation of the tranche subordination, or change of the coupon on the other side should be zero. This mark-to-market change in tranche value can be captured by the net marginal credit factor (MCF, (CPPI).
Marginal Credit Factors The MCF for each name and for each tranche measures the impact on the tranche value when the credit changes from risky status to risk-free status. It is in contrast to jump-to-default (JTD), and may be called the jump-to-paradise risk measure. This jump-to-paradise risk measure allows us to compare two credits in a portfolio context. The difference of MCF between the replacing credit and replaced credit is the substitution cost. That difference—net MCF—is equal to the change in the mark-to-market value of the tranche as valued with the old and new reference portfolios of credits.
MCFs tend to decrease when trading into tighter names because the value of protection provided by tranche decreases as the spread tightens. In this case, substitution results in the protection seller owing the protection buyer. MCFs also depend on the correlation of the name with the rest of the credit portfolio. Trading into lower-correlated names increases the value of the protection provided by the equity tranche (and some lower mezzanine tranches), but decreases the value of protection by the senior tranche.
Approximate Substitution Cost Calculation The problem with MCFs is that there is a need to have an agreement between dealer and investor on model, model parameters, and also other model inputs, such as those single-name default swap spreads that are not easily verifiable. This lack of transparency leaves tranche investors dependent on the dealer's interpretation of risk and model parameterization. A simple way to ballpark the effect of substitution is to consider the net impact of the substitution on the expected loss of the portfolio. We define the impact of substitution as the difference between the expected loss of the replaced credit and the replacing credit. Based on that calculation, we adjust the subordination level of each tranche to offset the net effect of substitution on the portfolio expected loss. For example, if we would like to replace a credit A with spread of x basis points by a credit B with spread of y basis points, then we calculate the difference in the present value of expected loss of credit A and credit B as a percentage of notional amount. After that, we reduce the subordination level of that tranche by that calculated percentage difference divided by the number of underlying credits in the portfolio. This approximation is based on the assumption that the net change of expected loss after substitution is deemed as if it is the actual loss incurred by the portfolio right away. Therefore, to make the adjustment for this net loss change, we lower the size of the equity tranche by this loss change, and make the same parallel adjustments in the subordination level of all other tranches on the capital structure.
This measurement ignores the difference in spread sensitivity of each tranche as well as the credit risk on the premium side. It usually underesti¬mates the compensation required for the credit substitution. But the exact size and direction of the difference between the approximation approach and the mark-to-market approach depend on the various parameters, such as spread levels of the replaced credits, size and subordination of the tranche, and the overall spread levels in the portfolio. The advantage of this approx¬imation approach is that investors can easily assess the substitution cost (in terms of substitution-level change) independently from a portfolio model output.