In this article we introduce the construction process of Fubon Group's first managed CDO, Silk Road 2003-1. The first step was to build a reference pool of 50 credit-default swaps using our selection criteria. We then determined the size of each tranche, given the rating and spread of LIBOR, using Moody's Investors Service Binomial Expansion Technique. The final stage was to explore the effect of the diversity score on the funded size of the synthetic CDO and look at the subordination of debt tranches under different diversity score scenarios.
The Reference Pool & Structure
Some 420 quotations of credit-default swaps were provided by the structuring firm, Citigroup. An optimization program was then used to maximize weighted average spread constrained by pre-determined conditions, for example regional and industry concentration limits, collateral quality tests and minimum diversity score. The conditions are as follows:
In the collateral selection model of the synthetic CDO, the objective function and all the constraints are linear, except the diversity score constraint. We employed Moody's diversity score table for the program.
As a result, we generated our reference pool and the summary information is listed below.
With the selected reference pool and given the required rating and coupon of each class, we attempted to determine the level of each subordinate tranche of the deal using iterative computation. The computation follows Moody's Binomial Expansion Technique and the priority of payments schedule along with sequential proceeds paydown and coverage tests.
In this case, we used Citigroup AA rated bonds as collateral. The main structure is described below.
Diversity Score & Tranching
We simulated the synthetic CDO by varying diversity scores to understand the influence on the required funded size of the synthetic CDO and performance of tranche D. Given the pre-determined rating of each tranche, we tried to minimize the funded size of the synthetic CDO to reduce the subordination of tranche D under different diversity score scenarios. Our simulation results also show that the higher the diversity score, the smaller the tranche D's expected loss becomes.
Furthermore, by drawing cumulative portfolio default distributions under different diversity score scenarios, we can understand that default probability falls as the diversity score rises.
All other things being equal, larger diversity scores can diminish the funded size of a synthetic CDO and thus accelerate the synthetic execution. Because the super senior tranche is cheap it decreases the funding cost of the partially funded deal and improves the equity return.
Conversely, a larger diversity score means the collateral manager must monitor more reference entities from different industries and regions. For example, the number of reference entities almost triple, when the diversity score increases from 31 to 58. That will boost the complexity to estimate correlations between underlying assets, recovery rates and probabilities of default of reference entities. We also find the marginal benefit of increasing the diversity score decreases dramatically. Additionally, assuming the super senior swap premium is cheaper by 40 basis points than the cash AAA spread, we can calculate the saving cost under different diversity score scenarios. Although the total saving cost increases while the diversity score enlarges, the marginal saving cost decreases. An originator has to seek the break-even point between saving cost and management efficiency.
Conclusion
We simulated that when the diversity score increases, we can enlarge the size of the super senior tranche and reduce the funded size simultaneously. Therefore, it diminishes the funding costs of the synthetic CDO and improves the return on the equity tranche. On the other hand, while the diversity score increases, the marginal saving cost falls. Consequently, an originator has to find out the break-even point to maximize profit and management efficiency.
This week's Learning Curve was written by Ti-Jen Tsao, project assistant manager, Gang Shyy, advisor, and George Huang, senior project manager in the fixed income and derivatives department at Fubon Group in Taipei.
