Contents

CPDOs enable rated coupons

New 'CPPI' structure set for launch

A new type of constant proportion portfolio insurance (CPPI) structure is being prepped for at least three CDO deals. Dubbed constant proportion debt obligation (CPDO), the new format offers for the first time rated interest payments in line with the fund's principal rating, but, despite this, CPDOs may not suit all investors.

CPDOs vary from traditional CPPI products in that the principal is not guaranteed, but the aim of the structure is to attract investors who are looking for greater income certainty. In the case of three deals being put together by ABN AMRO - Chess II, Rembrandt Australia Trust No. 2006-2 and Rembrandt New Zealand Trust No. 2006-1 - interest payments are rated in line with the funds' principal rating (triple-A from Standard and Poor's).

However, one structurer at another bank describes the CPDO format as "cynical", arguing that the "super conservative" structure appears to be designed around meeting rating agency criteria. "It's basically a ratings agency arbitrage that looks more like a market value CDO than a genuine CPPI product," he says.

Consequently it may not be right for all investors. "It's fine if you want something to sit in your portfolio and look good on your books - triple-A but paying Libor plus 200 or whatever - but it should not be confused with a dynamically managed CPPI deal. It is a concern that that could be missed by less sophisticated investors," says one source.

A CPDO takes variable leveraged exposure to a credit portfolio in order to generate sufficient returns to enable the stated coupon payments to be made. In the case of the deals currently being marketed, the credit portfolio comprises two credit indices: the investment grade on-the-run Dow Jones CDX and iTraxx Europe. The risk of these indices will be passed on to investors through CDSs.

The total notional amount of protection sold on the credit index portfolio will be such that the present value of the expected income will cover sufficiently the difference between: (i) the present value of the coupons and the principal due under the note, and (ii) the net asset value (NAV) of the note.

The total notional amount is equal to the target portfolio size, with NAV calculated as the sum of the deposit value and the mark-to-market of the credit index portfolio.

In addition, the target portfolio size has certain maximum size constraints. If the actual credit portfolio size differs from the target credit portfolio size by more than 25%, then the actual credit portfolio size is adjusted to equal the target credit portfolio size, subject to the maximum size constraints.

In other words, the CPDO uses only the leverage it needs to make the scheduled principal and interest payments. If the NAV increases, the target portfolio size will generally decrease as the portfolio needs to generate less income to meet coupon and principal payments. This mechanic constitutes the dynamic leverage control formula.

Once the current note NAV equals the present value of the payments under the note, the credit index portfolio will be unwound and no further credit exposure will be taken (otherwise known as a cash-in event). If this occurs, all future payments due under the notes will be made.

Conversely, if the current note NAV is equal to or lower than 10% of par, the credit index portfolio will be unwound and no further credit exposure will be taken (a cash-out event). If this occurs, all coupon payments under the note will cease and the proceeds of the cash deposit will be returned to the noteholders.

ABN is at the early stages of marketing the deals and declined to comment further.

Chess II comprises three tranches: EUR²00m Class A notes, US$200m Class B notes and Yen2bn Class Cs. Rembrandt Australia Trust No. 2006-2 and Rembrandt New Zealand Trust No. 2006-1 will issue one class of notes each totalling 100m in their respective currencies (A$ and NZ$). All three deals have a legal maturity of 2016.

Funds drive tranche trading

Hedge funds lead mezz selling

CDX and iTraxx credit indices were relatively stable as the summer slowdown took full effect over the past week, but tranche volumes have been unusually high for August. Hedge funds have led the way in Europe, while in the US positive auto news has generated activity.

The iTraxx 5y and 7y were most affected by the move, with both segments tightening by around 7bp in a week. "There is quite decent activity in the standardised tranches and in the bespoke business there are also deals going through," says Marcus Schueler, md Integrated Credit Marketing at Deutsche Bank.

In the iTraxx tranches the main theme of the last week has been the selling of 3-6% protection in 5, 7 and 10 years. Activity was to a large extent hedge fund driven, but with some hedging from banks seen as well.

Schueler continues: "Most of the value has gone from the mezzanine piece into the super senior, particularly in 5 and 7 years, but it is difficult to say what has driven the move. Selling of 3-6% is normally the result of hedging, but this time that's not the case. There is a history of mezz tending to tighten before the index roll and maybe the expectation of that is behind the activity."

Meanwhile, the positive news emanating from the US auto sector last week appeared to drive CDX tranche trading. By August standards, last week was fairly busy for the 'off the run' standardised index tranches. CDX IG4 3-7% and 7-10% tranches traded in reasonable size, particularly in 7y and 10y. 7-10% tranches were busy in IG5 and IG6 as well, across several maturities; in fact, over US$250m traded on Thursday alone.

"There was a lot of CDX tranche trading last week, considering the time of year. The flows and timing suggest that it was autos related," says Michael Hampden-Turner, Structured Credit Strategy at Royal Bank of Scotland.

"Many auto names are in XO and HY indices now but used to be in IG indices. CDX IG4 for instance, contains many auto names such as LEA, FMC and GMAC," he explains. The CDX standardised tranche markets became increasingly quiet into this week, although healthy volumes of 7y and 10y CDX IG6 3-7% and 7-10% tranches were traded on Monday.

Despite such activity spreads moved little, but single name CDS on US auto firms did narrow to significant levels last week. For example, GMAC 5y without restructuring moved under 200bp for the first time since December 2004 on the back of GM's announcement that its $89bn US pension obligation was cut by $3.9bn and its $81bn retiree health-care obligation by $19.3bn after 34,400 workers agreed to leave the company.

At the same time, Ford Motor Credit 5y CDS slipped under 365bp for the first time since last October following union confirmation that it is willing to discuss further restructuring plans, scheduled for announcement in September, and continued speculation around the sale of its Jaguar division.

Investment and management

Pierre Emmanuel Juilliard, head of Structured Finance, AXA IM, answers SCI's questions this week

Pierre Emmanuel Juilliard

Q: When, how and why did your firm become involved in the structured credit markets?
A: We have been involved in structured credit since the early 1990s - initially it was a tactical move to spice up our fixed income portfolios. We bought our first ABS in 1992; our first CDO in 1995; traded our first credit derivative in 1997; bought our first infrastructure loan in 1998 and our first leveraged loan in 2000.

By 2000 it became clear that we needed to decide whether or not we should consider structured credit as a core asset class for our clients and cease to view it as a strategic business. We were strong believers that the financial markets would continue to disintermediate, which would offer investors new asset classes not previously available.

Indeed, we have seen credit disintermediation from the banks, with them increasingly becoming agents rather than lenders. We have also seen disintermediation from the corporate world, with companies selling their receivables, for example, and also disintermediation of the insurance industry through the hedging of liabilities and the selling of some of its catastrophe risk. In addition, we felt that advanced risk transfer technologies, such as credit derivatives and securitisation, could help us to maximise the value we could get out of that disintermediation.

That combination of a fundamental trend and the availability of the right tools convinced us that structured credit offers a lot of value for investors and that we should build a business in its own right in the area with people dedicated to being involved in those markets. Initially, we created a team dedicated to buying CDOs, which at first focussed on CDO equity. From then on, we became a large CDO manager, before creating teams focussing on leveraged loans and ABS, adding an investment grade platform in 2002 and more recently launching a global infrastructure equity business.

Q: In your view, what has been the most significant developments in the credit markets in recent years?
A: Liquidity has improved in a number of structured credit asset classes, but one of the most significant examples is European leveraged loans, which used to be a very clubby market. In 2000 it was still pretty much a bank-only market, but last year EUR32bn of loans changed hands between a wide variety of market participants - for example, we traded EUR400m of leveraged loans in the secondary market as both buyer and seller.

Another key development is the growth of the CDO market, which now - with more than US$200bn of issuance every year - means that the products are on the radar screen of many more people than ever before and there is a much wider acceptance of the value proposition of CDOs.

Q: How has this affected your business?
A: We feel that the overall increase in liquidity - across many credit sectors from investment grade CDOs to credit derivatives - has helped us to bring new sources of alpha and enhanced risk management to our products. We are less reliant on the primary market and can consequently move up and down the capital structure with greater ease.

Meanwhile, the growth in CDOs and their users has caused spread tightening in the products and lowered the cost of financing, meaning that you can now issue CDOs backed by ever tighter spread assets and therefore widen the scope of assets that can be included far beyond the early type of CDOs that were mainly backed by high yielding assets.

Q: What are your key areas of focus today?
A: Apart from day-to-day investment management, a key aspect of what we do is to regularly look at potential new asset classes that could offer great value for investors and we do a lot of upstream diagnosis in this area. For example, at the moment we are considering SME direct lending and looking at real estate debt. Similarly, we keep a close eye on developments in the risk transfer technologies available.

Our aim is not to be a one-stop source for structured finance, but instead to offer access to the most value added structured finance asset classes. We have five focus areas: leveraged loans, CDOs, asset-backed securities, managing investment grade synthetic CDOs and infrastructure. This focus represents our belief that those asset classes offer the highest value for investors when complemented with our core competencies.

Q: What is your strategy going forward?
A: Very much more of the same - to focus on our competencies and to try to grow our business and our people to give certainty of performance for our investors. At the same time, we will continue to look for new opportunities for clients and do our homework on new asset classes and techniques.

Q: What major developments do you need/expect from the market in the future?
A: We are a strong believer that financial markets tend to commoditise quicker than people expect. A prime example of that is the, above-mentioned, leveraged loan market in Europe - in only five years there has been a boom in liquidity, the market now has credit derivatives of its own and will soon have synthetic CLOs backed by loan CDS and its own index. No-one would have bet five years ago that you would have a large credit derivatives market on that asset class.

That is evidence of what has become almost a standard cycle for new structured credit asset classes: emergence; followed very quickly by securitisation; then you have credit derivatives; then an index is introduced; liquidity follows and commoditisation has taken place before you realise. This means that value comes less from entering a new asset class, but more from the active management of an investment manager - and that's why we feel that the market going forward will benefit the managers who have the culture of risk management and active management to produce additional return on top of what an asset class produces as standard.

About AXA Investment Management
AXA IM's Structured Finance Division (SFD) is an award-winning manager of Structured Finance products, including CDOs across a diverse range of asset categories. With over 50 professionals dedicated exclusively to the structured finance business, SFD offers breadth and depth of investment, research and structuring expertise. Its capacity to combine collateral and structural innovation with broader market enhancements, such as liquidity and transparency, has led to groundbreaking deals that have revolutionised the structured credit industry.
As of March 31, 2006, SFD manages EUR²8.8bn in assets.

"We need to cater for all!"

Profiling SunGard's Front Arena

In the latest of our series of Provider Profiles we talk to Pontus Eriksson, product manager, credit and interest rate derivatives; and Peter Banham, global head of product and marketing groups, at SunGard's Front Arena.

SunGard is one of the superpowers of financial technology: 110 separate companies and over 400 individual solutions have been either organically developed or acquired over the years. However, the group, now owned by a private equity consortium, has recognised the potential for confusion that such a large, disparate organisation has for clients and internal teams alike - potentially having sales teams competing with each other for new clients, while customers may possibly not be clear on what's being offered, and by who, is obviously not ideal.

As a result, SunGard has brought in four distinct areas of practice to tackle the front, middle and back office. Derivatives specialist Front Arena, acquired in 1992, sits at the forefront of SunGard's Financial Services Group.

Pontus Eriksson

Having begun to provide solutions for the credit derivatives sector in the late 1990s, Front Arena has been well placed to see distinct patterns of need emerge from the IT departments of the large investment banks and also, with hedge fund managers providing a steady flow of revenue of late, the quickly evolving needs of the buy-side. Both of these sides of the credit derivatives business present their own challenges to vendors.

On the sell-side, the news is fundamentally good - the dealer community's spend is up for structured credit IT systems and utilising a third party system is no longer an issue according to Pontus Eriksson of SunGard's Front Arena. However, investment banks demand an architecture that offers sufficient flexibility to allow it to be adapted in the future by the bank on its own as it builds bigger trading volumes and trades new structures and asset classes. In addition, in today's fast growing markets banks also need to be up and running with the new technology quickly.

"We use the term 'controlled variability' to describe how we install technology that allows banks to manage the expansion of the software on their own" explains Eriksson "Banks typically want a system that will take them 80% of the way there, allowing sufficient flexibility to let them complete the last 20% (of the build) themselves. We still see some tier one banks building purely in-house, but the trend is slowing once they appreciate how sophisticated third party systems have become."

Peter Banham

Meanwhile, the many hedge fund managers that have moved over from the sell-side face a huge cultural shift, coming out of well resourced IT departments into small boutiques with little or no dedicated technology resource. Nevertheless, buying a vendor's system is really their only long term solution, argues Peter Banham, SunGard Front Arena's global head of product and marketing groups. "We talk to many hedge funds that demand a turn-key solution and one that interfaces well with existing systems," he says.

Eriksson goes further: "We usually see a 'patchwork of excel sheets', each one of which has to be integrated, along with their systems. Hedge funds really want a 'Plug and Play' solution if they can get it; IT budgets are usually a problem, and they need to get up and running on a new system in matter of months, not a year to 18 months."

SunGard has risen to that latter challenge. "We have completed an installation in as little as 62 days so far for one hedge fund, and 90 days for another," claims Banham.

As for smaller hedge funds with even more limited budgets, Eriksson claims that an asp model, where you pay directly for the amount of the software you use, on a system hosted by a third party, isn't a robust enough solution for these smaller funds that might not have the budget for a full license. SunGard clearly understands that a toolkit approach would also be wrong for this part of the sector that demands the 'Plug and Play' alternative, so as some of the larger hedge funds have bought their technology as a bank might, by purchasing a traditional license, SunGard can provide a different solution for smaller funds to allow them the access that these funds recognise they need.

"We've partnered with hedge fund administrators to provide a system that they host and which the smaller hedge funds can access. It's a win-win situation, as the smaller players now get access to the power of a big system, but at a fraction of the cost." says Eriksson. "We get a fee for each additional user on the systems; the hedge fund administrator adds value to its service offering and the traders get to control their spend by avoiding a big upfront charge."

In addition to specific buy- and sell-side challenges, there are others that all involved face. For example, keeping up with every innovation in terms of new instruments in the structured credit arena and introducing a sophisticated position keeping capability to capture these trades poses an enormous challenge for both market participants and vendor alike. Hence Eriksson comments that "We need to cater for all!"

Similarly the vast amounts of ever changing data that now floods through the credit markets can pose an operational risk for users that only need a small sub-set of that data, but need to draw on heavy memory usage to access it. At the same time there can be issues surrounding the need for data integration and the need to accommodate for adjustment factors as a result of market activity.

In the face of these newly emerging risks, however, some standardisation is slowly emerging out of the markets, as the technology to deal with, for example, flow CDS trades is now relatively mature. Eriksson says that Front Arena's technology is evolving to provide such "sets of modules" to cover this emerging standardisation and this can only benefit a quicker adoption of technology by both dealers and investors. This, in turn, can only benefit the structured credit markets as a whole.

Bear brings new ABS CDO

A round up of this week's structured credit news

Bear brings new ABS CDO
In a new twist on the normal CDOs of ABS, Bear Stearns has launched the EUR450m Colonnade I, a partially synthetic CDO of European mezzanine ABS, for the Morgan Stanley Global Proprietary Credit Group. Typically CDOs of ABS are cash, and although this has in some ways been made to look like a cash deal it involves a synthetic transfer of risk into the SPV.

All assets are referenced at the full market value, reinvestments will be at market value and there is a cashflow waterfall. This means there are IC and OC triggers, along with additional coverage tests that would be expected in normal cash deals. The deal comprises a EUR324m super senior retained piece and five tranches, A through to E, rated Triple A, Double A, Single A, Triple B minus and Single B, all with a 9.05-year WAL. As a result of its unusual structure the deal paid a slight premium across the capital structure to where cash flow European mezzanine deals trade/price.

Taiwan CDO market enters new phase
Fitch Ratings reports that issuance of primary CLOs and asset-backed commercial paper are likely to dominate Taiwanese structured credit issuance in the short to medium term.

In 2005, CDO technology was used to repackage illiquid Taiwanese structured bonds and this led to explosive growth in Taiwan's CDO market. Fitch believes the Taiwanese CDO market is entering a new phase in 2006, with some new drivers emerging. While the agency expects overall CDO issuance in Taiwan to remain stable, it expects more issuance of ABCP rather than term notes in coming months.

Fitch recently rated the first Taiwanese ABCP transaction backed by a local insurer, Taiwan Life 2006-1 ABCP Securitisation Trust. "This transaction is likely to provide the impetus for other Taiwan insurance companies to explore how they can advance their risk-return profiles through the use of CDO technology," says Jackie Lee, associate director in Fitch's Structured Credit team in Taipei.

ESF says CDOs fastest growing sector
The European Securitisation Forum's summer 2006 data report finds that CDOs, including funded cash and synthetic deals, were the fastest growing product sector and continued to raise their share of issuance volume to 8.2% in the second quarter. CDO issuance surged to EUR31.5bn in the first six months of the year, about 61% higher than the EUR19.5bn during the first half of 2005. Arbitrage CDO issuance accounted for 48% of aggregate CDO issuance, with the remaining 52% being balance sheet CDO.

"The percentages confirm the resurgence of balance sheet CDO issuance that began late in 2005. It is expected that a number of bank balance sheet CLO transactions will come with issuers motivated by economic and regulatory capital issues arising from Basel 2," ESF says.

Principia launches V5
Principia Partners, a provider of end-to-end processing solutions for structured finance and capital markets, has announced the release of V5, an improved version of Principia's structured finance platform. Improved features in the software aim to facilitate and automate the manually-intensive tasks associated with managing ABCP conduits, securities arbitrage conduits, structured investment vehicles (SIVs) and credit derivative product companies (CDPCs).

"CDPCs represent an important growing trend in the structured finance world, merging the best practices and economic benefits of credit derivatives and securitisation," states Douglas Long, Business Strategy at Principia. Indeed, CDPCs are widely predicted to quickly become a major component in the credit derivatives market.

Fitch Synthetic Index Quality Remains Stable
Fitch Ratings says its Synthetic Collateralised Debt Obligation (SCDO) index showed stable credit quality in H106. The index's Weighted Average Rating Factor (WARF) deteriorated 7% in H106, compared to 8% deterioration in H105. The weighted average credit quality of the index was more stable in Q206 than Q106, with 2% deterioration in the index's WARF in Q206 compared to 5% deterioration in Q106.

Following a rebalancing carried out in July, the index has been refined to better account for merger-related activity. There have also been some changes in the most widely referenced speculative-grade names. Following its downgrade to speculative grade, Albertsons is now the second most widely referenced and VNU remains the most widely referenced speculative-grade.

By country and industry, the index remains concentrated in US banking and finance names. Exposure to the US automobiles sector has decreased; it is now the fifth most widely referenced sector in the index, having fallen from the fourth in April. Exposure to the US telecommunications sector has been increasing, reflecting increased confidence in the sector just four years after the credit event on WorldCom. Exposure to this sector has increased in spite of it suffering the second highest number of downgrades in H106.

T-Zero signs up BGC
STP service provider T-Zero has announced an agreement to provide connectivity and post-trade affirmation to derivatives broker BGC partners. BGC will initially utilise T-Zero's post-trade technology for CDS single names and CDS indices and tranche trades.

T-Zero claims participation of 80 buy-side firms, as well as a significant number of other clients including, Bloomberg, several banks and operations service providers such as DTCC Deriv/SERV and GlobeOp, Calypso and Thunderhead. Five major banks are expected to join the service in the coming weeks.

Fitch releases ABS CDS case study
A report released by Fitch Ratings suggests that available funds caps (AFC) shortfalls are not a material issue for synthetic ABS CDOs. Fitch has studied the ABX.HE CDS index to analyse the potential for AFC induced interest shortfalls and the implications for single name ABS CDS and synthetic ABS CDOs in particular. In the US, equity holders would most likely feel the impact of any AFC shortfalls within a synthetic CDO in the form of reduced returns, while credit enhancement in the form of over-collateralisation typically would be unaffected.

US CLO issuance falls
Standard and Poor's LCD (SPLCD) reports that after totalling US$11bn in June, CLO issuance fell to a six-month low of US$5.3bn in July. This brings year-to-date issuance to US$47 billion, up from US$21 billion during the first seven months of 2005.

"Looking ahead, inflows are expected to remain strong. On the CLO front, collateral managers expect issuance to continue to register US$6-8 billion per month. August, in fact, got off to a strong start. During the first week of the month five new CLOs printed for a total of US$2.3 billion. Even so, the calendar remained at a robust US$12 billion as of Aug. 4, right in the middle of its recent range," SPLCD says.

H1 rating transitions show improvement
Moody's and Standard and Poor's have released their updated rating transitions studies for the first half of 2006. Both reports showed that worldwide structured security credit performance remained strong in the first six months of the year.

Moody's found that the global structured finance market experienced 292 rating downgrades and 918 upgrades in the first half of 2006, producing an upgrade-to-downgrade ratio of 3.1. Standard and Poor's report provided similar results showing an upgrade rate of about 2.3 times the downgrade rate during the first half of 2006.

Standard and Poor's went on to say that global CDO performance continues to improve and that transactions backed by credit cards and auto loan ABS and prime jumbo and second-lien RMBS have experienced increases in credit quality, as have high-yield CBOs and CLOs, synthetic emerging market CDOs, and recent-vintage CDOs of ABS.

A primer on valuing synthetic CDOs

Richard Hrvatin, md in Fitch Ratings' credit products group in New York, describes the inputs necessary for estimating the market value of single-tier CDOs.

Richard Hrvatin, md in Fitch Ratings' credit products group in New York, describes the inputs necessary for estimating the market value of single-tier CDOs.

In a funded synthetic collateralised debt obligation (CDO), a special-purpose vehicle (SPV) sells protection on an underlying reference pool by synthetically referencing a portfolio of single-name credit default swaps (CDS). The SPV offsets this risk by issuing notes that provide investors with exposure to tranches of the underlying reference portfolio.

Investors receive a premium for selling protection on the reference portfolio via the SPV. However, should sufficient defaults occur in the reference portfolio, the SPV may need to pay cash settlement amounts to the swap counterparty, reflecting the losses incurred on the defaulted assets. Generally, the notional of the SPV's notes are then similarly reduced, and both future interest as well as the notional received at maturity are reduced. Should sufficient defaults occur, the investor will not receive any principal at maturity.

There is a priority scheme for the tranches to absorb pool losses. An investor starts to suffer losses on a tranche when losses in the portfolio breach an attachment point (AP), which is typically expressed as a percentage of the total pool notional. Losses stop being allocated to a tranche when portfolio losses are greater than the detachment point (DP), which is also typically expressed as a percentage of the portfolio notional.

Synthetic CDOs can be funded or unfunded. In an unfunded CDO, the investor pays the recovery-adjusted notionals upon default of a name in the pool once losses have breached the AP. The recovery-adjusted notional is also commonly known as the loss given default (LGD). In a funded CDO, the investor pays the tranche notional upfront and, at the maturity of the CDO, receives the remaining notional that has not been used to compensate for losses beyond the AP.

At a high level, for an investor providing default protection, the value of a synthetic CDO tranche is simply the difference between the expected premium payments and the expected default payouts, which is expressed as:

Value = Expected Premium Payments - Expected Payouts due to Defaults

The expected premium payments leg is the sum of the future payments the investor expects to receive as a result of taking on the risk of defaults in the pool, discounted to today. The expected payout due to default leg is the discounted sum of all the future payments that the investor expects to make as a result of providing protection on defaults in the pool. The undiscounted payout will be equal to the greater of zero and the sum of the recovery-adjusted notional of the defaulted names in the pool minus the AP.

Both the expected premium payment leg and the expected payout due to default leg depend on the expected losses in the underlying pool, i.e. they depend on the defaults that are expected to happen at some point in the future. These future default events are represented by the portfolio loss distribution.

Portfolio Loss Distribution
The portfolio loss distribution represents the probability of experiencing a given level of loss over the transaction's term. This loss distribution is central to understanding the value and risk inherent in CDO products.

Overlaid on the portfolio loss distribution are the loss functions for an equity and mezzanine level tranche. The equity tranche absorbs the first losses. Hence, it is affected by the portion of the portfolio loss distribution from zero to its DP. The mezzanine tranche, on the other hand, is concerned with the probabilities of larger losses occurring.

Correlation is one of the key drivers of the shape of this loss distribution and so the magnitude of the losses that can be experienced. Consider first the case of 0% default correlation between the names in the pool. In this case, all the names in the pool will default independently of each other. As the correlation is increased towards 100%, the names increasingly default in clusters. At 100% default correlation, all the names will behave in the same way, with either all the names defaulting together or none of the names defaulting.

Chart 1 illustrates the effect that more subtle changes in correlation may have on a portfolio. In both cases, all the names have the same probability of default. However, changing the correlation from 0% to 10% has a significant impact on the shape of the distribution. In the portfolio with a 10% correlation between the assets, there is a higher probability of extreme events, i.e. a large or small number of defaults occur more frequently than for a portfolio with 0% correlation. Notice, however, that the mean expected loss is 2.2% in both cases.

In the absence of correlation, the portfolio loss distribution for a pool of assets with the same default probabilities can be calculated analytically using the binomial probability distribution.

If the effects of correlation are to be considered, it is difficult to compute the portfolio loss distribution using the binomial probability distribution. To include this information, a copula model is generally used. A copula model establishes the joint default behaviour between each of the assets in the pool.

One-Factor Gaussian Copula Model
In a one-factor Gaussian copula model, the correlated defaults in a portfolio are driven by random variables that describe the timings of the defaults. When any one of these variables drops below a specified boundary, a default occurs. The lower the value of the variable, the earlier a default is likely to occur.

This random variable is often interpreted in the context of a Merton model, as the value of a company's assets, or asset value. In the Merton model, a company will default when the value of its assets falls below the value of its liabilities. This level is known as a default threshold.

The asset value is driven by two components. The first component is a systemic component. A systemic component can be thought of as the portion of the asset value that is driven by market factors, such as the state of regional or sector-specific economies. The correlation of the names in the portfolio is captured through the sensitivity to these market factors.

The second component of the asset value is an idiosyncratic component. This component is specific to an individual name and affects the default likelihood of only that asset. In a Gaussian copula model, it is assumed that both the systemic and idiosyncratic components, and hence the asset value itself, are normally distributed.

To determine if an obligor is in default at a given time, the asset value is compared against the liability value. This default boundary is determined by mapping the risk-neutral probability of default to the normal distribution. Risk-neutral default probabilities are described in the box below.

In a Monte Carlo simulation, random numbers are drawn for the names in the portfolio to represent the change in their asset value. The random numbers for each asset are then compared to their respective default thresholds. If a random number is less than the default threshold, the name has defaulted; if not, then it survives. Each name in the portfolio is tested in the same manner to quantify single or multiple default events. The degree in which the random variables move in unison is dictated by the asset correlation assumptions.

Correlations
As described in the previous section, correlations are required to determine the loss distribution. One approach is to look at historical measures of default correlation. However, with the introduction of standard CDO tranches, such as those that reference the CDX and iTraxx credit-default swap indices, investors are now able to extract market-implied correlations.

Initially, investors focused on compound correlation, which is a single correlation that re-prices the tranche to fit market prices or theoretical values. However there are several problems with this approach. When the implied correlation is determined using a Gaussian copula model for each tranche of a full-capital structure CDO, it resembles a smile. This indicates that a Gaussian copula does not produce the required tail dependence implied by market CDO tranches. In addition, there can be two possible correlations for a single mezzanine tranche in some cases. Finally, it is problematic to apply implied correlation to the pricing of CDOs with maturities or APs or DPs that differ from the standard index tranches.

Because of these disadvantages, it has become standard market practice to quote base correlations instead of implied correlations. Base correlations are the correlations required to match quoted spreads for a sequence of first loss tranches of the standard index tranche. The basic idea behind base correlation is that each tranche can be decomposed into two equity tranches. The value of the tranche is then the difference between the two equity tranches with DPs equal to the original tranche's AP and DP. The series of base correlations is then found for each DP by determining the implied correlation such that the observed market prices can be replicated.

As the DP increases, the base correlations also increase, forming an upward sloping skew. If the Gaussian copula accurately captures the tail dependence of the market prices then the base correlation would be approximately the same for all APs.

When pricing a CDO with the same reference pool as the index but differing APs and DPs or maturities, the base correlations are determined by interpolating the base correlation surface derived from the relevant index. When pricing CDOs with a different reference pool than any of the indices, the base correlations are determined through an algorithm, which re-maps the base correlation surface based on the expected loss of the reference pool.

Valuing the CDO
Once the portfolio loss distribution is known, the expected loss can be determined, and the CDO can be valued. In practice, however, hundreds of thousands of Monte Carlo simulation paths are required to determine a stable portfolio loss distribution. As such, it is standard market practice to use semi-analytic techniques to determine the portfolio loss distribution. The most popular of these is Hull-White's recursive technique.

It is interesting to take a look at the effects of correlation on the value of a typical synthetic CDO. In the following example, an equity and a senior tranche have been valued in RAP CD - the Risk Analytics Platform for Credit Derivatives, Fitch Ratings' market risk analytics solution for synthetic CDOs - under various asset correlation assumptions.

Chart 2 shows how the expected loss varies for increasing correlation. For the equity tranche, the value of the expected payouts due to the default leg decreases as correlation increases. As correlation increases, the probability of all the names defaulting together or none of the names defaulting at all also increases. As the equity tranche would be eroded even if there were a few defaults, this will result in a lower value of the expected payouts due to the default leg.

On the other hand, for the senior tranche the opposite result is observed. The senior tranches are concerned with the region of the loss distribution that spans larger losses. An increase in correlation will increase the likelihood of all the names defaulting together and hence will result in an increase of the value of expected payouts due to the default leg.

Conclusion
The standard approach for valuing a CDO is calculated by subtracting the expected loss of the tranche from the expected premium amounts the investor will receive. The expected premium and loss amounts of the tranche are estimated by looking at several factors, namely default probability, recovery rate, correlation and maturity.

Copyright 2006 by Fitch, Inc., Fitch Ratings Ltd. and its subsidiaries. This Research Note was originally published on 26 July 2006, under the title 'A Primer on Valuing Synthetic CDOs of Corporates'.