Contents

CDR Liquid Index data as at 22 January 2007

Source: Credit Derivatives Research

CDR Liquid Indices
The CDR Liquid indices represent the CDS levels of the most-liquid names in their respective markets and ratings classes. Liquidity is measured by the number of bid-offers a credit receives. Index values are simple averages of on-the-run five year CDS levels.

CDR Global Market Depth™
The CDR Global Market Depth Index is a daily measure of how many names are actively traded. Liquidity is measured by the number of bid-offers a credit receives. Index values are counts of the number of names that exceed CDR's Liquidity Floor.

CDR Global Market Activity™
The CDR Global Market Activity Index is a daily measure of activity within the global CDS market. Liquidity is measured by the number of bid-offers a credit receives. Index values are simple averages of total bid-offers of all names that exceed CDR's Liquidity Floor multiplied by CDR's Global Base Liquidity Constant.

Rare opportunity finds favour

Investors embrace new European stressed credit opportunities fund

A first-of-its-kind credit opportunities fund focussing on sub-par European credit is understood to have launched last week, heavily oversubscribed thanks to intense interest from structured credit investors. The fund, Fugu Credit, was structured and is managed by Babson Capital Europe – which is prohibited from talking about the deal because of US disclosure rules. It is believed to have involved a US$100m equity investment backed by a US$600m total return swap (TRS) financing facility provided by Bank of America.

Fugu has a hedge fund type structure where investors buy units in the fund and the TRS provides the manager with leverage capability. It is not a structured deal in the usual sense, as there is no tranching or rating agency involvement.

However, Fugu does have some structured credit characteristics and borrows quite significantly from market value CLO technology in terms of the way the TRS is set up, how and what concentration limits are applied, and the triggers for selling assets that have been put in place.

"I'm not sure this kind of fund would have been set up if market value CLOs hadn't been established a while ago," says one investor. "It has had a lot of uptake from CLO investors who actually like to buy equity valued at par on day one rather than CLOs where, if you take out all the up-front costs, you've lost probably 12 points of value."

He adds that the advantage of a CLO is the cost of debt is marginally cheaper than on a TRS, but if looked at over, say, a five-year timeframe and amortising the upfront fees, Fugu is economically viable. "It's just a lot cheaper than most structured credit products that have to go down the route of paying rating agencies fees and bank placement fees on the debt."

Fugu's appeal goes beyond its costing, however. It is the first credit opportunity fund to target European sub-par credit that isn't necessarily distressed, but is underperforming. The aim of the fund is to position itself for a future point in the credit cycle when the stressed market is more broadly attractive, but at the same time take advantage of a current gap in the sector.

There appears to be an opportunity for investors in credits trading between 90 and par at the moment. CLOs usually focus on par plus paper and don't tend to have big enough teams to be able to cope with looking at underperforming companies – and, if anything, anecdotal evidence is that CLOs are net sellers of underperforming companies. On the other hand, hedge funds, particularly distressed funds, are looking for sub-80 credit with 20% IRRs.

That is not to say Fugu is restricted to exclusively investing in sub-par paper. The manager has a remit to invest wherever in the credit market it sees value. Its only restriction appears to be that the TRS is a variable leverage facility dependent on the quality of the assets in the portfolio, so if Babson were to only buy stressed assets the US$600m would be commensurately reduced.

MP

Tighter and tighter

Index markets move slowly ever inward as curve plays become a focus

Dealers report quiet market conditions in the main indices as historic or near historic tights continue to be breached, following considerable excitement last week when the Crossover broke 200bp for the fist time. There has, however, been some single name and curve-related activity.

Marcus Schüler, md integrated credit marketing at Deutsche Bank, says: "Normally in late January it will be really busy but this has been a rather quiet week. We are back to the situation we were facing in December with gravity pulling the market ever tighter in an environment that remains favourable."

On Wednesday morning London time, the Crossover traded at a record 195bp and the iTraxx main traded just 1/8bp shy of its tightest level of 22.5bp. Meanwhile, overnight the CDX IG had narrowed to 31.5bp.

Elsewhere in the market, traders report occasional moves on single names - there have been flurries of interest around Tate & Lyle and Alcatel, notably. Telefonica had been expected to be a focus too this week in light of its new 7-year bond issue, but the CDS only widened by 1bp on announcement of the deal details, and since issuance has been trading around re-offer.

The previous week had seen significantly more single name activity as investors looked to position for event risk. Flows were significant enough to cause both the media and paper sectors to widen.

One area of interest that has followed through into this week has been an increasing focus on curve plays. The major curves found steep levels last week with CDX reaching 26.5bp, iTraxx main 21bp and Crossover 105bp.

They have flattened since to 25.25bp, 19.5bp and 100bp respectively, with dealers reporting some support at these levels, but it could simply be profit taking. Trading accounts are understood to be in favour of further steepening and have positioned accordingly, but there remains the spectre of potential 10-year structured credit supply which could cause further curve flattening.

Consequently, most are adopting a wait and see approach. As Schüler concludes: "If you want to have a position in this market one way or the other you will be long overall. Many may not feel comfortable at these tight levels but in the current environment it's the only option. Many people came up with a list of the single names they thought most likely to be impacted by event risk this year and consequently put on shorts last week. But now, with these short established, like everyone else, they are waiting for something to happen and event risk to strike."

MP

Omicron and WestLB bring LSS twist

Innovative leveraged super senior structure combines with actively managed CDO of European ABS

He explains: "What is unusual about this transaction is the way we go about the super senior funding. In order to minimise the funding costs, which is fairly crucial for European ABS given that spreads are tight on the senior side, we and WestLB came up with a leveraged super senior [LSS] structure which means investors invest in the most senior tranche on a levered basis to give them the benefit of higher spread."

LSS tranches – either in stand-alone deals or part of other CDOs – are normally structured around a trigger event based on weighted average rating factors, realised losses or mark-to-market changes, which unwinds the trade if the tranche hits one of these triggers. In Carnuntum's case the LSS loss trigger is a ratings-based one, which should appeal to investors as it is an easier methodology to follow.

Klug says: "The trigger is based on assets defaulting or being downgraded to a double-C rating from S&P. In order to trigger, a couple of securities will need to be downgraded from wherever they started between triple-A and single-A down to double-C, which is obviously a long way. In addition to that, the deal is actively managed by us."

Carnuntum fits well with Omicron's market views, according to Klug. "European ABS is one of our core strategies and we felt that, given the fundamentals of the market from triple-A to single-A, it makes sense to attach there from a risk-return perspective. We continue to see good relative value in European ABS, particularly in the higher rated categories as spreads of triple-B and double-B rated tranches have been quite compressed by excess demand from investors," he says.

The indicative capital structure comprises: triple-A rated class A-1, A-2 and A-3 notes of €820m, €80 and €50m respectively; €25m of double-A rated class B notes; €10m of single-A Class C notes; €5m triple-B class D notes; €5m double-B class E notes; and €5m unrated class F notes.

The transaction is Omicron's first European ABS CDO since it was founded in November 2005 (see SCI issue 7 for more details on the firm), but it has already taken over management of a US mezzanine CDO-squared – Stanton CDO I. In addition, in December 2006 Omicron launched the Omicron ABS Income Fund, a closed-end fund investing in European ABS securities, with HSBC as arranger and LBBW as placement agent for German savings banks.

MP

Basel II possibilities

Granularity rules provide arbitrage potential

Despite efforts to refine Basel II prior to its final release, some distortions remain in the formulaic IRB approach. These types of anomalies not only create arbitrage opportunities for issuers, but also for investors to determine when and where they may occur, according to new research from Royal Bank of Scotland.

The paper notes that among the interesting prescriptions in the IRB's securitisation approach was to set the definition of "non-granular" pool at six, or more, exposures. Exposures are defined as the sum of exposures at default, squared, divided by the sum of each exposure at default squared, i.e.,

Where N equals the number of exposures and EADi equals the exposure at default for the ith instrument in the pool.

Under the rules, up to 3-1/2 times capital is required for a non-granular pool over a granular one. As a result, a rigid rule of six exposures makes single-loan transactions, such as large property CMBS, look less attractive to bank investors.

However, there has been much discussion in some jurisdictions over what is an "asset". For example, in a CMBS transaction, is an asset the loan itself or the properties securing the loan, or cashflow from each of the tenants in the properties securing the loan?

Even so, Ron Thompson, head, ABS and structured finance research at RBS, says: "By using CDO technology, one may create a new security backed by six or more single-asset bonds. This technology can convert a series of non-granular transactions into a granular pool, enabling investors to access lower risk weightings. Single tranche CDO technology may provide capital arbitrage by allowing low rated (or equivalent) or higher securities to qualify as senior notes. Similarly, a CDO backed by a pool of non-granular notes may qualify as granular."

The RBS paper utilised an example of an IRB bank using this technology. It converted six equally-weighted subordinated tranches of non-granular "pools" into one senior tranche of the granular pool, reducing risk weights from 35% to 10% and thereby reducing capital required by over 70%, from 2.8% to 80bp.

"This arbitrage stems from the risk weights provided on non-granular pools (regardless of whether they are senior or subordinated) morphed into a senior tranche by using CDO technology. Senior tranches of granular pools are eligible for lower risk weights than subordinated ones down to a triple-B rating," says Thompson.

Such trades are creating plenty of interest among investors as present. "These opportunities are certainly something that investors are talking about and are also the starting point for many other trade ideas," Thompson observes.

MP

Strength and depth?

Q-WIXX questions from the buy-side

Q-WIXX, Creditex's new electronic platform for trading credit derivatives portfolios, is expected to launch globally early this quarter. While the platform is designed to streamline the trading process and has some supporters on the buy-side, others have indicated certain drawbacks.

Goldman Sachs, JP Morgan, Deutsche Bank, Credit Suisse and Cairn Capital undertook the first portfolio trade of 131 North American and European CDS names, totalling $1bn and €500m in December (see SCI issue 20). "The first trade on the system went very smoothly for us, with no hitches. Our investors participated in transferring a billion dollars of risk in a real live auction and we look forward to using the system again," says Tim Frost, director at Cairn Capital in London.

He feels Q-WIXX is entering the market at an opportune time, due to substantial progress in processing the backlog of trade confirmations. Appetite for such a product may have been limited when unconfirmed trades had spiked up to 100,000 in September 2005, but subsequent developments in trade affirmation and STP connectivity have streamlined operations and helped CDS volumes to increase substantially, doubling to over US$40tr last year compared to 2005.

"The ability of the market to cope with increasing volumes has been constrained by its technology and infrastructure. Q-WIXX is a logical development; it gives the market the capacity to process more risk more speedily," he says.

Frost believes the system will have a fundamental impact within the structured credit industry. "Q-WIXX is a fairly significant development in the credit market and, going forward, you won't be thinking about executing bespoke-type portfolio trades without doing them on Q-WIXX," he says.

An executive at a credit-oriented hedge fund in the US believes Q-WIXX is by far the most competitive offering in the market. "The system is terrific. Intuitively it is a great interface, consistent with how people trade and easily integrates into the operating infrastructure of dealers and clients," he says.

Nonetheless, he believes one constraint is offering competitive prices from just four dealers. "Only going out to four at a time is a restriction and that limits your access to liquidity, especially in a deep market like North America where you need broad access to the dealer community," he says. "This is less of an issue in Europe, where the trading dynamics are very different as you can go to say six dealers and get exactly what you need."

Others are waiting for the service to gain more traction before considering its uptake. "Q-WIXX needs to reach more depth before we start looking at it," says Jonathan Laredo, partner at Solent Capital Partners in London.

A trader at a London-based specialist credit manager adds that "liquidity is also a function of relationships", suggesting there is some scepticism about the depth of support the system will actually get from the dealer community.

The US-based executive adds that Q-WIXX may attract a greater share of the less frequent, low volume players rather than the sophisticated and high volume houses. "The larger shops have already made substantive investment in execution and operating infrastructure and it will be a nice add-on for potential productivity reasons by freeing up a lot of trading capacity. But it will have more of a material effect on the smaller shops or new entrants in structured credit who are unaccustomed to the operational complexities," he says.

Another danger is that liquidity becomes bifurcated in the market with the less frequent players using Q-WIXX or an equivalent system and the regular players who demand high liquidity provision preferring to access a wider range of dealers via the phone.

MarketAxess has a competing product in the market that is understood to have also undergone beta testing late last year.

HD

"Control, validate and audit the entire process"

This week's Provider Profile looks at documentation generation vendor Thunderhead

However plain (vanilla) the world of documentation generation and client communications may seem, getting this aspect of a business right nevertheless plays a crucial part not only in effective client and counterparty relationships, but also in helping buy- and sell-side firms reduce operational risk and failed trades. Efficient documentation can also provide an audit trail should things go awry when a credit event takes place.

The electronic route to documentation efficiency is itself the vanilla route out of what traditionally for many banks has been a very complicated, costly and burdensome way of dealing with data capture and communications.

To this end, the curiously named Thunderhead (it's all to do with an unusual kind of cloud that the firm's founder, Glen Manchester, was once 'struck' by) aims to reduce the paper trail, replacing it with an efficient, auditable and editable trail of electronic records that reduces costs and risk in counterparties' OTC derivatives dealing.

The structured credit market is by no means Thunderhead's only sector of focus, which spans investment banking, insurance, retail banking and the public sector. But given the somewhat uncontrolled growth of recent years, Thunderhead has provided sell- and buy-side institutions within the credit markets with a viable solution to the growing pains of the back office.

Kevin Thorogood

"When the Fed called together the 14 dealers back in the autumn of 2005 this was in many ways a watershed moment for our clients in the credit derivatives markets as banks suddenly had to put real impetus behind streamlining not just confirmations, but the entire back office set-up," says Kevin Thorogood, Thunderhead's director of investment banking solutions.

The firm now provides the in-house solution for the derivatives confirmations of Morgan Stanley, Nomura and UBS, plus a handful of hedge funds. It is the provision of an open standard format template, and the flexibility offered in the product that has won over such big names, the company says.

"It's fairly easy generating documentation for vanilla trades, but once a firm starts trading structured products the process becomes intensively manual as each trade can look dramatically different from the last and each can be especially complex. The back office requires tremendous flexibility from the templates we provide in order to accommodate such complexity," explains Thorogood.

Anecdotal evidence, according to Thorogood, suggests that at some point in its life cycle, every OTC trade requires some form of manual intervention, and therefore automation is the key to driving down cost. "Microsoft solutions, traditionally seen in a back office, are un-audited and uncontrolled; what we supply enables the client to control, validate and audit the entire process. We also employ a workflow environment such that the user can employ full risk management controls at each stage of the process," he says.

"Banks have also built their own in-house systems but these are often built by technology departments without the users' needs in mind, and so what often results is that these users get frustrated and eventually switch back to using word, which they're more comfortable with. Lots of time and money is consequently wasted in many areas of the bank and they're still no more efficient," claims Thorogood

As a result, Thunderhead is now seeing banks increasingly considering third party systems for documentation generation, as the sell side prioritises its technology between what it considers must be built in-house and what it can outsource. Banks are also increasingly turning their backs on a 'silo' based approach to solving individual technology problems in distinct departments, and will adopt a cross-asset solution where possible, says the firm.

The usability of a vendor's system therefore becomes a key determinant in a bank's choice of partner. Thunderhead tracks and audits all changes to a document and provides complete management reporting, which is particularly important when dealing with operationally risky transactions in, for example, emerging markets.

Thorogood observes: "The product range is huge in all derivatives, and especially when you add in emerging markets. Even though the volumes are smaller, you are still faced with close to total manual intervention at some point in the trade with your confirmations, so why not choose to automate the process as far as possible with a flexible template-based system?"

Links to trading platforms such as Murex, Openlink, Calypso and Summit have added to the appeal of the system, and templates based on Thunderhead's XML standard can be produced in days instead of weeks, claims the firm. Complementing the offering still further, Thunderhead now has links to the DTCC so that client firms can build links via Thunderhead to Deriv/SERV.

This is seen as a particularly attractive part of the offering, according to Thorogood "The arrival of the DTCC Trade Warehouse means that firms on the buy- and sell-side have to keep up with operational changes that much more," he says.

"We've witnessed tremendous co-operation between banks to make the initiative a success. The warehouse offers a big opportunity for adding efficiencies through its lifecycle management of a trade, but requires initial effort from both sides of the transaction; our rules based formatting tool will streamline the process for many," Thorogood concludes.

JW

Lehman acquires to expand in Asia

The latest company and people moves

Lehman acquires to expand in Asia
Lehman Brothers has agreed to buy 100% of Grange Securities Limited, one of Australia's leading investment and advisory firms, and one of the country's biggest CLN issuers. The terms of the agreement were not disclosed.

Lehman says the move aims to create a new force in the Australian investment banking market and will deliver enhanced services to Grange's broad range of corporate, institutional, government and individual clients. Grange will become part of Lehman Brothers' Asian operations, while retaining its name.

Established in 1995, Grange Securities has successfully created leading market positions in the Australian fixed income, structured credit, hybrids and high yield markets. The firm has expanded its range of activities in recent years to include investment management, equities, corporate finance, asset management and private client services.

Lehman Brothers' Asia ceo Jesse Bhattal says that Lehman Brothers and Grange have enjoyed a strong working relationship for several years and Grange is a natural partner for Lehman Brothers' expansion into the fast growing Australian market.

The transaction is expected to close in February, subject to regulatory approvals and other closing conditions.

RBS and Renaissance to co-operate in Russia
RBS Global Banking & Markets and Renaissance Capital have agreed to enter into an exclusive co-operation agreement to jointly provide credit, currency and interest rate derivatives to their government, corporate and institutional clients in Russia.

The banks say that the combination of Renaissance Capital's large local presence and extensive client relationships with RBS's derivatives expertise and balance sheet will enable us to deliver an unparalleled range of financing and risk management solutions to both firms' client bases. Renaissance Capital is the largest and most experienced private investment bank in Russia with a pre-eminent Russian capital markets franchise and the strong senior-level local relationships required to originate transactions.

Francovicchio joins Bear
Daniela Francovicchio has joined Bear Stearns as a cash CDO structurer from Morgan Stanley where she had a similar role. She now reports to Mark Moffat, head of Bear Stearns' European capital markets group.

Moody's KMV appoints new Tokyo team
Moody's KMV, the quantitative credit risk measurement and management solutions provider, has appointed a new management team in Tokyo, led by credit industry veterans Philip Jones, Japan country head, and Setsuko Nishiyama, director. The Tokyo team will spearhead the provisions of default probability, portfolio management, valuation and other products and services to Japanese banks and other entities, the company says.

Before joining Moody's KMV, Jones was general manager at Kamakura Corporation-Japan. Prior to his tenure with Kamakura, he was director of financial institutions for Fitch Ratings, where he conducted ratings and research on major Japanese banks and securities firms.

Nishiyama joined Moody's KMV in London in 2000 after launching her career with a large Japanese bank, where she worked on major international credits. Prior to her current position with the Tokyo-based team, Nishiyama was a Moody's KMV director, responsible for global banks in the London market.

Markit recruits ABS specialists
Markit Group has hired James Savitsky and Thomas Geraghty as directors within the company's global ABS sales and product development teams. Both Savitsky and Geraghty will be based in New York.

Savitsky will coordinate Markit's ABS sales effort globally, distributing the firm's data and analytics services for the structured finance markets. Savitsky joins from Trepp, where he headed sales and business development for the firm's CMBS platform.

Geraghty joins Markit's North American structured finance product development team, with a specific focus on data and the modelling of structured securities. Prior to joining Markit, Geraghty was an md at Wall Street Analytics, where he was responsible for product development.

MP

DBRS revises CDO criteria

A round up of this week's structured credit news

DBRS revises CDO criteria
Dominion Bond Rating Service has announced changes to its methodology for arbitrage-type transactions entered into by Canadian commercial paper issuers and funded by DBRS-rated Canadian asset-backed commercial paper. The agency explains that it has recently declined to approve many of the arbitrage-type CDO transactions (also known as structured financial asset or SFA transactions) proposed by CP issuers.

Consequently, the ratings agency believes it is appropriate to outline to market participants the basis on which DBRS would find new SFA transactions acceptable for funding by ABCP. DBRS would welcome the opportunity to consider CDO-related SFA transactions that:

(1) Provide for resilient credit characteristics that surpass the DBRS CDO Toolbox minimum triple-A attachment point;
(2) Contain limited exposures to any one particular industry and to non-investment grade entities;
(3) Are supported by liquidity facilities from DBRS-approved liquidity providers which contain conditions to draw that are not limited to market disruption and are not dependent on a confirmation of the then-current ratings; and
(4) Are proposed by CP issuers that maintain a superior level of information disclosure to ABCP investors, which in particular relate to the type of SFA transactions executed, the nature of the collateral and hedging transactions employed by the CP issuer, and whether or not the CP issuer is exposed to contingent funding obligations.

The Canadian ABCP market has grown rapidly over the past two years, DBRS says, with growth largely being attributed to the contemporaneous growth of SFA transactions. The most common type of SFA transaction funded by ABCP involves CDOs that reference corporate obligations.

Recently, leveraged super senior (LSS) structures have been the most prevalent type of CDO transaction executed by Canadian CP issuers. SFA transactions currently represent approximately 30% of Canadian ABCP market outstandings and LSS technology is used in transactions that account for approximately 22% of ABCP outstandings.

ABX.HE indices roll
The roll of the ABX.HE synthetic ABS index of US home equity asset-backed securities took place last Friday. The resulting series, ABX.HE 07-1, references a new set of underlying deals issued within the past six months.

Unlike the CDX and iTraxx indices, where the roll concept is designed as a way for investors to retain exposure to the most liquid series of credits and where liquidity tends to be concentrated in the most recent "on-the-run" series, ABX.HE is designed so that each series provides a unique vintage profile, namely:
• ABX.HE 06-1 represents home equity underwritten in the second half of 2005;
• ABX.HE 06-2 represents home equity underwritten in the first half of 2006; while,
• ABX.HE 07-1 represents home equity underwritten in the second half of 2006.

CPDOs to dominate in Asia?
A new report from Moody's Investors Service says that synthetic bespoke transactions dominated the Asian market in 2006, mirroring the situation prevailing in 2005. However, towards the latter part of the year the hot topic was constant proportion debt obligations (CPDOs). While these were mostly structured in Europe, Asian investors' interest in this product has led arrangers in the region to show increased interest in structuring these types of transactions locally.

It remains to be seen whether CPDOs will dominate the synthetic market in 2007, the agency says. However, a trend is developing towards more emerging market credits – continuing from last year, when for the first time Moody's rated a transaction involving a portfolio consisting entirely of Indian credits.

Meanwhile, more synthetic balance sheet CLO deals are anticipated this year, not just from existing issuers but from a number of new issuers as well.

According to the report, Chinese banks may look to issue more domestic CLO cash transactions this year, driven by capital relief requirements and a desire to gain technological expertise. Moody's also expects several Chinese banks to issue cash CLO transactions denominated in local currency.

And growing popularity for the securitisation of SME loans in the region could mean more activity in this type of transaction, including from Korea, Malaysia and India.

Loan pricing service expands
Information supplier FT Interactive Data has announced enhancements to its bank loan pricing service that aim to help investors more efficiently update critical information about the syndicated bank loans in their portfolios. The service, which provides access to independent valuations of syndicated bank loans, now also automates the delivery of refinancing, termination and substantial amendments to loans, as well as the effective date of the change.

The bank loan pricing service uses a web-based user interface to deliver information for a specified universe of loans to clients. Bank loan prices are provided by Markit Group and drawn from more than 70 dealers in the bank loan market.

S&P takes SROC-related action
Following its December global SROC (synthetic rated overcollateralisation) report (see last week's News Round-up), Standard & Poor's has taken credit rating actions on 54 European synthetic CDO tranches, as follows:
• Ratings on two tranches were placed on CreditWatch with negative implications.
• Ratings on 24 tranches were removed from CreditWatch negative and lowered.
• Ratings on two tranches were lowered and remain on CreditWatch negative.
• The rating on one tranche was lowered.
• Ratings on seven tranches were removed from CreditWatch negative and
affirmed.
• Ratings on 17 tranches were removed from CreditWatch with positive
implications and raised.
• The rating on one tranche was raised.

MP

Trading ideas - waste tightener

Dave Klein, research analyst at Credit Derivatives Research, looks at an outright long trade on Allied Waste

When we have a fundamental outlook on a credit, we prefer to put on positive-carry, duration-neutral curve trades. In general, this means putting on flatteners when we are bullish and steepeners when we are bearish. Flatteners can be difficult to put on simply because their roll-down often works against us. With the current steepness of credit curves, positively economic steepeners have been positively difficult to find recently.

Of course, we can always put on an outright trade (long or short a credit) and accept that we are not hedged against parallel curve shifts. Indeed, if our fundamental view is strong enough, an outright trade might be preferable as we expect to capture plenty on the upside.

In today's trade, we express our improving fundamental outlook for Allied Waste (AW) in an outright short protection (long credit) position. Given AW's bond levels and curve flatness, this is the best trade available and possesses nice economics.

Go long
Given our improving fundamental outlook for AW, we want to be long the credit. We can take this position either by buying bonds or selling CDS protection.

In order to evaluate opportunities across the term structure, we compare CDS levels to bond z-spreads, which we believe is the most straightforward way to compare the two securities. Exhibit 1 compares AW's bond z-spreads to market CDS levels as well as our fair value CDS levels.

Exhibit 1

Clearly, AW's bonds are rich (z-spreads lower) than its equivalent CDS levels. This focuses our search for carry on selling protection. Additionally, given our improving fundamental outlook, we'd expect the CDS curve to flatten rather than the bond z-spread curve to steepen.

In order to estimate CDS fair values, we regress each segment (3s-5s, 5s-7s, 7s-10s) across the universe of credits we cover. This results in a set of models with extremely high r-squareds. In our case, we see that AW's 3 years are trading close to fair value, its 5 years are trading above fair value (good for us), its 7 years are trading below fair value (bad) and its 10 years are trading above (good).

Given that we see 5s and 10s as the best potential maturities, we drill down and look at the trade economics. Specifically, we look at carry, roll-down and the bid-offer spread of each potential trade. AW's 5s have a bid offer of 10bp whereas the 10s trade at 20bp difference.

Additionally, the roll-down on the 5s is positive and negative on the 10s, although the carry earned is better on the 10s. Putting these numbers together, selling 5 year protection presents the best opportunity.

We estimate that the trade will break even in 6 months time even if AW sells off to 215bp offered. Exhibit 2 details the trade economics of selling 5Y AW CDS protection.

Exhibit 2

After settling on selling 5Y protection, we look at the behaviour of AW 5Y CDS compared to fair value over the past few months. As stated earlier we calculate 5Y fair value based on curve steepness across the universe of credits we cover.

Over the past few months, AW has moved both above and below fair value although the difference has generally been small as shown in Exhibit 3. This strengthens our confidence that AW will tighten back to fair value and, given our improving fundamental outlook, hopefully tighten beyond that as the credit rallies.

Exhibit 3

Risk analysis
This trade takes an outright short protection (long credit) position. It is unhedged against curve movements. Additionally, we face 10bp of bid-offer to cross. The trade is significantly positive carry which protects the investor from any short-term mark-to-market losses.

Entering and exiting any trade carries execution risk, but this is not a major risk as AW has good liquidity in the credit derivatives markets.

Liquidity
Liquidity is a major driver of any longer-dated trade – i.e. the ability to transact effectively across the bid-offer spread in the bond and CDS markets. AW has good liquidity in the CDS market at the 5Y tenor with a bid-offer of 10bp.

Fundamentals
This trade is based on our improving fundamental outlook. Taking an outright short protection (long credit) position by its nature means we are placing a lot of faith in our fundamental view of the credit. While we have chosen a security and tenor that we believe offers the best opportunity for profit, our bullish view on the credit is the driver of this trade.

Evan Mann, Gimme Credit's High Yield Business Services expert, has initiated an improving fundamental outlook for AW. Evan believes that favourable industry conditions and the underlying strength of the economy have benefited the company and notes that margins expanded on the back of lower labour and vehicle maintenance costs. Evan believes that EBITDA and cash flow generation will continue to improve over the next several quarters although the company may be limited in its ability to pay down debt.

Summary and trade recommendation
We find ourselves in high-yield land again this week, expressing our bullish view of AW. With a lack of positively-economic curve trades available for the credit, we look to take an outright long credit position. After analysing both the bond and CDS markets for the best opportunity, we have settled on selling 5 year protection on AW.

Excellent carry, roll-down and the potential profit of a return to fair value (and beyond) strengthen the economics of the trade. Given our improving fundamental outlook and the current wide levels for the company, we feel this outright position presents the best opportunity for trading this name.

Sell US$10m notional Allied Waste 5 Year CDS protection at 185bp to gain 185 basis points of positive carry

For more information and regular updates on this trade idea go to: www.creditresearch.com

Copyright © 2007 Credit Derivatives Research LLC. All Rights Reserved.

Note: This article is intended for general information and use and does not constitute trading advice from Structured Credit Investor (see also terms and conditions, below, section 12).

Trading equity tranches - part 3

In this series of three articles, Richard Huddart and Domenico Picone of the structured credit research team at Dresdner Kleinwort look at some of the different ways to trade equity tranches and analyse them

Combo note investors
As we documented in our publication CDO Combo notes, 11 November 2005, the prime motivation for Combo note investors is to combine an equity participation with a more senior tranche of the capital structure in order to create a rated note that has increased upside potential coming from large equity tranche returns, along with an investment grade principal rating.

In a similar fashion to the ideas we have considered in this report therefore, both default timing patterns and the equity coupon structure are important factors in determining Combo note returns. The possible restructuring of equity tranches, such as in the ways that we have seen, provide Combo note investors with yet more flexibility, depending on their view of when defaults may occur in addition to their risk appetite.

Higher risk, higher return – go for running coupons
As we have seen, all-running coupon equity structures have both higher upside and higher downside potential than their equivalents that pay returns all-upfront. The all-running tranche will outperform the upfront version when no or few defaults occur, or defaults are back-loaded. They will underperform in the opposite scenario of front-loaded defaults.
When defaults are expected to be 'back-loaded'

Combo note investors who take the view that any defaults will be back loaded, or that the equity is currently pricing in too many defaults, could therefore benefit from structuring a Combo note to combine a senior tranche element with an equity tranche participation that pays all returns in the form of a running coupon. Combo note investors who are willing to take on some equity tranche principal risk could therefore combine a senior tranche with an all-running coupon junior tranche.

Investors who want full principal protection on the other hand may consider combining a PO strip of a senior tranche (zero-coupon tranche in the funded case/all-upfront in the unfunded case) or even a government security with an IO strip of the equity tranche. In this case, the principal rating would be provided by the senior tranche, with coupons coming from the IO strip. We remind investors here that the majority of Combo notes seen in the market have a principal only rating.

Maximum possible return for a Combo note
The maximum possible return for a Combo note with a given relative senior/equity combination would be realised when coupons are paid on an all-running basis and no defaults materialise. If, on the other hand, a significant spate of defaults large enough to wipe out the entire equity tranche was to occur very early in the deal, then the equity contribution to the Combo note could theoretically also be very small.

More stability – trade the return upfront
On the flip side of the coin, trading all equity returns on an upfront basis provides for more stable performance, as default time dependency is massively reduced (in the unfunded case) or even completely removed (in the funded case of a zero-coupon equity tranche).

When defaults are expected to be 'front-loaded'
Combo note investors who believe that defaults will be more front loaded than the equity price suggests, or who want to remove default timing as a return-effecting variable, should therefore prefer a note that combines a senior tranche element with an equity participation that trades returns on an upfront basis. For more on different CDS curve scenarios see box below.

More stable return
Compared with the running coupon equivalent, potential returns are lower, as the equity portion is capped at the size of the upfront coupon; however the downside is also more limited, as the coupon will always be paid, regardless of the loss scenario that unfolds. Our discussion of the Greeks (in part 2) also tells us that such a note will show less MTM volatility. For simplicity, this could facilitate the creation of a Combo note where all returns are traded on an upfront coupon basis – i.e. both the senior and the equity contributions.

For a much fuller discussion of Combo notes, including their use in synthetic structures, see CDO Combo Notes, 11 November 2005.

Some more exotic equity trades

Zero Initial Cost Protection
Zero Initial Cost Protection is an innovative structure, which allows market participants to buy protection on a tranche or the index without paying anything at all until defaults occur in the reference portfolio. The protection premium paid steps up with each default, although it is capped. The chart below shows indicative spread levels paid to purchase protection as a function of cumulative portfolio defaults on the 5y iTraxx S6 index as of 21 September 2006. Note that the spreads quoted are in basis points of the original index notional.

As can be seen, the protection buyer benefits from paying nothing for his protection so long as no defaults have occurred in the underlying portfolio, although he is hit harder than the regular index protection cost when multiple defaults accumulate. The strategy is therefore suited to those who want to hedge themselves against defaults but have a positive view on the asset class they hold exposure to, such that they do not believe defaults will materialise, at least in the short term. We shall show how this strategy performs in relation to buying standard index protection under different default scenarios soon.

Product construction: Using the unfunded equity IO strip
The Zero Initial Cost Protection strategy utilises regular financial instruments, and as such provides no new difficulties to dealers with respect to hedging. There are essentially three legs to the trade, which we introduce as follows:

? Leg 1: Purchase protection on the instrument in question - here the 5y iTraxx index - on an all-upfront basis. This upfront outlay is funded by the difference in upfront payments on legs 2 and 3.
? Leg 2: Pay a running spread of Xbp on the full notional, regardless of defaults in the portfolio. In compensation for this, the investor receives the PV of this annuity upfront.
? Leg 3: Receive Xbp running in the form of an unfunded 0-3% equity tranche IO strip, whose tranche notional is equal to the full notional that payments in leg 2 are based upon. This IO strip will cost the investor Equity DV01 x X upfront.

Leg 2 is worth more than leg 3 on an upfront basis, as its payments are guaranteed to always be made based on the full notional. As a result the investor will gain more upfront as payment for leg 2 than he will pay out for his IO strip in leg 3. This net gain at day zero is used to purchase the index protection on an all-upfront basis in leg 1. Premium X is chosen such that this net cash flow at day zero is equal to zero.

To better illustrate this construction we now present an example of how the strategy is constructed for the 5y iTraxx S6 index as of 21 September 2006. We note that all prices are purely indicative and that bid-offer spreads and other costs are disregarded.

An Example: Zero Initial Cost Protection on 5y iTraxx index
The three 'legs' of the trade in this case would be as follows:

? Leg 1: On September 21, the 5y iTraxx S6 index traded at 30bp with a DV01 of 4.764. Buying index protection upfront therefore costs 142.9bp.
? Leg 2: Pay 194.8bp on a running basis on the full notional over 5y. This stream generates an upfront income of 935.2bp.
? Leg 3: Receive 194.8bp running in the form of an unfunded IO strip – this equates to receiving 194.8bp running on the outstanding 0-3% equity tranche notional. The equity tranche had a DV01 of 4.068 and so this leg cost 792.3bp upfront.

The cash flows of this strategy are summarised in the table below – including how each leg of the trade contributes. A positive cash flow is a cash inflow for the protection buyer (such as what he receives on the equity IO strip leg) and a negative cash flow is a cash outflow (such as his net protection payment).

Having purchased the index protection leg on an all-upfront basis, it should be clear that the running protection payment made after n defaults is driven by the difference in what is paid out on the annuity (leg 2) and what is received on the unfunded 0-3% tranche IO strip (leg 3).

Scenario Analysis
As we documented above, standard 5y iTraxx S6 protection could be purchased on the same date for an annualised running spread of 30bp. We remind readers here that this 30bp spread would be paid on the outstanding index notional, whereas the spreads quoted for Zero Initial Cost Index Protection would be paid on the initial notional. In the charts below we compare the performance of this iTraxx S6 protection strategy for 2 different default scenarios. In both cases there are two defaults in the reference portfolio – in scenario A they occur at the start of quarters 14 and 18 (corresponding to the start of 2010 and 2011 – there are 21 quarters between September 2006 and maturity in December 2011). In scenario B they occur at the start of quarters 6 and 10 (corresponding to the start of 2008 and the start of 2009).

As can be seen from the charts, Zero Initial Cost Protection significantly outperforms the regular way of purchasing iTraxx index protection on an all-running basis when defaults occur late, although it underperforms when defaults occur early. This is reiterated in the following table, which shows the present values of premiums paid under the two strategies for each scenario. We also note that the spread paid for protection quickly steps up when defaults do start to occur.

The extreme cases
When purchasing protection through a Zero Initial Cost strategy, it is important to understand the risks and rewards associated – and as such we briefly discuss the extreme cases here.

On the upside the extreme case is clear – if there are no defaults in the reference portfolio then the protection buyer essentially receives his protection for free, right up to maturity. It is this kind of motivation that may persuade many to take on such a strategy if they have a positive view with respect to defaults yet need to free up regulatory capital by hedging credit risk on their book.

The downside extreme can be quite damaging however – if we were to assume that the entire equity tranche was to be wiped out very quickly, then the protection buyer would end up paying the maximum possible protection premium (in this case 194.8bp based on the original index notional) for almost the entire time until maturity.

From the illustrative table on the last page, it should be clear that the point at which the protection premium becomes capped coincides with the point at which the equity tranche is totally eradicated – and as a result the equity IO coupon payments become zero. Note that a recovery rate assumption of 37.5% was chosen in this situation for ease of illustration, as this means that six defaults exactly coincides with the equity tranche being exhausted.

The implicit long unfunded equity IO strip
Given the way in which Zero Initial Cost Protection is constructed, the protection premium that the protection buyer pays increases in line with decreases in the coupon paid on the equity IO strip leg. As a result, the protection buyer is implicitly long an unfunded equity IO strip, and so should understand the sensitivities of this product. We refer the reader back to the earlier sections of this report at this point. Of particular note is the fact that the unfunded equity tranche IO strip is long in correlation, and so the Zero Initial Cost Protection buyer is also somewhat long in correlation.

Applying the strategy to other instruments
Whilst we have shown an application to the case of purchasing index protection, the Zero Initial Cost Protection strategy could also potentially be applied to tranches. One interesting case is the 0-3% equity tranche. Indicative protection premium levels for this trade are shown as a function of cumulative portfolio defaults in the following chart.

Whilst the idea of obtaining equity tranche protection at zero cost may sound extremely attractive, the downside potential makes this trade incredibly risky. There are two key points to note here:

? Purchasing equity tranche protection on an all upfront basis is extremely expensive, and as a result the size of the spread paid on the annuity (leg 2) and equity tranche IO strip (leg 3) must be very large in order to make the strategy zero-initial cost (cost of upfront equity protection must equal the difference in PVs of legs 2 and 3). This means that the equity tranche protection premium steps up very quickly with each default.
? The protection premium payable is capped, but at a very large value for the equity tranche (at 54.8% in this example). Moreover, a key difference between a regular index protection contract and the Zero Initial Cost Protection approach is that in the latter case all protection premiums are paid based upon the original tranche notional, rather than what is outstanding. When six defaults occur in the portfolio, the premium steps up to its largest possible amount – but this is also the point at which the equity tranche is fully wiped out. As a result, the protection buyer would end up paying 54.8% of the original equity tranche notional per annum to protect a tranche that no longer exists. In fact, the protection buyer could end up being much worse off than if he had sold protection on the tranche, even though the whole tranche has been wiped out!

These two points should serve to highlight the massive downside potential that make it in many ways unfeasible to apply this protection strategy to an equity tranche.

Less leveraged, more senior tranches should present more realistic opportunities to rationally apply the Zero Initial Cost Protection Strategy however, as neither of the two points we just made in reference to the equity tranche would be directly applicable. In any case, it is important to realise that the protection buyer is always implicitly long an unfunded equity IO strip of some magnitude.

The reserve ledger and the IG rating
As we touched on earlier in this report, the possibility of achieving an investment grade rating on a tranche that both attaches and detaches within the traditional 'equity' region of the capital structure has increased the potential investor base at the junior end of the capital structure. Obtaining such a rating will typically require employing a mixture of some or all of a high-grade portfolio, a reasonably short time to maturity and bespoke structural features. Here we document a structure that has been successfully used to gain a Moody's IG rating on a managed pure equity tranche (i.e. one that attaches at 0%).

The reserve ledger
The key difference between this structure and that of a regular funded all-running equity tranche transaction is that instead of paying out a large coupon on a quarterly basis, only a relatively small coupon (0.7% on top of EURIBOR) is paid out to the investor regularly, with the remainder (9.7%) being invested into a so-called reserve ledger on an annual basis. This reserve ledger then essentially acts as a first layer of protection for the equity tranche holders, thus providing them with some extra subordination.

Losses are settled at maturity
Losses in the structure are only settled upon termination of the transaction, and hence investors only suffer principal losses if the cumulative total of losses resulting from defaults as of the maturity date is larger than the amount accrued to the reserve ledger over the lifetime of the transaction. As a result, the quarterly coupon paid to note-holders is guaranteed.

Amounts paid to the reserve ledger are calculated based on the tranche notional net of defaults however. At maturity, any value remaining on the reserve ledger once all defaults are covered is paid out to the investors.

Trading gains and losses
Under certain conditions, the transaction also allows trading gains or losses to increase or decrease the reserve ledger. The manager's trading ability is also restricted in the event of the tranche being significantly downgraded.

If, upon termination of the transaction, the IRR of note-holders is above that of a hypothetical bond paying EURIBOR+500bp, then the portfolio manager is entitled to receive 25% of the redemption amount that is in excess of this threshold. This subordinated portion of the management fee helps to align the interests of the manager with those of the investors.

The unfunded IO strip – structured as an all-running swap
The unfunded IO strip, as we have documented in this report, allows market participants to take a view on 'how long' the equity tranche will last (in terms of the lifetime of the tranche notional). Additionally it completes the unfunded picture, from the point of view that the sum of the all-upfront tranche and the unfunded IO strip is the same as the standard unfunded tranche. As a result it can be a useful hedging tool.

IO strip as all-running swap
This IO strip could also be structured as an all-running swap. In this case, rather than paying the PV of the 500bp coupon stream upfront, the IO investor would pay a quarterly premium in exchange for a quarterly 500bp coupon (the 500bp coupon is calculated based on the outstanding tranche notional). In terms of what the IO investor pays out, the constant quarterly premium to be paid would be such that the PV of this stream of cash-flows is equal to the upfront cost of the corresponding 'regular' unfunded IO strip that we discussed earlier. From the point of view of the investor, the following payments would be made/received on a quarterly basis:

Such a trade may be more appealing to some market players who wish to take a position on the 'realised duration' of the equity tranche but do not want to put up the full value of the IO strip upfront. In fact, if the equity tranche performs well then it is possible that the player will never have to make any payments at all – he will simply receive a regular premium for the 'coupon risk' that he has taken on. As we have already documented, IO strips perform well when the number of realised defaults is less than what is originally 'priced in' and when defaults are back-loaded.

An example
The relative cash flows (from the investor/seller of protection point of view) for both the 'regular' and all-running unfunded IO strip are shown in the charts below. Once again we assume a portfolio of 125 CDS names of equal notional exposures, a fixed recovery rate of 35% and a fixed LIBOR rate of 4%. We also assume for simplicity that all coupons are paid on an annual basis and that one default occurs at the beginning of each of years four and five.

As can be seen from the right hand chart, when the full tranche notional balance is still performing, the coupon received is larger than the IO premium payment made such that the net swap payment benefits the IO investor. Once enough defaults have occurred, however, the 500bp coupon is paid on a smaller performing balance and so it becomes the case that the IO investor has to make a net payment.

Replicating the super-senior tranche

A popular trade over the past year or two has seen market participants sell protection on the super-senior tranche (22-100% for iTraxx, 30-100% for CDX) whenever 'pockets' of value have opened up there. This is typically done on an unfunded basis, or by funding only a small portion of the super-senior region in a Leveraged Super Senior (LSS) strategy.

Selling protection on the super-senior tranche directly is not necessarily the most attractive option, particularly as these tranches are not the most liquid. The super-senior tranche can be replicated, however, by selling protection on the index and buying back protection on all tranches below the super-senior region in the appropriate amounts. To sell protection on €78m of iTraxx Europe, for example, one would sell €100m of iTraxx index protection and buy protection on the 0-3%, 3-6%, 6-9%, 9-12% and 12-22% tranches of the same portfolio notional (i.e. not tranche notional).

'Buying back' equity protection
When 'buying back' this portion of protection on the 0-3% equity tranche, it would clearly not be very appealing to buy the protection in the form of a standard market contract for equity, as this would require paying 500bp running but critically also an upfront premium. This issue can be solved by buying the appropriate amount of protection on an all-running version of the 0-3% equity tranche.

The index, on which protection is sold, and the other standardised tranches, on which protection is bought back, all pay running coupons on a quarterly basis, and so replicating the super-senior tranche in this way would ensure that it is also effectively structured as an all-running swap, with no upfront-outlay necessary.

Enhancing the short correlation view
Relative value players selling super-senior tranche protection are taking a short view on correlation, as increased systemic risk increases the potential for losses at this part of the capital structure. Ceteris paribus, super-senior tranche protection sellers will therefore make MTM gains when the super-senior correlation assumption decreases.

Equity protection sellers are long in correlation. When buying back equity protection as part of the super-senior replication therefore, the investor is short in correlation on this equity leg.

As we saw in the section on correlation risk, all-running tranches are the most long in correlation of the different equity structures, and so they are the most short in correlation when buying protection. Using the all-running tranche for the super-senior replication will thus offer the biggest MTM profits should the super-senior protection seller's negative correlation view be realised.

A note on pricing

As we have already noted, the standard way in which the market quotes prices for 0-3% equity tranches is as a 500bp running spread plus an upfront premium. In order to see how such a price can be translated into prices for other coupon structures, we need to understand some basics of how the tranche price is derived. It is easiest to start in the unfunded case.

Unfunded tranches
In determining the spread of an unfunded CDO tranche, the tranche is effectively treated like a credit default swap written on (in the case of an equity tranche) the first loss piece of a reference portfolio. There is hence a 'loss leg', which relates to principal losses resulting from defaults in the pool, and a 'coupon leg', which relates to coupon payments made to the investor. The fair price of the tranche should be the spread that makes the PVs of the loss and coupon legs equal.

When tranche principal is at risk to the investor, the PV of the loss leg will be the same regardless of the coupon structure chosen. We therefore need only focus on the coupon leg.

Standard equity tranches trade with an upfront spread (in %) and a running coupon of 500bp, however we prefer to begin with the simpler all-running coupon format, which is most analogous to a standard CDS. Whilst the DV01 of a tranche is normally defined as the change in MTM value given a 1bp change in its spread, it can also be thought of as the weighted average number of coupons that the investor would expect to receive (on a PV basis), should defaults occur at the intensity that the individual name CDS spreads in the reference portfolio would suggest.

For the all-running structure, the present value of the coupon leg can therefore be written as the spread multiplied by the tranche DV01. Following this, the fair tranche spread should satisfy the following expression (remembering that PV coupon leg = PV loss leg):

Simply speaking, this is how the running spread for a vanilla tranche would be calculated. We also remind readers that DV01 is model dependent, and therefore unless the same standard Gaussian model is used, different prices will be calculated.

The case of the all-upfront unfunded equity tranche is relatively very simple, as in order to make the PV of the coupon leg equal to the PV of the loss leg, we simply need to set the upfront coupon equal to the PV of the loss leg. Using the result from above we then see that:

The tranche DV01 does not vary across coupon structures. As a result, in order to switch a portion of the running spread into an upfront coupon, we simply need multiply the reduction in running spread by DV01 in order to give us this upfront coupon component.

Following this, to arrive at the fair upfront spread of a standard unfunded equity tranche, we just need to modify (1) as follows:

Using these results allows us to express the prices of the different unfunded equity tranches in terms of standard market quotes as follows:

Funded tranches
The prices of funded tranches cannot be so easily related to the standard market quotes seen above however. There are two main reasons for this.

First of all, in the funded case running coupons are paid as LIBOR + spread and therefore in addition to shifting the 'spread' component between upfront and running, we must also be able to value the contingent LIBOR stream on a PV basis. Whilst the 'spread' can be shifted using DV01 (tranche DV01 is the same regardless of whether the tranche is funded or unfunded), the PV of the LIBOR stream must be calculated by taking the shape of the forward curve into account.

Secondly, in contrast to unfunded position, in the funded case all losses are paid for at maturity, and so this must be accounted for in the price.
What the funded tranche investor pays for the credit linked note should be equal to the PV of everything he expects to receive in the future – that is the PV of his running coupons plus the PV of what he expects to receive back at maturity.

With this consideration, we can express the funded tranche prices as follows (Where both standard and all-running tranches are priced with par=1):

Zero-coupon tranches: a simple way to calculate returns
Given that the redemption value of the (funded) zero-coupon tranche depends only on the absolute size of defaults and not on the timing of defaults in any way, the redemption value of the CLN can be succinctly summarised in the following formula:

where i=1,...,nd are the nd assets in the reference portfolio that default before maturity, N%i is the reference entity notional percentage of defaulting asset i, Ri is the recovery rate of asset i, TN is the tranche notional and AP and EP are the attachment and exhaustion points of the tranche respectively. For an equity tranche, the attachment point is clearly zero.

In the special case of fixed recovery rates (Ri=R for all i) and equal notionals of all assets in the reference portfolio (N%i=N% for all i), the expression for the redemption value of the CLN can be simplified even further:

This means that in this special case of equal notionals and fixed recovery rates it is possible to draw up a simple redemption table (number of defaults against redemption amount at maturity) as soon as the portfolio and fixed recovery rates are set. Therefore, the investor will know from day one exactly how much he will lose if x defaults occur at any time before maturity.

Such formulae also allow us to express the price of the zero-coupon funded tranche in a relatively simple way – the purchase price of the tranche should simply be the expected value of this redemption value discounted by the risk-free discount factor (derived from the risk-free interest rate) over the life of the transaction, or:

where rfDF is the risk-free discount factor and E is the expectations operator. We assume here that the risk-free discount factor is uncorrelated with default and recovery rates, such that it can be taken outside of the expectation.

The challenge comes in calculating the expected cumulative principal loss term (the term under the expectations operator in square brackets). This is essentially the same problem that has to be solved in pricing any CDO tranche and is done by way of a copula model.

A copula model is a multivariate statistical model that takes the basket of individual reference entities, extracts their implied default profiles from their CDS curves, and imposes certain correlation assumptions to come up with an aggregate default profile for the basket. Given a set of recovery rate assumptions, this default profile can then easily be translated into an expected loss.

© 2007 Dresdner Kleinwort. All Rights Reserved. This Research Note was first published by Dresdner Kleinwort on 6 October 2006.