The right tools

Single-tranche CDOs’ complex blend of correlation and credit risk can easily trip up unwary investors. What tools are dealers providing to help investors select reference portfolios?

Despite the speed, ease and high degree of tailoring that characterise the single-tranche collateralised debt obligation (CDO), these bespoke deals remain controversial. Ratings arbitrage (Risk January 2003, page 42), credit substitution rights (Credit Risk special report May 2003, page S4) and adverse selection are just some of the problems that have troubled the buy side. So portfolio selection is a fundamental concern among investors.

Dealers are being asked to put together deals more transparently. “Investors are increasingly keen to put portfolio selection for single-tranche deals on a more quantitative basis,” says Alan Shaffran, London-based head of European credit derivatives at Citigroup. He says the help that Citigroup gives to potential investors ranges from discussing different approaches to Merton-type credit risk models, to leveraging Citigroup’s fundamental credit and derivatives modelling resources.

Sean Rice, New York-based director in credit structuring and marketing at BNP Paribas, says his firm encourages clients to take advantage of commercially available models “to the extent that they think there’s value in doing so”. He stresses, however, that BNP Paribas does not endorse any particular portfolio selection methodology.

So, faced with a choice of approaches, what is an investor to do? Is there a methodology that is clearly ahead of the pack? One firm that appears to be at the cutting edge in offering quantitative reference portfolio selection tools to clients is Bank of America. In December 2002, it launched Credit Option Adjusted Spread (COAS) – a tool that gives a forward-looking estimate of the risk-return profile of individual credits – and Lighthouse, a model that quantifies the distribution of mark-to-market risk in reference portfolios and allows portfolios to be constructed optimally in terms of investors’ risk-return requirements (see box below).

Additional insight
“By using more market data than most other models, we are able to get additional insight into the assessment of credit risk,” says Jeffrey Rosenberg, New York-based head of Banc of America Securities’ credit strategy team. One of COAS’s main differences from standard Merton-type models is that it uses option market implied volatility as an input. Rosenberg cites an example using recent price data that demonstrates that the traditional approach of using stock prices can be flawed: on October 15, 2002, average spread to Treasury of investment-grade credit was around 280 basis points. By April 15, 2003, the average had halved to around 140bp. However, the S&P 500 on these two dates was the same – around 880. “Despite a significant decline in credit risk, equity prices – a common variable in nearly all other models – effectively did nothing,” says Rosenberg. “It was only by looking at option-implied volatility that a signal for this decline could be seen,” he adds.

This relationship is easy to understand. Creditors have a capped upside, and relative to this, a very large downside. Implied volatility measures the market’s view on the future uncertainty associated with a stock price. A high level of implied volatility indicates a high probability of a large move in the stock price. If this large move is realised and is positive, it has little effect on the creditor. However, if it is negative, the stock price could approach zero and the issuer could default on its debt.

Credit Suisse First Boston makes a similar credit risk model available to all clients – ranging from bond portfolio managers to single-tranche CDO investors. However, Rosenberg says Bank of America’s model has an edge over others available in the market. “There is an art and science to the modelling – the latter is the calculation engine, based on the Merton model,” he says. “But the classical assumption of constant asset volatility is unrealistic, and smile adjustments are required – that’s where the art comes in.”

So in addition to recasting its model to give answers in more intuitive terms of option-adjusted spread and credit risk, it is COAS’s treatment of the smile that singles it out. Notwithstanding the dramatic increase in investment-grade defaults during 2002, there’s still a lack of default data in absolute terms. This precludes an assessment of the smile in absolute terms. “Unlike in the options market, the asset volatility smile is not easy to observe. But we are able to assign smile measures on a relative basis that are sensible,” Rosenberg says.

An intellectual diaspora Bank of America’s credit portfolio model – consisting of both the Credit Option Adjusted Spread (COAS) and Lighthouse methodologies – is one of the most sophisticated tools openly available to portfolio credit investors. The fact that some elements of the US bank’s methodology are similar to that employed in the PortfolioRisk+ tool that Credit Suisse First Boston (CSFB) launched last year (Risk March 2002, page 10), is no coincidence. Much of the Swiss dealer’s pioneering work in creating sophisticated quant tools for investors occurred in its credit strategy team – led by David Goldman – who left CSFB for Bank of America last summer. Around a year ago, Bank of America hired some senior members of CSFB’s team – including Goldman, who is now head of global markets group research. The slew of appointments also included Mingsung Tang and Elizabeth Bram – now in portfolio strategy – and Jeffrey Rosenberg. Bank of America – building on its newly hired expertise – then created the COAS and Lighthouse models from scratch. An integral part of Lighthouse is the so-called saddle-point methodology that facilitates more efficient optimisations. It produces a semi-closed form solution that accounts for the entire asymmetric return distribution of each credit – allowing large numbers of non-normal distributions to be added-up without the need for time-consuming Monte Carlo simulations. The saddle-point technique’s application to portfolio credit risk was first discussed in a Risk technical paper written by London-based quants at BNP Paribas (Risk June 2001, page 91).

Lang Gibson, New York-based director of structured credit products research at Banc of America Securities, claims feedback from potential investors – especially in Europe – has been very positive. “We are also open about how it works – which is significant. Single-tranche CDOs are a relatively new product. Black box models are the last thing new investors want,” he says.

Philip Obazee, Philadelphia-based head of derivatives and structured products at Delaware Investments, says he is testing Lighthouse and plans to use it. “The use of implied volatility, saddle-point methodology and its aggregation of tail risk represent an advance on many other credit risk models,” he says. Delaware Investments – an asset management unit of Lincoln Financial Group – has more than $80 billion worth of assets under management.

Bank of America follows a two-step process in putting together single-tranche deals for investors. First, it works with the client to select a portfolio with Lighthouse, then the correlation desk separately handles the tranching. Overall, the US bank further expedites the process by publishing indicative prices for high spread and low spread, and US and global single-tranche reference portfolios. If a client is not satisfied with the pricing offered, the optimisation can be rerun with adjusted parameters.

But not everyone is convinced that a separation of portfolio selection and tranching is the best way forward. “The names you are sensitive to depend very strongly on where your [tranche’s] attachment points are in the CDO,” says Christopher Finger, New York-based head of research and development at RiskMetrics. The risk management services firm’s CDO Manager product was updated at the end of 2002 to be able to better handle pricing and risk analysis around sensitivity and correlation effects at different attachment points. “Interest in this functionality has increased significantly this year, and that’s mostly due to hedge funds,” Finger says, adding that most clients tend use the model for marking-to-market and marking-to-model existing deals.

Gibson stresses that it is vital to keep the optimisation of the reference portfolio’s risk, and tranching, independent. “The research team’s sole concern is to provide an objective forward-looking model that helps investors be comfortable that there is no adverse selection, and any ratings arbitrage is minimal,” he says. BNP Paribas’s Rice believes the best way for a dealer to address concerns about adverse selection and avoid potential conflicts of interest is to remain silent about portfolio selection. “We are, and will continue to be, agnostic about the make-up of portfolios in single-tranche deals,” he says.

But what do the investors say? Well, Delaware’s Obazee for one says that initiatives such as Bank of America’s Lighthouse tool are useful because investors want transparency: “If dealers can improve investors’ understanding of portfolio credit risk by offering quantitative models, then they absolutely should do so,” he says.

S&P debuts portfolio risk model for banks

The risk management consulting arm of Standard and Poor’s plans to launch what it claims is “the most sophisticated portfolio risk management model offered to the banking industry” this month. Dubbed Portfolio Risk Tracker, Standard and Poor’s Risk Solutions’ (SPRS) new bank-orientated portfolio credit risk tool tackles the thorny issue of correlation in several ways.

It offers three ways to estimate correlation: equity-based, spread-based and default-based measures. “Our empirical studies suggest the canonical approach of using equity correlations is not very robust,” says Arnaud de Servigny, London-based head of quantitative analytics and products for Europe at SPRS. “By providing a choice, we’re allowing users to better assess how economic capital and diversification are dependent on the correlation measure they use,” he adds.

The model also deals with a more subtle form of correlation – that between loss-given default and probability of default. “We are not aware of any other portfolio model that takes into account the correlation between default and recovery,” says William Perraudin, a professor at the University of London who helped develop SPRS’s model. This feature builds on research by, among others, Perraudin, New York University’s Edward Altman and regular Risk contributor Jon Frye of the Federal Reserve Bank of Chicago. “It has a real impact on economic capital calculations. Without a proper treatment of this correlation, economic capital requirements tend to be underestimated – especially during credit downturns,” Perraudin says.

The model tackles other common bugbears such as corporate default clusters triggered by sovereign defaults in emerging markets and the exposure at default of interest rate-sensitive instruments. This hybrid treatment of market and credit risk incorporates stochastic interest rates.

Difficult
Most existing bank portfolio risk models were devised before structured products such as collateralised debt obligations (CDOs) became common. “The impact of a CDO tranche on a bank’s VAR, or the diversification benefit of securitising a portion of the balance sheet has traditionally been difficult to model,” de Servigny says. This model addresses those issues. In addition to a more rigorous treatment of structured products, Perraudin says the new model’s fully dynamic nature is important: “It’s this feature that enables the model to properly handle complex securities while other models rely on less meaningful loan equivalent-type approaches.”