Reshuffling Risk: understanding CDO risk distribution


Trade in Collateralized Debt Obligations (CDOs) has been at the centre of the financial crisis. Global issuance peaked at $520 billion in 2006 and then slumped to a mere $4 billion in 2009, according to SIFMA. Yet CDOs remain important financial tools for distributing risk. Heron Tower - Besprent.comCDOs are at the core of the “originate and distribute” model, in which assets are pooled together, repackaged and redistributed to investors. How can assets that have the same risk rating be reallocated over a wide range of risk levels in what is essentially a zero sum game, as the asset class and risk of the underlying portfolio remain the same?

Reshuffling the risk

Imagine you have a box with ten gold coins. The ten coins represent 100% of its contents. Therefore, you could say there is a 0% chance of picking anything other than gold coins out of the box – it is guaranteed to contain all gold. CDO gfx 1 - Besprent.comIf you swap one of the gold coins with a copper one, that coin would account for 10% of the contents of the box. If you have two boxes with 1 copper coin and 9 gold coins in each and wanted to create an all-gold box you can empty the contents of both boxes into one large box. Now you have a box with twenty coins – 18 gold and 2 copper. You can then use the contents of the big box to refill two new small boxes with ten coins each, but you impose a rule that channels all the copper coins into one box. You now have one box with 0% copper coins and another with 20% copper coins. Note that the overall risk of choosing a copper coin across the twenty coins has not changed. In other words, if you owned both boxes there is still a 10% chance of choosing a copper coin from the boxes. You have simply split that risk in a different way.

Maths of CDOs

Replacing the small boxes with loans and the big box with a CDO demonstrates how the CDO can take securities with matching risk rates (or default rate) and produce new investments with different risk rates. Suppose you have two €100 loans, Bond-X and Bond-Y, both with a 5% default rate (i.e. a 95% chance of paying out). Combining the loans in a CDO creates a €200 investment instrument, with the same default rate of 5%.

5/100 + 5/100 = 10/200 = 0.05 x 100 = 5%

CDO gfx 2 -Besprent.comYou can then create two new €100 bonds, Safe-T and Risk-E, which pay out according to the following rules: Safe-T pays out if either Bond-X OR Bond-Y does not default, while Risk-E pays out only if both Bond-X AND Bond-Y do not default. The probability that Safe-Twill default is now greatly reduced to 0.25% as show by the calculation below.

1 – (1 – 0.95) x (1 – 0.95) = 1 – 0.25 = 0.9975 = 99.75%

100 – 99.75 = 0.25% The probability that Risk-Ewill default is much greater at 9.75%.

0.95 x 0.95 = 0.9025 = 90.25%

100 – 90.25 = 9.75% Together the two new bonds, Safe-T (at 0.25%) plus Risk-E (at 9.75%) have a combined default probability of 10%, but that default rate is for the total €200 of assets. Safe-T and Risk-Eeach make up half of the entire €200 CDO therefore the weighted average of each gives the CDO a 5% default probability, the same as the sum of Bond-Y plus Bond-Y.

0.5 x 9.75% + 0.5 x 0.25% = 5%

Again, the overall risk of the portfolio has not changed only how it is spread in the CDO. As an example, using an average based on Standard & Poor’s One-Year Global Structured Finance Default Rates would give the following ratings: Long Wall -

Safe-T _________0.025 AA

Bonds-X, Bond-Y __0.05 AA-

Risk-E __________0.0975 A


The waterfalls, or cascades principle is used in real CDOs to redistribute the risk of hundreds and thousands of assets to produce a number of new bonds, or tranches, each with its own rating. These tranches can then be sold off in smaller units, which carry the risk rating of the tranche. Payments to each tranche are allocated by the conditions set for the CDO — the ‘AND’ and ‘OR’ rule described above. The payments are allocated to each tranche according to its risk rating, with the safest tranche receiving payment first. In this hypothetical example, if no loan defaults all the tranches are paid. The more loans default the less money goes into the riskier tranches. At this stage the risk transformation is complete. The rating of the new bonds is influenced not by the quality of the underlying assets but by the priority of repayments received from the assets held in the portfolio.


The City - Besprent.comIn financial terms, the quality of a loan is ultimately expressed by the stability of the cash flows it generates — the confidence level that payments will be made. This stability depends on real life factors such as income, the performance of a company and economic stability. But in financial terms it boils down to a single number, the default rate — the odds that payments will be made for the duration of the loan.

A CDO can be used to vary the stability of some, but crucially not all, of the cash flows of a portfolio. This guarantee comes at a price, which is an increased default rate of other cash flows generated by the CDO. By doing so the CDO decouples the financial risk measure from its real life default probability. The risk is not so much transformed but reshuffled for a given number of loans in the portfolio.

Read more about pricing CDOs or download a pdf version of the full article at


FISMA – Global CDO Issuance (xls) – quarterly data from 2000 to Q1 2011 Updated 4/1/11.

Generational Dynamics – A primer on financial engineering and structured finance, 23 January 2008.

Besprent – The Financial Crisis & the Future of Financial Regulation, Adair Turner, FSA – Part I, 21 January 2009.

Solvency II news: 4 April 2011

NOTE: the Solvency II news updates have moved!

From now on the updates and other Solvency II material will be published on the Solvency II Wire website. To continue receiving Solvency II updates and articles please subscribe at I will continue publishing articles about economics on EasierCrisis. XUSET4JUDH3K 

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Contents: tight Solvency II deadline, Solvency II 101, addressing Catastrophe Risk in QIS 5, tweets

Practical preparation for Solvency II on “knife edge”

The  Solvency II legislative package will only be finalised in Autumn 2012. In the European Committee First Quarter Update, the ABI said the delay is a result to a number of changes to Omnibus II published in January this year.

The ABI said, “This does mean that, while companies remain supportive of 2013 as a start date, their ability to make practical preparations is on a knife edge.”

The Update also addresses a number of unresolved issues that emerged from the QIS 5 results, published last month, which could lead to higher capital requirements:

  • The recognition of an illiquidity premium for new business
  • Transitional arrangements for existing business (annuities, hybrid capital)
  • The definition of contract boundaries
  • SCR calibrations, in particular non-life catastrophe risk and counterparty risk for life and non-life
  • Equivalence with third country regimes.

Financial Times Solvency II 101 Read more of this post

Solvency II news: 1 April 2011

Contents: solvency II and cloud computing, solvency II-friendly investment, risk management slide presentation

Cloud computing under Solvency II

Cloud computing will have to comply with Solvency II outsourcing provisions. Lexology reports on the implications of the Directive for the UK insurance industry.

Cloud computing “is a form of outsourcing by which vendors can supply computer services to multiple customers over the Internet,” writes Patrick Devine of Chadbourne & Parke LLP.

“Firms will be required to have written policies relating to outsourcing setting out the goals, reporting procedures and processes to be applied,” he added.

Solvency II Article 49 states that firms remain: “fully responsible for discharging all of their obligations under this Directive when they outsource functions or any insurance or reinsurance activities.”

Searching for Solvency II-friendly investments  Read more of this post

Solvency II news: 31 March 2011

Contents: global insurance supervision, illiquidity premium criticized, standard model, banks v insurers on bonds II

Tottering toward global insurance supervision

A lack of consistency in global regulation is costing the insurance industry an extra $25 billion a year. The FT reports that the figure, calculated by KPMG, highlights the differences in international regulation between the banking and insurance; there is no Basel III equivalent in the insurance industry.

The International Association of Insurance Supervisors (IAIS), a body representing insurance regulators and supervisors in about 190 jurisdictions, is developing a global Common Assessment Framework, known as ComFrame. ComFrame aims to: “foster global convergence of regulatory and supervisory measures and approaches,” according to the IAIS.

The IAIS will publish a “Concept Paper” in July this year, which will discuss the three year implementation of ComFrame.

Illiquidity premium under attack  Read more of this post

Solvency II news: 29 March 2011

Contents: banks vs insurers over bonds, S&P’s new ‘M-factor’, impact of Solvency II on European equities markets

Conflict between banks and insurers over long-dated bonds

As banks must issue more long-dated bonds under Basel III, insurers shun these bonds under Solvency II. Bloomberg reports that higher charges may drive insurers to hold short-dated bonds and “hedge out the duration” using interest-rate swaps instead. The insurance industry currently purchases 60% of the long-dated bonds in the market.

Under Solvency II, “Firms must hold 8.2 percent of the face value of a five-year bond in reserve in case the issuer defaults and 16.5 percent for a 10-year bond,” according to a report by Morgan Stanley and Oliver Wyman Group.

Simon Hills, an executive director at the British Bankers’ Association, said, “One bit is saying you should have more funding with a longer duration and the other is saying watch out when buying this stuff if you are an insurance company.”

See this post for a discussion on implementing Solvency II.

S&P ‘M-factor’ could reduce economic capital requirements  Read more of this post


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