# Reshuffling Risk: understanding CDO risk distribution

May 21, 2011 Leave a comment

## Introduction

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. CDOs 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. If 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%

You can then create two new €100 bonds, * Safe-T* and

*, which pay out according to the following rules:*

*Risk-E**pays out if either*

*Safe-T*

*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

*will default is now greatly reduced to 0.25% as show by the calculation below.*

*Safe-T*### 1 – (1 – 0.95) x (1 – 0.95) = 1 – 0.25 = 0.9975 = 99.75%

100 – 99.75 = 0.25% The probability that * Risk-E*will 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

*(at 9.75%) have a combined default probability of 10%, but that default rate is for the total €200 of assets.*

*Risk-E**and*

*Safe-T**Risk-E*each 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: * *

*Safe-T _________*0.025 **AA **

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

*Risk-E* __________0.0975 **A **

## Waterfalls

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.

## Conclusion

In 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 www.besprent.com

**Sources:**

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.