Synthetic CDOs WorkshopCapital Markets Credit Analysts Society

Georges Benoliel, March 6 2007

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Disclaimer

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© 2006 Société Générale Group (“SG”), SG Americas Securities, LLC (“SGAS”) and their affiliates. All rights reserved. Société Générale Corporate & Investment Banking (SG CIB) is a marketing name for corporate and investment banking businesses of SG and its subsidiaries worldwide. Capital markets and investment banking activities and securities services in the United States are offered through SG Americas Securities, LLC, a broker-dealer registered with the U.S. Securities and Exchange Commission and member of the NYSE, NASD and SIPC. Securities products offered are not guaranteed or endorsed by SGAS, are not FDIC insured and may lose value. Lending, derivatives and other commercial banking activities are performed by Société Générale and its banking affiliates.

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Credit Default Swap (CDS) – Definition

A Credit Default Swap is a contract whereby the protection buyer transfers the risk that the Reference Entity will default

In return for protection the buyer pays a fee (the CDS SPREAD) to the protection seller

Upon occurrence of a credit event, the protection seller pays par for bonds or loans of the defaulted Reference Entity (the Physical settlement) …

Protection buyer has to deliver a portfolio of obligations of the Reference Entity

Protection seller pays the nominal amount

… or settle a net cash amount in case of Cash settlement

In case a Credit Event occurs the loss for the protection seller = 1- RECOVERY of the Ref Entity

Reference Entity

Protection Buyer

Protection Seller

Contingent Payment Upon Default

Risk

Spread

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Cash CDO vs. Synthetic CDO

SYNTHETIC CDO

Composed of credit default swaps (CDS)

Underlying assets not actually owned: “synthetic” exposure

Receives periodic Spreads as a CDS protection seller

Spreads received are used to pay the tranche coupons

Not all tranches need to be issued since the underlying assets are not purchased

CASH CDO

Composed of Bonds or Loans

Underlying pool of assets are purchased

Takes directly the credit risk of the underlying asset

Receive periodic coupons from Bonds or Loans

Coupons received are then used to pay the tranche coupons

The whole capital structure must be issued in order to raise funds to purchase the underlying assets

No conflict of interest between the equity holders and the other investors

More liquid for each pricing parameter has a bid/offer

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First Came the Static “Fully Tranched” Synthetic CDOs… (2000/2001)

Product developed in 2000/2001 Backed by the strong development of the CDS market

Benefits: Bullet maturity

Currency (EUR/USD)

Simplicity

Well known collateral (investment grade, blue chips)

Attractive returns for the mezzanine holders

Drawbacks: Distribution of the first loss (size limitation)

Static portfolios

Mostly driven by “rating arbitrage”

“Rating arbitrage”: Rating agencies models rely mostly on historical default rates (derived from the rating of the credit), historical recovery rates (derived from the country) and correlation (derived from the industry)

Hence banks were incited to select entities that were trading with a high risk premium (e.g. Philip Morris because of tobacco litigation risks) or with recent financial news that were not yet incorporated in the then rating of the company

Consequences: migration risk, overlap between different transactions

Credit Portfolio

Senior92%

Equity 1.4%

Rated Mezzanine

6.6%

Tranching/Pricing

CDS #1

CDS #2

CDS #3

…

…

CDS #119

CDS #120

Sources: Creditflux, S&P, Bloomberg

Illustration: “Repon 15”, March 2001

Class Size (EUR m) Rating % Spread

A 4.029,60 Super Senior 92.00% 10 bps

B 148,92 AAA 3.40% 40 bps

C 35,04 AA 0.80% 70 bps

D 43,80 BBB+ 1.00% 210 bps

E 30,66 BBB- 0.70% 375 bps

F 30,66 BB 0.70% 775 bps

G 61,32 First Loss 1.40%

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…then Came the “Fully Tranched” Managed Synthetic CDOs…

Initially derived from balance sheet transaction…

Loans were replaced by CDS, originating bank was retaining the equity tranche

Very light management, significant conflict of interests

…then structured in a way much closer to a traditional cash flow CBO

Structure closer to traditional cash flow CDO

Transaction Date Size (million) Gérant

Robeco CSO III Dec-01 1,000 Robeco

Blue Chip Funding Dec-01 1,000 Dolmen Securities

Sutter SCDO 2001-1 Dec-01 1,000 Wells Fargo

Port Royal Synthetic CDO Dec-01 1,000 Deerfield

GIA Synthetic CDO Jan-02 1,000 Global Investment Advisors

Jazz CDO I Feb-02 1,500 Axa IM

Robeco CDO IV May-02 1,000 Robeco

Cheyne Investment Grade CDO I Jun-02 4,500 Cheyne Capital

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…and the Revolution of the “Single Tranche” Synthetic CDOs

The development of credit risk modeling… Banks were often left with unsold pieces of fully tranches static transactions, and hence needed to hedge such

exposures

In the meantime, models were developed in order to manage the first to default transactions (first generation of correlation products)

Natural extension towards portfolio products

…resulted in the emergence of a new product… Thanks to the delta hedging technology, banks were able to offer “single tranche” CDO

Static portfolios of liquid CDS, equity and super senior retained by the bank

…and the birth of a new market (Correlation products)… Relevant pricing of the mezzanine tranche

Development of correlation trading desks

Investors learning curve

… and a large range of correlation products Capital guaranteed + Equity Tranche coupons, Combo Note, Funding support, …

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Single Tranche CDO: Definitions & Characteristics

Key Definitions SUBORDINATION = ATTACHMENT POINT

TRANCHE SIZE

DETACHMENT POINT = SUBORDINATION + TRANCHE SIZE

Mechanisms Losses are observed through a Cash Settlement mechanism (Floating or Fixed Recovery)

Tranche is unaffected as long as credit losses do not exceed the Subordination

Senior

Equity

Rated Mezzanine

Tranching/PricingCredit Portfolio

CDS #1

CDS #2

CDS #3

…

…

CDS #99

CDS #100

SG Investor

Packaging

Credit Default Swap

X bps

Cash Settlements

Key CDS parameters:

SPREAD

RECOVERY

CREDIT EXPOSURE

SUBORDINATION

DETACHMENT POINT

TRANCHE SIZE

-> LEVERAGE

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Synthetic Tranche – Numerical example

Portfolio: 100 Reference Entities equally weighted (1% per name)

Tranche characteristics:

6% Subordination, 2% Tranche Size

Economics:

One Credit Event => Loss = weight of the name * (1- Recovery)

Recovery = Final Price = highest bid resulting from request to 5 dealers

Assuming R = 50% for each defaulted Reference Entity: 1 Loss = 1% x 50% = 0.5%

The tranche can sustain 12 defaults (= Subordination / 1 Loss = 6% / 0.5% = 12)

The initial Nominal represents 4 defaults (= Tranche Size / 1 Loss = 2%/0.5% = 4)

– For each subsequent default from the 13th to the 16th the Initial Nominal will be reduced by 25%

– => LEVERAGED investment

If 16 defaults occur the tranche will not reimburse anything

Flows in case of a Credit Linked Notes:

Coupons are paid on the remaining nominal of the tranche during the life of the transaction

The Redemption price at maturity = the remaining nominal of the tranche

= Tranche Size – Losses on the Tranche

= Tranche Size – min (max (Total losses in the portfolio – Subordination, 0) ; Tranche Size)

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Synthetic Single Tranche: a Tailor-Made Product

Customized portfolios: different asset-classes: IG, HY, ABS, CDO

The investor has a full flexibility and can rely on its own experience to select names, sectors and region exposures (not driven by banks balance sheet or equity investors)

Static, Self managed (i.e. Substitutions by investor) or Managed

If Managed: light or dynamic management

Subordination level

Size of the tranche

Target rating

Coupon: Floating/Fixed, CMDS, CMS, Range Accrual, Zero-Coupon

Maturity

Currency

Recovery: Floating (determined upon default) or Fixed (known at inception)

Losses (if any) settled when Credit Event occurs or at Maturity

Format: Swap or Note (listed or not)

Liquidity (just need to unwind the hedge)

Risk return profile: i.e. rating/spread choice

leverage of the structure customized

Pricing & Sensitivities

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Synthetic Tranche: main Pricing parameters

Recovery Rates

Assumptions derived from historical rates, industry specificities or balance sheet analysis

For very risky names Recovery can be observed in the CDS market (upfront quotes)

Emergence of “Recovery swap”

Tranche sensitivity to this parameter is relatively low

Default Probability

Derived from market spreads (and not from historical default rates)

Can be deducted from the whole credit curve

Default Time Correlation: a Fundamental Pricing Parameter

i.e. the likelihood of multiple credits to default together over a given period of time

Asset

CDS Portfolio

Senior

Liabilities

Equity

MezzanineK2

K1Attachment points, or strikes

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Systemic risk and Idiosyncratic risk

Study of default exposure and spread sensitivity

“Relative” spread risk of equity tranches is low

Mezzanine/senior are more exposed to systemic risk (general widening of spreads)

Equity is more exposed to idiosyncratic risk (individual widening/default)

Correlation market is hence exhibiting the distribution of value between these two factors

Senior AAA

Mezzanine BBB

Equity NR

Default Exposure Spread Sensitivity

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Correlation and CDO Spreads (I)

The relationship between a CDO spread and correlation depends on the subordination of the CDO tranche:

Equity Spread Tightens when Correlation Increases Senior Spread Widens when Correlation Increases

0

200

400

600

800

1000

1200

1400

0% 25% 50% 75%

Correlation

Tra

nch

e S

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ad

Equity [0%,3%]

0

20

40

60

80

100

0% 25% 50% 75%

Correlation

Tra

nch

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Senior [12%,22%]

Strikes = [0%, 3%]. Average spread = 43bp, maturity = 5yrSource: SG Credit Research

Strikes = [12%, 22%]. Average spread = 43bp, maturity = 5yrSource: SG Credit Research

Idiosyncratic Risk

Correlation up => “All or nothing”

=> Probability nothing happens increases

Systemic Risk

Correlation up => Risk higher for Senior

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Correlation and CDO Spreads (II)

Mezzanine tranches offer a remarkable feature:

For a given tranche, it is possible to exhibit one correlation so that the tranche is not sensitive to a change in correlation…

…this optimal correlation maximizes the spread of the mezzanine tranche

Tra

nch

e S

pre

ad

Mezzanine [3%,6%]

Optimum Spread

Correlation Considered

0

50

100

150

200

250

300

350

0% 25% 50% 75%

Correlation

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Correlation Sensitivity

When correlation increases, the risk of an equity tranche decreases: long equity tranche investments are long correlation positions (correlation up, MtM up).

Mezzanine tranches are close to a correlation-free level.

A long senior position is short correlation (correlation up, MtM down).

Correlation sensitivity (“Rho”):

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

3% 9% 15% 21% 27% 33% 39% 45%

Upper Attachment Point

Rh

o

Equity Tranche

Mezzanine Tranches Senior Tranches

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Other Risks Managed by the CDO Arranger

The dynamic delta hedging is a risk-free position only for a small spread variation

For larger movements SG’s position is still at risk: this second order risk is the spread convexity risk

The convexity risk is measured by the change in delta corresponding to the shift in CDS spread

Other second order risks are to be managed by the arranger:

Correlation sensitivity

Recovery Rate sensitivity

Risk of a sudden default

Time decay

In order to reduce these risks SG can:

Enter into offsetting trades on tranches with similar characteristics

Place other single tranches on the underlying credit portfolio that complete the capital structure of the whole CDO

In practice SG aggregates all tranches into a “correlation trading book” and manages the overall sensitivities of the book to all parameters

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Hedging Spread Risk (I)

The main risk (the first order risk) SG has to manage is the spread risk. Hedging is done by selling protection on every name of the portfolio via the CDS market

The amount of CDS to be sold on each name is called the delta ()

Investor

Tranche Spread

Tranche Losses

1 × CDS 1

2 × CDS 2

n × CDS n

Hedge on CDS 1

Hedge on CDS 2

Hedge on CDS n

The objective is to neutralize SG marked-to-market

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Hedging Spread Risk (II)

The delta on one name, for a given shift in the credit spread of that name, is the ratio of the sensitivity of the CDO tranche to the sensitivity of that name’s CDS:

The credit spread curve is shifted by a small amount, usually between 1 bp and 10 bps

The delta value ranges between 0% and 100%

The direction and magnitude of deltas depend on several factors: subordination of the tranche, CDS spread curve, correlation and time to maturity

As credit spreads move during the life of the tranche, SG has to adjust the deltas dynamically in order to get a risk free position: the gamma hedging

However there are limits to dynamic hedging:

The bid/offer cost on each rebalancing

The delta amount does not exactly correspond to the size of the traded CDS contract

The CDS contract in not liquid and the rebalancing in itself changes the price

iNameiName CDSMtMVariation

TrancheMtMVariation

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Sensitivity to Individual CDS Spread

A credit whose spread widens is expected to default earlier and is more likely to hit the equity tranche

Therefore, the delta of the equity tranche increases, while the senior tranche delta decreases

This is one of the senior tranches most remarkable features: their hedging requires selling less protection on the riskiest issuers, and more on the safest ones

0%

5%

10%

15%

20%

25%

30%

35%

25 30 35 40 45

Individual Credit Spread

Del

ta

Equity[0%,3%] Mezzanine [3%,6%] Super Senior [32%,100%]

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Average CDS Spread Impact

The higher the average spread of the basket, the greater the premium on the Tranche:

Sensitivity to the Average Spread of the Basket

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

0.50% 1.00% 1.50% 2.00% 2.50%

Average Spread

Tra

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Tranche Spread (8%-13%)Tranche Spread (3%-8%)

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Pricing Sensitivity – Illustration

Considered Portfolio:

iTraxx Index, 125 Refence Entities, 5yr, 100% European

Average Spread: 37bps

Tranche 3.00-6-00 pays ~ 87bps

Subordination

Lower Subordination > Higher Spread

2.50-5.50 tranche pays ~ 141bps

Tranche Size

Lower Tranche Size > Higher Spread

3.00-4.50 tranche pays ~ 127bps

Portfolio Spread

Higher Average Spread > Higher Spread

3.00-6.00 tranche with 42bps of average portfolio spread pays ~ 112bps

Leverage of about 6x (= (112 – 87)/(42-37))

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Delta Hedging & Leverage

Hedge ratio is higher than the tranche nominal…

Example: the 3%-6% Itraxx tranche (size = 3%) requires a total hedge of 15% of the underlying portfolio

Hence if the average spread of the portfolio moves by 0.01%, the spread of the tranche will move by: 0.01% × 15%/3% = 0.01% × 5 =0.05%

...Concept of “leverage ratio”

In the 3%-6% example the leverage is ~ 5

Behaviour of Leverage

Leverage is decreasing with subordination (like for an “in the money” option compared to an “out of the money” option)

Leverage is decreasing with the Size of the tranche

Leverage is decreasing over time for Senior tranches