CDO Training Program

8/3/2019 CDO Training Program

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CDO training program

CONFIDENTIAL


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- C:\USERS\Stephane DELAINE\STR -CDO CWA & investissement\presenations\post asian seminar slides -30/03/2007 17:07:02

CDO Technology Overview


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CDO training program3

CDOs

Concept is derived from securitisation

Pool, tranches

Pool with a very minimum of 10 to 20 assets

Below 10 / 20 assets => Exotic Credit Derivatives area

Usually the minimum is 50 (optimal number = 100 to 120 assets)

Tranches = debt securities format

Senior (super-senior = AAA tranche)

Mezzanine (upper, lower)

Equity (most junior debt)

Also called first loss trancheSENIOR

MEZZ.EQTY.

Less risk

More risk


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Mecanism

Lets assume the following tranching

and 3 different senarios:

If over the CDO life, the cumulative losses of the pool = 3

Senior tranche is not hit

Mezz tranche is not hit

Equity tranche is hit by 3 Eqty tranche investors partially lose their investment


Senior tranche is not hit

Mezz tranche is hit by 5 Mezz tranche investors partially lose their investment

Equity tranche is totally hit (by 5) EQTY tranche investors lose all their investment


Senior tranche is hit by 5 Senior tranche investors partially lose their investment

Mezz tranche is totally hit (by 15) Mezz tranche investors lose all their investment

Equity tranche is totally hit (by 5) EQTY tranche investors lose all their investment

CDOs (contd)

Pool

100

Senior: 80

Mezz : 15

Eqty : 5

Increasingnumber

of defaults


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Different Asset Classes


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Different Asset Classes

Corporate risks

High Grade

High Yield

Mix of both

Asset Backed Securities (ABS)

2 main caracteristics:

Default rate < to those of corporate assets class

Relatively higher stability of ratings (more resilient to economic downturns)

SME Loans (small & medium companies)

CDO tranches ( CDO-squared)


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Different Structures


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Different types of structures: 4 criteria

Objective Balance Sheet vs Arbitrage CDO

Balance sheet = credit portfolio management, reglementary issues, capital optimization,

Arbitrage = taking advantage of the difference between the average return on the reference portfolio and the payments made to the tranches

investors (= excess spread)

Transfer mode Cash vs Synthetic

Cash = True sale of the underlying credit assets portfolio

Synthetic = risk transfert via CDS

Cash Flow CDO vs Market value CDO

Cash flow = CDO revenues driven by those of the underlying credit assets portfolio + revenues allocation to investors according to note seniority (=

cash flow waterfall)

Market value (CDS based technology) = CDO performance linked to the variation of the underlying credit assets market value

Static vs Managed CDO

Static = Credit assets reference pool is defined at implementation and remain unchanged during all the life of the transaction

Managed = Credit assets reference pool can fluctuate over time according to CDO manager trading decisions


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Flurry of innovations wont be discussed

CDO^2

CPPI (Constant Proportion Portfolio Insurance)

CPDO

CDO with equity buckets

Mix between debt and Eqty in order to enhance the CDO return profile

L/S (Long / Short structure)

Hedging vs market spreads variations

Etc


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Lets focus on 3 cases

Funded Loan Securitisation

Partially Funded Synthetic CDO

Single-tranche synthetic CDO


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Cash CDO / Funded Loan Securitisation

Pool of

credit assets

Assets face value= 100%

Senior DebtAAA

Face value = 66.5%

EURIBOR + 45bp

Mezzanine

BB

Face value = 20%

EURIBOR + 90bp

Equity

Face value = 13.5%

Assets

SPV

Liabilities

Senior

exposure

Intermediary

exposure

First loss

exposure

Reference pool

Assets face value

= 100%

Bank

= Transaction

Sponsor / Manager

Borrower 1

Borrower 2

Borrower 3

Borrower 4

Loanagreement

Loan

agreement

Loan

agreement

Loan

agreement

Management

Agreement

True sale

Investors

= protection

providers

Notes

Notes

Notes

Notes proceeds

The bank selects a pool of loans

to be securitized

Cash(=Notes proceeds)


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Funded Loan Securitisation (contd)

Named Cash CLO (Collateralised Loan Obligation)

True sale to an SPV for the full amount of the CLO

The SPV can already exist, but in most cases, it is created for the sole purpose of the CDO

SPV issues rated securities (with various tranches from AAA/Aaa to BB/Ba3 in general) that are all placed to Investors

Securities rated by rating agencies (S&P, Moodys, Fitch, )

Rating based on

Default statistics (historical data)

Sponsors commitment = Equity retention

Bank commits itself to keep the first losses unhedged in order to prove its good faith to investors vs any arbitrage temptation

Many drawbacks (= heavy structure) but some advantages

in terms of funding stability (vs synthetic CDO that are non-funded structures)

Good for banks with weakening rating interest level (swap rate + spread) defined the day the structure is implemented and remainsunchanged through the life of the deal (=usually 5 years)

In terms of rating


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Partially Funded Synthetic CDO

Bank A

Reference

potfolio

of credit

assets

Portfoliotranching

AAA: 90%

AAA: 3%

A: 3%

BBB: 3%

EQTY : 1%

Bank B(20% BIS weighted)

Super senior

CDS

Premium

(20bppa)

Treasuries(0% BIS

weighted)

CLN : 9%

SPV

Notes

proceeds

Market

Collateral

(Treasuries)

Subordinated

CDS

Premium

EQTY: 1%

1. Pledge Collateral

Intermediary

exposure

First loss

exposure

2. Pledge Collateral

Non

funded part

Funded partCash

Cash

Eqty tranche can be kept by the bank in order to enhance the risk profile of the structure

1. Pledge collateral to Bank A:

Neutralizes bank A exposure towards SPV

Enables bank A to benefit from a 0% BIS weighted treatment

2. Pledge collateral to investors:

Neutralizes investors exposure towards Bank A credit risk

Enables Bank A to issue AAA rated notes though itself rated AA (or below)


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Partially Funded Synthetic CDO (contd)

RWA & Capital before securitization of the pool

(H): Pool = fully drawn corp. credit assets for a total amount

of 100MEUR

RWA = 100MEUR

Reg cap RWA * 8% = 8MEUR

RWA & Capital after securitization of the pool

Super senior tranche

RWA = 90MEUR * 20% = 18MEUR

Reg Cap = 18MEUR * 8% = 1,44MEUR

Mezz tranche

RWA = 9MEUR * 0% = 0MEUR

Reg Cap = 0MEUR * 8% = 0MEUR

Eqty tranche

Reg Cap = 1MEUR (1:1 ratio)

New total RWA = 18MEUR

Such synthetic CDO deal :

Enables the bank to reduce its RWA from 100MEUR to 18MEUR

Leaves Tier 1 component of Reg cap unchanged (pre and post securitization)

Enables a huge benefit on the [Core Reg Cap / RWA] ratio that is dramatically increased

Eqty tranche nominal deducted from Tier3 component on a 1:1 basis

Focus on reg. Cap. Optimization (Basle I)


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Premium

(45bppa)

Subordinated

CDS

Portfolio

tranching

Single tranche Synthetic CDO

Bank A

Reference

potfolio

of credit

assets

AAA: 90%

AAA: 3%

BBB: 3%

EQTY : 1%

CDS Market

Correlation desk

Protection provider

A: 3%A: 3%

Delta

hedging

Position dynamically managed

vs

long & hold strategy type


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Single-tranche Synthetic CDO (contd)

Only one tranche is created and sold to an investor.

The capital structure is not entirely distributed

Single-tranche synthetic CDOs are also called Bespoke tranches

Indeed, the investor can customize various caracteristics (= portfolio composition, term, rating,tranche size, subordination, )

Structure that can be self managed or externally managed

Bilateral instrument (= no distribution)

Non publicly rated structure

Correlation desks are the natural counterparties

Correlation desk traders Delta-hedge their position in the CDS markets

Tranche underlying names need to be liquid

Pricing & rating of single tranches will now be examined in part 2


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Base Case

Loss distribution characteristics


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Base Case CDORom use

Let our base case be an homogeneous portfolio with

200 names with a nominal of 100M each Pool total nominal = 20.000M

Equally weighted, 0.5% each

With the same 3-year bullet tenorfor all the names

With the same 1.71%- PD for all names (typically they are all Baa3)

With the same 30% recovery rate for all names

The key parameter discussed is correlation

In our base case, we assume a level of correlation at 10%

Correlation is supposed to be the same across the portfolio


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Base Case - Portfolio Loss distribution graph

Loss Distribution

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

0.0

%

1.5

%

3.0

%

4.5

%

6.0

%

7.5

%

9.0

%

10.5

%

12.0

%

13.5

%

15.0

%

16.5

%

18.0

%

19.5

%

21.0

%

22.5

%

24.0

%

25.5

%

27.0

%

28.5

%

30.0

%

31.5

%

33.0

%

34.5

%

36.0

%

37.5

%

39.0

%

Probabilities

%o

fpo

rtfolioloss


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Base Case Zoom on [0%-3%] and [8%-11%] tranches

Prob = 1

Loss Rate Probabilities Cum Prob

0.0% 14.76% 0.147581667

0.1% 0.04% 0.147986833

0.2% 0.06% 0.148552667

0.3% 0.05% 0.149101167

0.4% 17.66% 0.325696

0.5% 0.23% 0.328024

0.6% 0.10% 0.329017667

0.7% 0.21% 0.331104167

0.8% 15.44% 0.485512167

0.9% 0.25% 0.487974667

1.0% 0.12% 0.489143333

1.1% 12.14% 0.610565333

1.2% 0.40% 0.614605167

1.3% 0.15% 0.616134833

1.4% 0.12% 0.617369167

1.5% 9.23% 0.709715833

1.6% 0.31% 0.7128165

1.7% 0.11% 0.713940667

1.8% 5.94% 0.773310167

1.9% 1.13% 0.784625667

2.0% 0.17% 0.786371333

2.1% 0.10% 0.787376333

2.2% 4.98% 0.837185167

2.3% 0.28% 0.839991667

2.4% 0.09% 0.840908167

2.5% 1.49% 0.855773167

2.6% 2.33% 0.87903

2.7% 0.16% 0.880650667

2.8% 0.07% 0.881380667

2.9% 2.64% 0.907799833

3.0% 0.22% 0.909956167

Loss Rate Probabilities Cum Prob

8.0% 0.01% 99.77%

8.1% 0.00% 99.77%

8.2% 0.01% 99.78%

8.3% 0.03% 99.81%

8.4% 0.01% 99.82%

8.5% 0.00% 99.82%

8.6% 0.02% 99.84%

8.7% 0.01% 99.86%

8.8% 0.00% 99.86%

8.9% 0.00% 99.86%

9.0% 0.02% 99.88%

9.1% 0.00% 99.89%

9.2% 0.00% 99.89%

9.3% 0.01% 99.90%

9.4% 0.01% 99.91%

9.5% 0.00% 99.91%

9.6% 0.00% 99.91%

9.7% 0.01% 99.93%

9.8% 0.00% 99.93%

9.9% 0.00% 99.93%

10.0% 0.00% 99.94%

10.1% 0.01% 99.94%

10.2% 0.00% 99.95%

10.3% 0.00% 99.95%

10.4% 0.01% 99.95%

10.5% 0.00% 99.96%

10.6% 0.00% 99.96%

10.7% 0.00% 99.96%

10.8% 0.01% 99.96%

10.9% 0.00% 99.97%

11.0% 0.00% 99.97%

[0%-3%] Tranche [8%-11%] Tranche


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Base Case - El & Ec. Cap. inferred from Distribution

Expected Loss equals 256 million which represents 1.28% of the pool nominal (= 256,29M / 20.000M)

An 1.28% EL over a 3-year period roughly corresponds to a 42 bppa spread, which is consistent with a Baa3 pool

Ec Cap 99.8% equals 12% of the pool nominal (= 2.359M / 20.000M)

Ec Cap = 9 times EL The capital buffer amount is very important

EL

Cum. Prob. 50.00% 90.00% 95.00% 99.00% 99.90% 99.98%

Port. Cum. Loss 265 574 781 1,202 1,861 2,359 256

Capital Economique


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Main drivers

of Cum Loss Distribution


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Portfolio Loss distribution

What are the main drivers of the loss distribution?

Key 1 factor = Default rate of each entity

The higher the PD rate of the portfolio, the more important the cumulative losses

Key 2 factor = Correlation

The higher the correlation, the more fat tailed the cumloss distribution

Key 3 factor = Tenor

The higher the CDO maturity, the more important the cumulative losses

Other parameters of lesser impact

Diversification (# of names)

LGD

Impact level

on thecumloss curve

EL Ec Cap Fat Tail Rating Spread

Default Prob Increase Increase Increase Deteriorate Increase

Tenor Increase Increase Increase Deteriorate Increase

Correlation Neutral Increase Increase

Increase on Senior tranche

Decrease on Eqty tranche

Neutral on Mezz. Tranche

Increase on Senior tranche

Decrease on Eqty tranche

Neutral on Mezz. Tranche

Impacts on Cum Loss Distribution


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Tenor impact

on portfolio loss distribution


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Tenor impact on EL & Ec Capital

The longer the tenor, the bigger the EL and the Ec. Cap.

In other words, the longer the tranche maturity, the lower its rating

Expected Loss & Capital @ 99.98%

0

1000

2000

3000

4000

5000

6000

7000

0 5 10 15

Tenor (year)

Million

EL

EC99.98

Tenor

(in year)

EL

(MEUR)

Ec. Cap. 99.98

(en MEUR)

1 63 991

3 256 2,359

6 554 3,738

9 845 4,762

12 1,282 6,035x2.2 x1.2


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DP Impact



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The higher the DP, the bigger the EL and the Ec. Cap.

In other words, you have higher probabilities to have big losses with low rated pool.

Loss Rate (Default Probability) impact on EL & EC. Cap.

1% 1,5%

Probability

Portfolio losses in % of pool nominal

- 1% loss rate curve

- 1.5% loss Rate curve


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Correlation impact



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In theory two correlation extreme cases

No correlation

No link between the various default

Binomial calculation

Sample with (n) elements, probability of default (p) each.

Proba of having (k) defaults is

P(X=k) = C(n,k) * p^k * (1-p) ^(n-k)

With X being the number of defaults, and K [0;n ]

BINOMDIST(3, 200, 1.71%, FALSE)

And of course, the sum of the probabilities for k= 0, 1, 2

etc is 100%

Maximum correlation

Bimodal distribution

Either no loan default or all the loans of the pool default

Binomial case

0%

5%

10%

15%

20%

25%

0 816

24

32

40

48

56

64

72

80

88

96

Number of defaults amongst 100

Probability

ofeach

situation

Binomial

100% Correlation case

0%

10%

20%

30%

40%

50%

60%

70%

0 816

24

32

40

48

56

64

72

80

88

96

Number of defaults amongst 100

Probab

ility

ofeach

si

tuation

Full Correl

C \USERS\St h DELAINE\STR CDO CWA & i ti t\ ti \ t i i lid 30/03/2007 17 07 02


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In real life Intermediate cases

The intermediate cases with correl 10% or correl 20% etc are a kind of blend between correl = 0% and correl 100%

The higher the correlation, the more fat tailed the distribution looks like.

The higher the correlation, the more important the impact of the 100% correlation bimodal distribution ( Higher probabilities for extreme

situations)

Greater probability to have no loss at all the curve moves to the left

Greater probability to have all the underlyings defaulting at the same time the curve moves to the right

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Probabilities

Correl = 10% Correl = 20% Correl = 30%



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C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02


Correlation @ 10% vs Correlation @ 20%

-10% correlation

2.8%

Probability

Portfolio losses in % of pool nominal

3% 6%

The pricing of the trancheis proportional to

the sub area Below the curve

CumProb

= 90.78%

CumProb

= 88.29%

CumProb

= 8.19%

CumProb

= 8.59%

CumProb

= 1.05%

CumProb

= 3.12%

-20% correlation

Same mean



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Correlation @ 10% vs Correlation @ 20% (Contd)

The two distributions have the same mean ( = 2.8%)

Correlation impacts the standard deviation of the cumloss distribution

Correlation increases the sub area of senior tranches ( Loss distribution attracted to the right)

For the correlation @10%, there is a 1.05% probability that cumulative losses over 3 year will fall in the [6% - 100%] intervalof pool size

For the correlation @20%, there is a 3.12% probability that cumulative losses over 3 year will fall in the [6% - 100%] intervalof pool size

Naturally those expected losses will drive the tranche pricings

The larger the area of the tranche below the curve, the higher the spread

Correlation increases Senior tranche price

Correlation decreases Eqty tranche price

Correlation has a relatively neutral impact on Mezz tranche

Note: such statement is no longer true for very high correlation levels (impact of the 100% correlation bimodal distribution)



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Pricing in theory:

only one correlation



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(Approximate calculations*) Eqty Mezz Senior Global Pool

[0% - 3%] [3% - 6%] [6% - 100%] [0% - 100%]

Correlation @ 10% 36.31 3.28 0.41 40

Correlation @ 20% 35.32 3.43 1.25 40

* Duration concept not taken into account

Conversion of CumLoss into bppa of pool nominal

In the base case, we assume an average CDS spread for the pool @40 bppa of pool nominal

For a 10% correlation

The [0%-3%] loss tranche having a cumulative probability of 90.78% (see p.4), the corresponding tranche pricing is 36.31bppa

of pool nominal (= 40bpba * 90.78%)

x3

Most sensitive tranche

in terms of correlation



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(Approximate calculations*) Eqty Mezz Senior

[0% - 3%] [3% - 6%] [6% - 100%]

Correlation @ 10% 1,210 109 0.44

Correlation @ 20% 1,177 115 1.33* Duration concept not taken into account

Translation into tranche pricings

For 10% correlation, equity tranche

The [0%-3%] cumloss tranche size being 3% of pool nominal, the

corresponding tranche pricing is 1210 bppa of tranche nominal (=

36.31bppa / 3%)

Same type of calculations apply to mezzanine and senior tranches

Mezzanine

3.28bppa of pool nominal (= 8.19% * 40 bppa)

109bppa of tranche nominal (=3.28bppa /3%)

Senior tranche

0.42bppa of pool nominal (= 1.05% * 40 bppa)

0.44bppa of tranche nominal (=0.42bppa /94%)

Key point : pricing of upper tranches are quiete close to 0 bppa

Return carried by the Eqty

tranche = 12% of

the pool nominal



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Pricing in real life:

not only one correlation!



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CDO training program 37

Compound correlation model limits

Step 1: Determination of the spread of each tranch of a portfolio using the historical unique correlation @ 6% (used by rating

agencies) via the Normal Copula Model

Step 2: Calculation of correlations using market spread

Market spread are not deducted from one level of correlation but various levels of correlation according to tranche attachment

and detachment points

Correl Pricing bppa

Tranche

[0% - 3%] 6% 1 610[3% - 6%] 6% 140

[6% - 9%] 6% 10

[9% - 12%] 6% 0.6

[12% - 22%] 6% 0.02

Step 1 : tranche pricing calculated from a unique correl

Market Spread Correl Deducted

1 046 20%86 6%

33 30%

12 40%

6 50%

Step 2: Correls calculated by the market

Theory single correlation model Real life various correlation levels

Pricing not so close to 0



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Real market pricings are not so close to zero!

Determining tranche pricings through a CumLoss approach with a unique correlation figure is indeed possible around the equity zone

But when applying the same approach to upper mezz and senior tranches, you find spread levels extremely low (near to zero bp)

Whereas the market quotes hardly fall below 1 or more bppa

Who would sell protection at 0.1 bppa?

The law of supply and demand leads to higher market spreads,and hence higher correlation levels

Such a market practice explains the correlation smile (same as for the options markets)

The more senior the tranche, the higher the level of correlation induced by the market



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Correlation Smile: Theory vs market prices

Though only one correlation figure should prevail for the entire

portfolio & tranche pattern

Indeed, when a default occurs, only one correlation will apply

to the whole portfolio

market quotations cannot be derived from a model with only 1

correlation

Correlation varies according to the tranch seniority

Market needs to ensure liquidity for upper tranches

The smile reflects the fact that market does not believe in a single

correlation model

Smiledecorrlation

Smiledecorrlation

Europe Bid/Ask Mid-market

implied correlation

[0% - 3%] 28.25/33.25 + 500 19.9%

[3% - 6%] 235/275 7.3%

[6% - 9%] 95/115 18.8%

[9% - 12%] 50/65 24.8%

[12% - 22%] 18/26 30.4%[3% - 100%] 13.5/17.5 20.9%



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Base correlation related to x% is the correlation of the [0, x%] equity tranche on a standardised portfolio

Recursive calculation of the base correlation curve

[0%-3%] tranche spread known from mkt

BaseCorrrel (3%) then calculated f-1(Spread [0% - 3%]) = compound Correlation

[3% - 6%] tranche spread known from mkt

Given that [3% - 6%] tranche pricing depends on BaseCorrel (3%) and BaseCorrel (6%),

Spread [0% - 6%] = Spread [0% - 3%] + Spread [3% - 6%]

BaseCorrrel (6%) then calculated f-1(Spread [0% - 6%])

6%- 9% tranche spread known from mkt

BaseCorrrel (9%) then calculated etc.

Bootstrapping is a calculation method that derives the BaseCorrel of a senior tranche from a more junior tranche

Bootstrapping method



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Base Correlation curve after bootstrapping calc

Skew measures the steepness of the BaseCorrel curve

In other words, the skew is the slope of the BaseCorrel

curve with a proportionality factor in the definition)

A steepening of the skew conveys a spread increase of the upper

tranches

The skew level is ruled by the law of supply and demand

Smile effect

Smile

Effect



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Mezzanine tranche pricing is sensitive to skew

(H): Portfolio spread = 54bppa

[15% - 25%] 228bppa [15% - 26%] 211bppa

[16% - 25%] 248bppa [16% - 26%] 231bppaBase Correlation Skew

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0% 5% 10% 15% 20% 25%

Detachement Le vel

Correlation

Initial Correlation Skew Mouvement

Parallel shift in the correlation

level does not impact

Mezz tranche spread level

whereas skew changes

Mezz tranche spread level

Base Correlation Skew

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0% 5% 10% 15% 20% 25%

Detachement Level

Co

rrelation

Initial Correlation Parallel Shift

Base Correlation Skew

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0% 5% 10% 15% 20% 25%

Detachement Level

Co

rrelation

Initial Correlation Parallel Shift



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Mezzanine tranche pricing is sensitive to skew (Contd)

Impact of changing correlation @ attachment point

All things being equal, the higher the correlation at attachment point, the bigger the tranche spread

The slope of the base correlation curve decreases

Impact of changing correlation @ detachment point

All things being equal , the higher the correlation at detachment point, the lesser the tranche spread

The slope of the base correlation curve increases

Its the slope of the base correlation curve that affects tranche pricing

Note: A parallel shift of the base correlation curve only impacts the spread levels of Eqty and Senior tranches

Neutral impact on Mezz. tranche



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Mark-to-Market



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Base case

Closing

Pool @ 25 bppa

Tenor 5 year 14 days

Correlation_Attach 15%

Correlation_Detach 23.8%

Tranche [3% - 6%]

Nominal Tranche 3 billion

Nominal pool 100 billion

After 1 year

Pool @ 40 bppa

Tenor 4 year 14 days

Corelation _Attach 12%

Correlation_Detach 22%

Tranche [3% - 6%]

Nominal Tranche 3 billion

Nominal pool 100 billion

Amount% of

Invested Notional

Tranche Value 641,753 0.02%

Market Spread

Bp Value

Amount% of

Outstanding Portfolio

Number of Names

Outstanding Portfolio Notional

Portfolio Expected Loss -1,263,720,256 -1.26%

125

100,000,000,000

CDS Portfolio

CDO Tranche (Unfunded transaction)

4.71

0.56%

Amount% of

Invested Notional

Tranche Value -35,225,919 -1.17%

Market Spread

Bp Value

Amount% of

Outstanding Portfolio

Number of Names

Outstanding Portfolio Notional

Portfolio Expected Loss -1,615,837,376 -1.62%

125

100,000,000,000

CDS Portfolio

CDO Tranche (Unfunded transaction)

3.83

0.87%



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At Closing,

Portfolio spread = 25 bppa ( CDS cost of the whole pool)

Tranche spread = 56 bppa ( CDS cost for the tranche)

Thus, my tranche represents 6.7% of the portfolio global cost of carry

Cost of carry of the tranche related to pool nominal = 56 bppa * 3% = 1.68bppa

This cost related to the global cost of carry of the pool = 1.68bppa / 25 bppa = 6.7%

It can be noted that the lower the tranche seniority, the higher its relative cost of carry, and thus the more important its Delta

In other words, the delta of the tranche is 6.7%.

It means that the tranche behaves like 6.7% of the portfolio in terms of MtM

Delta-hedging (by a correlation desk) will thus be done on a nominal of 6.7% * 100 billion = 6.7 billion

MtM (for the investor) = - 6.7% * [0.40% - 0.25%] * [3.7 year] * 100 billion

MtM (for the investor) = - 37 million

Calculation looks like the MtM of a Bond

Explanation of MtM in order of magnitude

Tranche

converted

into pool Variation in

Underlyings spread

Duration Pool nominal



47/59

Greeks or portfolio sensitivity to risk factor

shifts



48/59


shifts

Delta



49/59


Delta: Volumetry

In this example, the correlation desk must realise its delta hedge on a nominal equal to almost 6 times the tranche notional

5.7 * 30MEUR = 171MEUR or 17.1% of the pool nominal

Premium

Subordinated

CDS

Portfolio

tranching

Bank A

Reference potfolio

of credit Assets

1 GEUR

[9% - 100%]

910MEUR

[6% - 9%]: 30MEUR

[0% - 3%]: 30MEUR

CDS Market

Correlation desk

Protection provider

[3% - 6%] : 30MEUR[3% - 6%] : 30MEUR

Delta

hedging

(H): Delta = 5.7 * tranche notional



50/59


Tranche Delta is used:

By investors (correl desk) to hedge their exposure to movements in the CDS spread of the underlying credits

Delta = definition of the CDS underlying nominal that needs to be sold / bought to hedge a short/long synthetic CDO tranche position

By CDO sponsors to manage the transactions

Delta = indication of the cost of substituting underlying credits.

Delta main features

Tranche delta range from 0% to 100% of pool nominal

Tranche delta are usually quoted in terms of notional amount needed to hedge the tranche against spread movements of the particular

underlyings.

Delta = (Tranche spread var. / CDS on the specific underlying spread var.) * Tranche notional

Tranche Delta depends on:

Attachment point (= subordination)

Tranche thickness

Pool spread

Time to maturity

Default correlation

Delta: generals



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Delta: Tranche attachment point impact

The more junior the tranche, the higher its delta

Tranches that are lower in the capital structure are more risky as there is less protection against default risk

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

[0% - 3%] [3% -6%] [6% - 9%] [9% - 12%]

Tranche

D

elta

Delta in % of pool

Tranche

Tranche

size

Tranche spread

with portf. spread

@ 25 bppa

Tranche spread

with portf. spread

@ 26 bppa

Delta in %

of pool

Base Correl

AP / DP

[0% - 3%] 3% 648.07 668.80 62.19% 15% / 15%

[3% -6%] 3% 51.28 55.46 12.54% 15% / 23.8%

[6% - 9%] 3% 16.33 17.33 3.00% 23.8% / 30.7%

[9% - 12%] 3% 6.18 7.04 2.58% 30.7% / 36.9%



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Delta: Tranche detachment impact

The larger the tranche, the higher delta

For a fixed level of subordination (here = 3%), a wider tranche is exposed to a larger band of losses, and is therefore more

risky

Note that the increase in tranche delta flattens out once the limit of possible losses is reached

Tranche

Tranche

size

Tranche spread

with portf. spread

@ 25 bppa

Tranche spread

with portf. spread

@ 26 bppa

Delta in %

of pool

Base Correl

AP / DP

[3% - 6%] 3% 51.28 55.46 12.54% 15% / 23.8%

[3% - 7%] 4% 43.98 47.46 13.92% 15% / 26.1%

[3% - 8%] 5% 38.62 41.73 15.55% 15% / 28.4%

[3% - 9%] 6% 33.8 36.4 15.60% 15% / 30.7%

0.00%

2.00%

4.00%

6.00%8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

[3% - 6%] [3% - 7%] [3% - 8%] [3% - 9%]

Tranche

D

elta

Delta in % of pool



53/59


Delta: other factors impacts

Pool spread:

Tranche deltas are linked to the risk profile of the pool. The riskier the pool,

the greater the delta of the Eqty tranche

the lower the delta of the senior tranche

Time to maturity:

As the time to maturity tends to 0, defaults becomes less likely to occur,

the delta of the Eqty tranche converges to 100% of the pool nominal,

and the deltas of all other tranches converge to 0%

: Default correlation

As correlation level increases,the risk is shifted to the senior tranche (= higher probability of joint default),

the delta of the Eqty tranche decreases

and the delta of the senior tranche increases



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shifts

Time to maturity


V i ti f MtM ith th ti t t it


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-0.80%

-0.70%

-0.60%

-0.50%

-0.40%

-0.30%

-0.20%

-0.10%

0.00%

0 1 2 3 4 5

Years

MtM

All parameters being equal

We look at the [3% - 6%] tranche

We make strong assumptions:

Portfolio spread (= 25bppa) remains unchanged all along the life of the CDO

Correlation curve remains unchanged (Attachment point = 15% / Detachment point = 23.8%)

To explain the curve shape, lets simplify the MtM formula by ignoring the Delta impact (negligible since moving into a relatively narrow corridor)

MtM (for the investor) = - [Tranche spread variation * Duration * tranche nominal] As time to maturity decreases, the MtM deteriorates (there is less time for defaults to hit the [3% - 6%] mezzanine tranche Tranche less risky

Tranche spread decreases)

up until a certain point of time when MtM increases again until reaching 0 at maturity ( time decay impact on tranche MtM superior to

spread reduction impact)

Variation of MtM with the time to maturity

Point of time GCPM MtM in % of tranche nominal

Issuance -0.02%

+ 1Year -0.37%

+ 2Years -0.70%

+ 3Years -0.70%

+ 4 Years -0.54%

+ 5 Years(Residual maturity = 14 days) -0.02%

Source: SG CDO Pricer tool



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shifts

Spread parallel move test




57/59


[0%- 3%] Portfolio spread Tranche spread Duration

(bppa) (bppa) (year)

25 872 3.84

50 1,727 3.18

75 2,556 2.68

100 3,372 2.3125 4,179 2

[3% - 6%] Portfolio spread Tranche spread Duration


25 56 4.71

50 216 4.58

75 436 4.4

100 686 4.18

125 942 3.97



We look at the[0% - 3%] tranche and the[3% - 6%] tranche

Maturity = 5 years

We make strongassumptions:

Correlation curve remains unchanged: 15% /15% for the tranche [0%-3%] and 15% / 23.8% for the tranche [3% - 6%]

We move the portfolio spread from 25bppa to 50 bppa

[0% - 3%] tranche spread moves from 872 bppa (core) to 1727 bppa The ratio 34.2/1 is the leverage of that tranche

[3% - 6%] tranche spread moves from 56 bppa (core) to 216 bppa The ratio 6.4/1 is the leverage of that tranche

Eqty tranche is the most sensitive to portfolio (and single-name) wide spread moves

Note that tranche spread vs pool spread curve is sligthly convex

x2 x2

x2 x4

0

5001,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

25 45 65 85 105 125 145

Portfolio spread (bppa)

Tranc

hespread(bppa)

[0% - 3%] spread (bppa) [3% - 6%] spread (bppa)



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shifts

Duration


Duration


59/59


Duration


We look at the [0% - 3%] tranche and the [3% - 6%] tranche

Maturity = 5 years

We make strong assumptions:

Correlation curve remains unchanged: 15% /15% for the tranche [0%-3%] and 15% / 23.8% for the tranche [3% - 6%]

Duration can be defined as a kind of discounted average life time

The riskier (= more junior) the tranche the higher the number of default the smaller the duration

The higher the portfolio spread the higher the number of default the smaller the duration

Note that American priced tranche will always have a smaller duration than European priced tranche

[0%- 3%] Portfolio spread Tranche spread Duration


25 872 3.84

50 1,727 3.18

75 2,556 2.68

100 3,372 2.3

125 4,179 2

[3% - 6%] Portfolio spread Tranche spread Duration


25 56 4.71

50 216 4.58

75 436 4.4

100 686 4.18

125 942 3.97

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150

Portfolio spread (bppa)

D

uration(years)

[0% - 3%] Duration [3% - 6%] Duration

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