CDO Training Program
Embed Size (px)
Transcript of CDO Training Program

8/3/2019 CDO Training Program
1/59
CDO training program
CONFIDENTIAL

8/3/2019 CDO Training Program
2/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO Technology Overview

8/3/2019 CDO Training Program
3/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
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 (supersenior = AAA tranche)
Mezzanine (upper, lower)
Equity (most junior debt)
Also called first loss trancheSENIOR
MEZZ.EQTY.
Less risk
More risk

8/3/2019 CDO Training Program
4/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program4
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
If over the CDO life, the cumulative losses of the pool = 10
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
If over the CDO life, the cumulative losses of the pool = 25
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

8/3/2019 CDO Training Program
5/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Different Asset Classes

8/3/2019 CDO Training Program
6/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program6
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 ( CDOsquared)

8/3/2019 CDO Training Program
7/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Different Structures

8/3/2019 CDO Training Program
8/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program8
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

8/3/2019 CDO Training Program
9/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program9
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

8/3/2019 CDO Training Program
10/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program10
Lets focus on 3 cases
Funded Loan Securitisation
Partially Funded Synthetic CDO
Singletranche synthetic CDO

8/3/2019 CDO Training Program
11/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program11
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)

8/3/2019 CDO Training Program
12/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program12
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 nonfunded 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

8/3/2019 CDO Training Program
13/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program13
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)

8/3/2019 CDO Training Program
14/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program14
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)

8/3/2019 CDO Training Program
15/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program15
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

8/3/2019 CDO Training Program
16/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program16
Singletranche Synthetic CDO (contd)
Only one tranche is created and sold to an investor.
The capital structure is not entirely distributed
Singletranche 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 Deltahedge 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

8/3/2019 CDO Training Program
17/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Base Case
Loss distribution characteristics

8/3/2019 CDO Training Program
18/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program18
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 3year 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

8/3/2019 CDO Training Program
19/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program19
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

8/3/2019 CDO Training Program
20/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program20
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

8/3/2019 CDO Training Program
21/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program21
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 3year 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

8/3/2019 CDO Training Program
22/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Main drivers
of Cum Loss Distribution

8/3/2019 CDO Training Program
23/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program23
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

8/3/2019 CDO Training Program
24/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Tenor impact
on portfolio loss distribution

8/3/2019 CDO Training Program
25/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program25
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

8/3/2019 CDO Training Program
26/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
DP Impact
on portfolio loss distribution

8/3/2019 CDO Training Program
27/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program27
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

8/3/2019 CDO Training Program
28/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Correlation impact
on portfolio loss distribution

8/3/2019 CDO Training Program
29/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program29
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 * (1p) ^(nk)
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

8/3/2019 CDO Training Program
30/59
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program30
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%
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
31/59
C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
CDO training program31
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
32/59
CDO training program32
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)
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
33/59
Pricing in theory:
only one correlation
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
34/59
CDO training program34
(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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
35/59
CDO training program35
(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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
36/59
Pricing in real life:
not only one correlation!
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
37/59
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
38/59
CDO training program 38
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
39/59
CDO training program 39
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 Midmarket
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%
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
40/59
CDO training program 40
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 f1(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 f1(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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
41/59
CDO training program 41
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
42/59
CDO training program 42
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
43/59
CDO training program 43
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
44/59
MarktoMarket
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
45/59
CDO training program 45
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%
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
46/59
CDO training program 46
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
Deltahedging (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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
47/59
Greeks or portfolio sensitivity to risk factor
shifts
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
48/59
Greeks or portfolio sensitivity to risk factor
shifts
Delta
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
49/59
CDO training program 49
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
50/59
CDO training program 50
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
51/59
CDO training program 51
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%
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
52/59
CDO training program 52
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
53/59
CDO training program 53
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
54/59
Greeks or portfolio sensitivity to risk factor
shifts
Time to maturity
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
V i ti f MtM ith th ti t t it

8/3/2019 CDO Training Program
55/59
CDO training program 55
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
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
56/59
Greeks or portfolio sensitivity to risk factor
shifts
Spread parallel move test
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Spread parallel move test

8/3/2019 CDO Training Program
57/59
CDO training program 57
[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
(bppa) (bppa) (year)
25 56 4.71
50 216 4.58
75 436 4.4
100 686 4.18
125 942 3.97
Spread parallel move test
All parameters being equal
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 singlename) 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)
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02

8/3/2019 CDO Training Program
58/59
Greeks or portfolio sensitivity to risk factor
shifts
Duration
 C:\USERS\Stephane DELAINE\STR CDO CWA & investissement\presenations\post asian seminar slides 30/03/2007 17:07:02
Duration

8/3/2019 CDO Training Program
59/59
CDO training program 59
Duration
All parameters being equal
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
(bppa) (bppa) (year)
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
(bppa) (bppa) (year)
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