Recent Developments in CDOs
Gloria Lu, CFA
Associate Director, Structured Finance Ratings
Standard & Poor’s
21st May, 2007
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Copyright (c) 2006 Standard & Poor’s, a subsidiary of The McGraw-Hill Companies, Inc. All rights reserved.
Agenda
• CDO Market Overview
• CPDO Index and Managed Trades
• Non Credit Trades
• Other Trades
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Global CDO Issuance Statistics
Global CDOs Issuance Size
Europe
Asia/Pacific
Total no of deal
(Million in USD)
600,000
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
500,000
400,000
300,000
200,000
100,000
0
2004
2005
2006
© Standard & Poor's 2007.
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2007YTD
Total no of Deals
USA
Asia (ex-Japan) CDO Issuance Statistics
Asia (ex-Japan) CDOs Composition by Cash Flow & Synthetic
Synthetic
No of Tranches
6,000
120
5,000
100
4,000
80
3,000
60
2,000
40
1,000
20
0
0
2002
2003
2004
2005
© Standard & Poor's 2007.
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2006
2007
Total no of Tranches
(Million in USD)
Cashflow
Asian CDO Market Recent Development
• Cash Flow
• Increased balance sheet CLO issuance
• Rising interest in Asian-flavored CDO
• Synthetics
• Stable vanilla STCDO issuance
• Variations on spread-based or market value- based products
 CPDO
 Credit CPPI
• Option based products
 Commodities
 F/X
 Rates
• Others
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CPDO - Economic Backdrop
5 year on-the-run IG CDS Jan 2005 to Feb 2007
Source: JP Morgan
• Given tight spread environment, there are few alternatives to achieve investment grade return targets except
through a rule-based, leveraged credit strategy.
• For an IG corporate index CPDO, the idea is migration to non-IG and default will have been flushed out,
potentially at a cost, when the index is rolled very 6 months.
• Leverage and controlled credit degradation will combine to produce an instrument that is highly rated and
pays an attractive coupon. But to do so, liquidity in the underlying index is crucial.
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CPDO – General Framework
• A CPDO is a leveraged trade on a portfolio of names
• The leverage is a clearly defined function that usually depends on the shortfall
Credit Portfolio =
Shortfall x
Multiplier
NAV
Ceiling (Positive
Cash out
amount)
Multiplier
Leveraged
Credit
Portfolio
Shortfall
• Thus we need to look at both the asset and liability side as both of these factors
effect the calculation of shortfall – very different from a Synthetic CDO where
only the asset side need to be modeled
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CPDO – General Framework
• Asset side
• Defaults
• Recoveries
• Asset Correlation
• Spread movements
• Interest Rates
• Liability side
• Interest Rates
• FX risks
• Waterfall
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CPDO - Index Trades Default Probability
• Index Deals – Have a portfolio where the constituents are regularly replaced (ie
CDX and iTraxx replace every 6 months)
• Default risk is greatly reduced as non-investment grade assets are removed
from the portfolio
• For Index trades a simplification is to adjust the default probabilities used in the
CDO Evaluator and use this model to generate default times for each of the
assets
• The default curve is generated by applying the probability of default between
year 1 and year 2 in the original Standard and Poor’s asset default table for
each year.
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CPDO – Index Trades Default Probability
• The graph below shows the effect of the reduction in asset default probabilities to
account for the rolling nature of the index
14.00%
12.00%
Standard PDs
Adjusted PDs
10.00%
Probability
8.00%
6.00%
4.00%
2.00%
No of Defaults in 10 years
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38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0.00%
CPDO - Index Trades Recoveries and Correlation
• Recoveries – If an asset in the portfolio does default there is assumed to be
some level of recovery.
• As with the standard CDO Evaluator recoveries are assumed to be follow a
Beta Distribution with the Mean and Standard Deviation levels the same as for
Synthetic CDOs
• Asset Correlation – We would expect to see more / less defaults in a portfolio
that has less / more diversity
• Use same assumptions in the standard CDO Evaluator
between
industries
within
industry
Within Country
local
regional
global
5%
5%
5%
15%
15%
15%
Within Region
local
regional
global
5%
5%
5%
5%
15%
15%
Between Regions
local
regional
global
0%
0%
0%
0%
0%
15%
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CPDO Credit Risk
• Credit Risk
– Defaults lead to a reduction in the portfolio NAV. The effect of
default is magnified as the structure is leveraged.
- Eg: 250-name portfolio, 15 times leveraged.
– With a 40% recovery, one default leads to a decrease in NAV of
[(1-0.4)÷250] x 15 = 3.6%.
– The decrease would only be 0.24% with an unleveraged
portfolio.
– However, the exposure to iTraxx and CDX indices limits default
risk since short-term exposure to IG names.
– BUT Credit risk may increase with other more complex
structures.
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CPDO - Index Trades Spread Movements
• Spread Movements of the index as a whole have been calibrated to follow an
Ornstein-Uhlenbeck process:
d log S (t )  k (  log S (t )) dt   dW (t )
• Where
•
log S is the logarithm of the
credit spread
•
•
•
k is the mean reversion
 is the long-term mean
 is the volatility
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Spread in CPDO Performance
• Spread Risk
– An increase in spreads causes initially a mark-to-market loss to the structure.
– Assume a structure contracting a 5-year CDS at 50bps and an increase of
spreads of 10bps. Compared to the market rate, the structure is earning
10bps less than the current risk investors are exposed to for a 5-year period.
The market value of the pool is negatively affected: the higher the leverage
the larger the decrease.
Assuming a 15 times leverage, the MTM decrease effect is approximately
10bps x 5 x 15= 7.50% (with no discounting).
– However, higher spreads are also a benefit to the structure due to the higher
premium earned over the next roll period.
– At 15 times leverage, a 10bps spread increase will lead to 1.50%
higher return per annum.
– Any MTM losses incurred from spread widening in the underlying assets can
be made back by increasing the leveraged exposure to this higher spread so
that the future risky income will compensate for this loss.
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CPDO - Index Trades Interest Rates
• Interest Rates – We need to model interest rates for two purposes
• On the assets side, in order to calculate mark-to-market value at each time
• On the liability side interest to calculate the interest accrued in the cash deposit account.
• Interest Rates are assumed to follow a Heath Jarrow Morton - This model allows us to
derive the term structure of forward or spot interest rates
• The stochastic process for the spot interest rate r(t) can be described by:
t
2
t 2
 ( t u )


r (t )  f (0, t ) 
1

e


e
dW (u )
2

0
2
• Where
•
•
•
the forward rate at initial time 0
f (0, t )
the forward rate volatility

the mean reversion parameter

• To date FX risk has not been explicitly modeled in these transactions – the risk has been
taken by the arranging bank
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CPDO - Index Trades Waterfall
• Leverage Function – The exact leverage function is transaction specific but a
typical example would be the following:
• Shortfall = PV (liability) ( 1+ Adjustment ) – NAV
• Target Notional = Gearing Factor * Shortfall / PV (CDS_Premium)
• Where
• PV (liability) – Is the sum of all remaining target coupons, fees and final principal
redemption paid to the investor discounted at the risk free interest rate
• Adjustment – Leverage Cushion
• NAV = Deposit Account + MtM of risky CDS portfolio
• Gearing Factor – Increase in leverage to account for defaults in the portfolio
• PV (CDS_Premium) – Sum of all remaining spread premium income until maturity paid
by the protection buyer discounted by the risky interest rate
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CPDO – Index Trades Results
Stochastic Spread Example - Stressed Defaults
1.2
2.00%
Stochastic Spread Example - Zero Defaults
Fixed Spread Example - Zero Defaults
1.80%
1
1.50%
20
1.60%
1.2
1.2
1.40%
1
1
18
1.30%
1.20%
0.6
1.00%
Spread of Assets
NAV / Cash In Amount
0.8
16
1.10%
0.80%
0.4
0.60%
14
0.40%
Cash In
NAV
Spread
12
0.70%
10
10
9
9.
5
8
8.
5
7
7.
5
6.
5
6
5.
5
5
4.
5
4
3.
5
3
2
2.
5
0.
5
1
0.00%
1.
5
0
0.6
0.6
Leverage
0.20%
Time (Years)
Stochastic Spread Example - Stressed Defaults
16
0.7
8
0.50%
14
0.6
0.4
0.4
6
12
0.30%
0.5
10
4
Cumulative Losses
Leverage
0.2
0.2
0.4
Cash
In
Cash In
8
0.3
NAV
NAV
Spread
Leverage
0.10%
2
6
0.2
00
Leverage
0.1
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10
9
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9.
5
8
8.
5
7.
5
7
6.
5
6
5.
5
5
4
4.
5
3
3.
5
2
2.
5
1.
5
1
0.
5
0
Time (Years)
5
9.
10
10
9
9.
5
5
8.
9
8
7.
5
7
Cumulative Losses
0
0
8
5
7.
8.
5
7
5
6.
6
5
Time (Years)
2
6
5
5.
6.
5
5
5
4.
5.
5
4
4.
5
3
2.
5
2
5
3.
4
3
5
2.
3.
5
2
5
1.
1.
5
1
1
5
0.
0.
5
0
0
17.
-0.10%
0
4
Spread of Assets
0.90%
0.2
0
NAV
NAV/ Cash
/ CashInInAmount
Amount
0.8
0.8
CPDO – Managed Trades
• The next generation of CPDOs is expected to be transactions that do not rely
on solely the CDX and iTraxx or therefore rolling every 6 months
• They can range from other indices (eg CDX XO, CDX EM, Credit Steepeners
etc) to completely bespoke portfolios
• Also the replenishment criteria can be different – eg roll every 12 months or
even remove a name the day it goes to a particular rating
• To model these portfolios there needs to be significant adjustment to the
modeling approach as the assumptions made will not be valid for different
portfolios
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CPDO - Managed Trades Transition Model
• To capture the much larger diversity in asset portfolios and roll mechanics the
modeling of asset ratings must be done using a transition model and not just a
default model
• Thus each asset in the portfolio is transitioned on a timely basis according to a
transition matrix
• If there are no substitutions in the portfolio the default rates at each point in
time are consistent with the standard CDO Evaluator
• This is a much more accurate measure of the MtM as this can now be
calculated on an individual basis as opposed to an index basis
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CPDO - Managed Trades Spread Model
Spread
Level
A
AA
Spread
Differential
Rating
Transition
AAA to AA
AAA
Spread
Differential
Same
Rating
5Yr
4.5Yr
4Yr
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t
Modelling Objectives for Commodities/FX
• Use of a simple/intuitive model across all asset classes
• A model based on statistical AND economic/market analysis
• Model calibration transparency
• Model compatibility with other asset classes
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Structure
Commodity Trigger Swap
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Model Specification: Commodities
Commodity Spot Prices:
dS
    ln S  dt   dW  dJ up  dJ down
S
Where
β:
speed of mean reversion
ξ:
level of mean reversion
σ:
volatility
W: Wiener process(random walk)
Jup/Jdown: uncorrelated up and down jumps adding fat tails to W
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Model Output
•
Typical example of a simulation process
•
Estimation of the default probability(PD) for a trigger swap (CTS,FXTS)
•
Mapping of PD to S&P credit rating for corporates
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Portfolio Analysis
•
STEP 1: Assign S&P rating to each individual PD according to the Default Tables of
CDO Evaluator for the specified maturity of the contract
Asset Description
PD
S&P
Rating
Aluminium struck at 40%
0.42%
A
Copper struck at 40%
2.46%
BBB-
Lead struck at 40%
14.40%
BB-
Nickel struck at 40%
9.08%
B
Tin struck at 40%
0.00%
AAA
Zinc struck at 40%
5.36%
B+
Gold struck at 40%
0.18%
AA
Silver struck at 40%
3.46%
BBB-
Platinum struck at 40%
1.30%
BBB+
Palladium struck at 40%
2.50%
BBB-
Brent struck at 40%
8.62%
BB
WTI struck at 40%
7.14%
BB
Gas Oil struck at 40%
7.50%
BB
Heating Oil struck at 40%
6.16%
BB+
Unleaded Petrol struck at
40%
7.34%
BB
5.52%
BB+
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Natural Gas struck at 40%
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Portfolio Analysis
•
STEP 2: Adjust the correlation table to reflect the correlation structure of the
commodity portfolio
–
Refinement of our methodology in Nov. 2006
–
The correlation structure is now based on the estimation of correlation on log-returns, using
appropriate methodologies
 More precise correlations between and among groups of commodities
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Portfolio Analysis
•
…And use CDO Evaluator with this adjusted correlation table
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Portfolio Analysis
• STEP 3: Run the portfolio with the following settings…
– Modified correlations assumptions,
– Modified default assumptions, in order to apply corporate default assumptions
– Standard number of simulations (500 000)
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Portfolio Analysis
• STEP 4: Obtain the loss distribution of the commodity portfolio and deduct the
appropriate level of subordination required to support the targeted CCO tranche
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Other New Products
• Non Credit
• FX Options
• Interest Rate Indices
• Interest Rate / Credit Mix
• Credit
• Operating Companies – CDPC/SIV
• LSS of ABS
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Conclusions
• A feature in the synthetic CDO market over the past couple of years has been
the development spread-based and option-based products in the rating space
• CPDO modelling depends on the following factors:
• Defaults/Recoveries/Asset Correlation
• Spread movements
• Interest Rates/FX risks
• Waterfall
• S&P’s CPDO Index model was released March 2007 and Beta 2 released in
April
• Next generation of CPDO is the managed CPDO which required a much more
refined approach to modelling rating transition and spread movements
• Rising interest in non credit asset or option-based classes – CCO, FX CDO
and IR Products
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Contact Information
For further information please contact:
Gloria Lu, CFA
Associate Director
gloria_lu@standardandpoors.com
Tel: (+852) 2533-3596
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