Vintage and Credit RatingWhat matters in the ABX data during the credit crunch?

Mardi DungeyGerald P. DwyerThomas Flavin

Purpose of Paper

• Vintage, credit rating and liquidity parts of prices of collateralized debt obligations (CDOs)

• Using Markit indices of prices– CDOs based on subprime mortgages– New indices in January 2006, July 2006,

January 2007 and June 2007

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

0

20

40

60

80

100

06-1 vintage

Abx Prices by Vintage

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

0

20

40

60

80

100

06-2 vintage

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

0

20

40

60

80

100

AAAAAABBBBBBm

07-1 vintage

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

0

20

40

60

80

100

07-2 vintage

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

020406080

100

AA

A

06-1 Vintage06-2 Vintage07-1 Vintage07-2 Vintage

AAA

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

020406080

100

AA

Abx Prices by Rating

AA

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

020406080

100

A

A

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

020406080

100

BB

B

BBB

1/1/2006 1/1/2007 1/1/2008 1/1/2009Date

020406080

100

BB

Bm

BBB-

Correlations of Changes in Log Indices

AAA06-1 A06-1 BBB06-1 AAA07-2 A07-2 BBB07-2

AAA06-1 1 0.745 0.556 0.777 0.429 0.336A06-1 0.745 1 0.715 0.679 0.587 0.456BBB06-1 0.556 0.715 1 0.485 0.606 0.493AAA07-2 0.777 0.679 0.485 1 0.505 0.355A07-2 0.429 0.587 0.606 0.505 1 0.485BBB07-2 0.336 0.456 0.493 0.355 0.485 1

1/1/2007

-0.2

-0.1

0.0

0.1

Cha

nge

in lo

garit

hm

Your text

AAA 06-1

1/1/2007

-0.2

-0.1

0.0

0.1

ABX indices 2006Changes in logarithms through December 5, 2008

A 06-1

1/1/2007

-0.2

-0.1

0.0

0.1 BBB 06-1

1/1/2007

-0.2

-0.1

0.0

0.1

Cha

nge

in lo

garit

hm

AAA 06-1

1/1/2007

-0.2

-0.1

0.0

0.1 A 06-2

1/1/2007

-0.2

-0.1

0.0

0.1 BBB 06-2

1/1/2007

-0.2

-0.1

0.0

0.1

Cha

nge

in lo

garit

hm

AAA 07-1

1/1/2007

-0.2

-0.1

0.0

0.1 A 07-1

ABX Indices 2007Changes in logarithms through December 5, 2008

1/1/2007

-0.2

-0.1

0.0

0.1BBB 07-1

1/1/2007Date

-0.2

-0.1

0.0

0.1

Cha

nge

in lo

garit

hm

AAA 07-2

1/1/2007

-0.2

-0.1

0.0

0.1 A 07-2

1/1/2007

-0.2

-0.1

0.0

0.1BBB 07-2

Factor Model

– where vintage i=06-1, 07-1, 07-2– rating j=AAA, A, BBB– t is time– yi,j,t is the change in the logarithm of the ABX series of vintage i with

rating j at time t– fwt is the “world factor” at time t– vi,t is the vintage factor for vintage i at time t– kj,t is the ratings factor for rating j at time t– fi,j,t is the idiosyncratic factor for vintage i with rating j at time t– liqt is a separately estimated factor at time t

“Liquidity” Factor

• liqt is an idiosyncratic factor estimated from CDS premia over 3-month Treasury bills

– where xi.t is the “excess return” on asset i at time t over 3-month Treasury bills

– i includes CDSs, AAA corporate bonds and A corporate bonds

– wt is a common factor

– fi.t is an idiosyncratic factor

Actual Liquidity Factor

• We find that wt is proportional to xA,t essentially, so we can write this

Estimation

• Estimate GARCH(1,1) models for the changes in log price series before estimation

• Include dummy variables that deal with the non-synchronous starts of series

• Estimate by Kalman filter• Data through May 30, 2008

Liquidity Factor

0

2

4

6

8

10

12

14

Jan-06 Jun-06 Nov-06 Apr-07

AAA: vintage 1w orld factor

-3-2.5

-2-1.5

-1-0.5

00.5

11.5

1 101 201 301 401 501

AAA: vintage 1vintage factor

-6

-4

-2

0

2

4

6

1 101 201 301 401 501

AAA: vintage 1ratings factor

-4

-2

0

2

4

6

1 101 201 301 401 501

AAA: vintage 1liquidity factor

-4-3-2-101234

1 101 201 301 401 501

A: vintage 1w orld factor

-2

-1.5

-1

-0.5

0

0.5

1

1 101 201 301 401 501

BBB: vintage 1w orld factor

-3

-2

-1

0

1

2

1 101 201 301 401 501

A: vintage 1vintage factor

-3

-2

-1

0

1

2

1 101 201 301 401 501

BBB: vintage 1vintage factor

-6

-4

-2

0

2

4

6

1 101 201 301 401 501

A: vintage 1ratings factor

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1 101 201 301 401 501

BBB: vintage 1ratings factor

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1 101 201 301 401 501

A: vintage 1liquidity factor

02468

10121416

1 101 201 301 401 501

BBB: vintage 1liquidity factor

0

0.5

1

1.5

2

2.5

3

1 101 201 301 401 501

Factor Contributions to 06-1 Indices

Common

Vintage

Rating

Liquidity

Factor Contributions to 07-1 IndicesAAA: vintage 2

w orld factor

-6-5-4-3-2-10123

1 101 201 301 401 501

AAA: vintage 2vintage factor

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5

1 101 201 301 401 501

A: vintage 2vintage factor

-1.5

-1

-0.5

0

0.5

1

1 101 201 301 401 501

AAA: vintage 2ratings factor

-1.00E-09-5.00E-100.00E+005.00E-101.00E-091.50E-092.00E-092.50E-093.00E-093.50E-09

1 101 201 301 401 501

A: vintage 2ratings factor

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

1 101 201 301 401 501

BBB: vintage 2ratings factor

-5-4-3-2-101234

1 101 201 301 401 501

AAA: vintage 2liquidity factor

0

0.1

0.2

0.3

0.4

0.5

1 101 201 301 401 501

A: vintage 2liquidity factor

00.20.40.60.8

11.21.41.6

1 101 201 301 401 501

BBB: vintage 2liquidity factor

0

1

2

3

4

5

6

1 101 201 301 401 501

A: vintage 2w orld factor

-4

-3

-2

-1

0

1

2

1 101 201 301 401 501

BBB: vintage 2vintage factor

-2-1.5

-1-0.5

00.5

11.5

2

1 101 201 301 401 501

BBB: vintage 2w orld factor

-5-4-3-2-10123

1 101 201 301 401 501

Common

Vintage

Rating

Liquidity

Factor Contributions to 07-2 IndicesAAA: vintage 3

w orld factor

-2

-1.5

-1

-0.5

0

0.5

1

1 101 201 301 401 501

A: vintage 3w orld factor

-2.5-2

-1.5-1

-0.50

0.51

1.5

1 101 201 301 401 501

BBB: vintage 3w orld factor

-2

-1.5

-1

-0.5

0

0.5

1

1 101 201 301 401 501

AAA: vintage 3vintage factor

-0.000000050

0.000000050.0000001

0.000000150.0000002

0.000000250.0000003

0.00000035

1 101 201 301 401 501

A: vintage 3vintage factor

-0.00000010

0.00000010.00000020.00000030.00000040.00000050.00000060.0000007

1 101 201 301 401 501

BBB: vintage 3vintage factor

-0.0000000050

0.0000000050.00000001

0.0000000150.00000002

0.0000000250.00000003

0.0000000350.00000004

1 101 201 301 401 501

AAA: vintage 3ratings factor

-1.40E-09-1.20E-09-1.00E-09-8.00E-10-6.00E-10-4.00E-10-2.00E-100.00E+002.00E-104.00E-10

1 101 201 301 401 501

A: vintage 3ratings factor

-0.05-0.04-0.03-0.02-0.01

00.010.020.030.04

1 101 201 301 401 501

BBB: vintage 3ratings factor

-1.5

-1

-0.5

0

0.5

1

1 101 201 301 401 501

AAA: vintage 3liquidity factor

0123456789

1 101 201 301 401 501

A: vintage 3liquidity factor

012345678

1 101 201 301 401 501

BBB: vintage 3liquidity factor

0

2

4

6

8

10

1 101 201 301 401 501

Common

Vintage

Rating

Liquidity

Conclusion

• Work in Progress• We think we’ve made some progress in

identifying a factor indicating liquidity and counterparty risk

• We interpret the estimation as being promising for estimating factors’ importance for CDO prices