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