Credit Analysis of Corporate Credit Portfolios--A Cash Flow Based Conditional Independent
Default Approach
Hsien-hsing Liao
Tsung-kang Chen
Department of Finance
National Taiwan University
1
Agenda
Introduction
The Model
Application Example
Conclusion
2
PART. I
Introduction
3
Introduction-1
 Most existing studies on portfolio credit
analysis are reduced from models and
 few of them are able to endogenously estimate
the portfolio recovery (loss) rate.
4
Introduction-2
 As a structural form credit models,
 this study combines
• a cash flow based valuation approach and
• a conditional independent default approach,
such as the factor copula or the Fourier transform methods
 to endogenously estimate the multi-period
default probability and expected loss rate of a corporate credit portfolio.
 We also exemplify how the proposed approach is
applied to
credit tranching and pricing of a cash funded CBO
5
Introduction-3
 Structure form credit modelconsidering
 A firm’s asset value distribution and default boundary
 Two key issues
• Estimating asset value distribution
• Determining default boundary
Lt
PDt   f t (V )dV
L
t
1
RRt 
V ft (V )  dV

Lt (PDt ) 0
6
Introduction-4
 Most Merton type structural form models obtain
asset value distribution by converting
• A firm’s equity market value with
• An Option-based theory
• Because
A firm’s Equity can be seen as the value of a call option with the firm
asset value as the underlying asset and debt balance as the exercise
price
• Implying that stock returns are normally distributed
7
Introduction-5
 Issues of market value based model are:
•
literature has shown that stock return
distributions are
 asymmetric
 fat tailed
 volatility smiled
• Equity market is efficient to reflect true stock
value
8
Introduction-6
 Alternatively,
•
We use corporate free cash flow (to firm) to
estimate a firm’s asset value (distribution)
• Intrinsic valuation vs. market-based valuation
• Cash flow based valuation is a common practice
in firm valuation
9
Introduction-7
 Conforming to a common understanding that
the growth rates of most economic indicators
are weakly stationary, this study suggests
 a mean-reverting Gaussian process to model
the common state process
10
Characteristics of FCF (1)
Trend Analysis for JNJ FCF
Trend Analysis for JNJ MAFCF
Linear Trend Model
Yt = 1.94E-02 + 2.25E-04*t
Linear Trend Model
Yt = 1.90E-02 + 2.50E-04*t
0.05
Actual
Fits
Actual
Actual
Fits
Fits
JNJ MAFCF
JNJ FCF
0.04
Actual
0.035
Fits
0.03
0.02
0.025
0.01
0.00
0
10
20
30
MAPE:
MAD:
79.9577
0.0104
MSD:
0.0001
40
Time
Figure 1. JNJ’s Original FCF per unit asset
0.015
0
10
20
30
MAPE:
MAD:
9.58904
0.00232
MSD:
0.00001
40
Time
Figure 2.JNJ’s MA FCF per unit asset
11
Introduction-8
 This study employs
 a state-dependent (mean-reverting) free cash flow
process to generate each component firm’s
•
multi-period asset value distributions and therefore
•
its multi-period default probabilities and recovery rates
endogenously.
 Given a specific state (path), the asset value
distributions of the component firms are independent
(C.I.D.)
12
Introduction-9
 Cash flow model Simulation
Multi-period Value distribution
Multi-period corporate credit analysis
• Probability of default
• Expected Recovery Rate
Extendable to Credit Portfolio
13
Introduction-10
 Multi-period loss distributions of the credit
portfolio can then be obtained through
conditional default approaches such as
• the factor copula or
• the Fourier transform methods.
 The multi-period loss distribution is useful in
the portfolio credit tranching and the tranche
pricing
14
PART. II
The Model
15
Definition of Free Cash Flow
 H&L: only consider non-discretionary capital
expenditures (same as COMPUSTAT)
Ct  C  E
o
t
•
c
t
Ct denotes a firm’s FCFF;
• Cto denotes a firm’s operating cash flow;
c
• Et denotes non-discretionary capital expenditure.
16
Setting of Cash Flow Model
 A firm’s Ct is affected by
• A set of macro states (factors)
Ft
• An idiosyncratic (firm specific) effect
k
Cit  E(Cit )    ij Fjt  it
j 1
t
it ~ N(0, 1  h it )
hi indicates the variance explained by the systematic factors
17
Setting of State Model
 We employ a mean-reverting Gaussian
process to model each state process as
dFjt  aFj [bFj  Fj ,t 1 ]dt   Fj dz j
18
Valuation of a Firm
 Simulation of Free Cash Flow
Estimate the a,b,s of F(t) by MLE
Simulate Fjt ,  i and then combined with factor loading to get
the FCF
Present Value of each company
•
•
•
FCFt+1 FCFt+2 FCFt+3
FCFT

t
t+1
t+2
t+3
T
 T

CiT (1  g)
Ci
Vit   

 t 
T t
 t1 (1   A )  (1   A ) ( A  g)
19
Implied WACC Estimation (Quarterly)
 The asset market value is estimated by Merton’s
(1974). Given the estimated constant growth rate and
future cash flows, the implied weight average capital
of cost (WACC) is estimated by an optimization
technique. where,
•
The mathematical expression is to estimate the
makes the following equation exist:
1
Vt 
N
•
 A that
N
V
i 1
it
Vt represents the current market value of the firm’s asset.
20
Calculation of PD, LGD
Firm value distribution under a given state path
Default
Vit
Default threshold (KMV)
=current liability + ½ long-term debt
PD: Probability of default
Simulate 100 paths of firm specific factor
i
under given state path
Get the number of defaults and divided by simulated firm paths (100)
LGD: Loss given default
Once default, account the loss=
( KMV-PVi )/ KMV if PV>0
KMV
if PV<=0
LGD= ( Total loss )/ ( number of default)
21
Simulation Framework
Vt
Vt+1
PDi LGDi
economic state 1
…………
For each
company
Simulate
10000
economic
states
Vt
Vt+1
PDi LGDi
economic state 10000
Time Axis
For each
company
( Multiple Periods )
Asset size, PDi, LGDi
FTM
22
PART. III
Application Examples
23
Data
The sample firms are U.S. firms.
Criteria of selecting sample firms:
•
•
•
Select non-financing firms with outstanding corporate
bonds which will mature within 10 years.
Exclude firms that have missing financial data.
For simplicity, we select 15 of 30 available firms to
construct our sample portfolio underlying CBO.
We set our pricing time at 2004/12/31
The data period is from 1995 Q1 to 2004 Q4.
24
Table 1. The industry information of empirical sample
Firm
Industry
Rating (2004/12/31)
1.Johnson & Johnson
Drug Manufacturers
AAA
2.ALCOA INC
Basic Material - Aluminum
A-
3.International Business Machines Corp.
Diversified Computer Systems
A+
4.BellSouth Corp.
Telecom Service
A
5.Coca-Cola Co.
Beverages
A+
6.McDonald's Corp.
Restaurants Service
A
7.Emerson Electric Co.
Industrial Electrical Equipment
A
8.Kellogg Co.
Food - Major Diversified
BBB+
9.International Paper Co.
Paper & Paper Products
BBB
10.Black & Decker Corp.
Small Tools & Accessories
BBB
11.Safeway Inc.
Grocery Stores
BBB
12.Clear Channel Communications Inc.
Broadcasting - Radio
BBB-
13.Masco Corp.
Industrial Equipment & Components
BBB+
14.Merck & Co. Inc.
Drug Manufacturers
AA-
15.AT&T
Telecom Service
BB
25
Macro State Factor Extraction
We use factor analysis to extract state factors.
Input data:
15 firm’s moving-average free cash flows per year
per unit asset form 1995 Q1 to 2004 Q4.
Database: COMPUSTAT
Results:
we determine 4 state factors that can explain about
81.94% of firm’s cash flow variation.
26
Parameters Estimation of the State Model
 We use maximum likelihood estimation (MLE) method
to estimate parameters of stochastic state model.
 Input data:
the time-series state factor values estimated previously.
Table 2. Parameters estimation of stochastic state model
aF
bF
F
Factor 1
0.1364
0.0856
0.4714
Factor 2
0.0968
0.2139
0.3940
Factor 3
0.1644
0.2695
0.5578
Factor 4
0.1889
0.0621
0.5570
27
Credit Analysis Results of the Model
Model PD(%)
Model Rating
Actual
Rating(Issuer)
AA*
6.38
BBB~A
A-
BDK*
8.23
BB~BBB
BBB
BLS**
12.74
BB~BBB
A
CCU*
4.58
BBB~A
BBB-
EMR***
0.00
AAA
A
IBM*
1.71
A~AA
A+
IP*
20.27
BB~BBB
BBB
JNJ*
0.00
AAA
AAA
K*
5.93
BB~BBB
BBB+
KO***
0.01
AAA
A+
MAS*
8.19
BB~BBB
BBB+
MCD*
2.97
BBB~A
A
MRK*
0.74
AA~AAA
AA-
SWY*
3.66
BBB~A
BBB
T*
38.16
B~BB
BB
Ticker
*: within the range of model's rating; **: above the range of model's rating; ***: below the range of model's
rating
28
Multi-period Portfolio Distribution (FTM)
29
The tranching results of the example CBO
by the Fourier transform method
•
•
•
The sustainable loss rate of each tranche is calculated by multiplying the expected loss rate by
its tranche weight.
We can obtain the tranche weights of Baa2 and equity tranches by considering following two
constraints. The first constraint is the sum of the sustainable loss rate of all tranches must be
equal to the expected loss rate of the CBO, 1.95%, which is estimated by the Fourier transform
method. The second constraint is that tranche weights must sum to 1.
The tranche weights of the Baa2 and the equity tranches are 23.37% and 1.63%. The expected
loss rate of each credit rating is obtained from Moody's idealized expected loss table.
Tranches
A
B
C
Equity
Rating
Aaa
A2
Baa2
N.A.
Tranche weight
50%
25%
23.37%
1.63%
Expected Loss Rate
0.0022%
0.3207%
1.0835%
100%
Sustainable Loss (%)
0.0011%
0.0802%
0.2532%
1.6300%
Total
100%
1.95%
30
Application Examples (3.2)
Figure 7. INTC’s Multi-period FCF distr.
Figure 8. INTC’s Multi-period PV distr.
31
PART. IV
Limitations---A final Remark
32
Limitations---A Final remark
 Fixed debt boundarystochastic debt ratio
 Stochastic Interest rate
 Find alternative construct on the state process
and the corporate free cash flow process
Thanks for your attention~
33