The Financial Soundness
of US Firms 1926-2013
Andrew Atkeson, Andrea Eisfeldt, and Pierre-Olivier Weill
Bank of Portugal, June 2015
Finance and the Real Economy
• 2008 Financial Crisis and Great Recession
New interest in old questions:
What is the role of financial frictions in business cycles?
Are recessions with financial crises different?
How can we measure the financial soundness of firms?
• Today: a contribution to measurement
Finance and the Real Economy
• We provide measurement, going ahead of the following theory:
Heterogeneous firms choose output, employment, investment
Financial frictions impact activity of financially unsound firms
⇒ Aggregate State = Cross-Section of Financial Soundness
• Measure financial soundness as Distance to Insolvency (DI)
Captures leverage adjusted for asset volatility
≈ Inverse of equity volatility
• DI, Financial Frictions, and Business Cycles:
Statistical view: low distance ⇒ likelihood of insolvency is high
Economic view: low distance ⇒ financial frictions are high
e.g. bankruptcy costs, debt overhang, risk shifting
What we find
• Three Big Recessions, Three Broad and Deep Insolvency Crises
1929-1933, 1937, 2008
Deep: Median firm in extreme distress
Broad: 95% of firms junk
Very different from other recessions
• Volatility vs. Leverage:
2008 contraction driven by an increase in asset volatility
Leverage did not play as big a role as previously emphasized
Majority contribution from idiosyncratic risk
What is New
Our contribution to measurement is:
• Extend back to 1926
• Utilize a broad cross section
• Decompose changes in finanancial soundness distribution into:
1 Component due to leverage
2 Component due overall volatility
a Contribution of aggregate volatility
b Contribution of idiosyncratic volatility
⇒ Stylized Facts to confront our quantitative models with.
Theory and Measurement
Distance to Insolvency
• Firm Balance Sheet: Assets and Liabilities
VAt : Expected DPV of cash flows from the firm’s assets
VBt : DPV of the promised cash flows on liabilities
• Insolvency = Assets worth less than Liabilities, VAt < VBt
• Distance to Insolvency:
VAt −VBt
VAt
1
σAt
The percentage drop in asset value that renders the firm insolvent,
measured in units of the firm’s asset standard deviation
60
0
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228
240
252
264
276
288
300
312
324
336
348
360
372
384
396
408
420
432
444
456
468
480
492
Value of Firm's
Assets and Debt
Leverage Adjusted for Asset Volatility
130
Value of Assets
Value of Liabilities
120
110
100
90
80
70
Time
𝑉𝐴𝐴 − 𝑉𝐵𝐵
𝑉𝐴𝐴
1
𝜎𝐴𝐴
Measurement
• Propose an approximate measure
Distance to Insolvency (DIt ) ≈
1
σEt
• Motivate with theory, calibrate and validate with data
• With unlimited liability, the approximation is exact:
Equity is a leveraged claim on assets: VEt = VAt − VBt
Instantaneous volatility of equity: σEt =
VAt
VEt
× σAt
Plug the first equation into the second one and take inverses:
1
=
σEt
VAt − VBt
VAt
1
σAt
Limited Liability: DI ≤
1
σE
≤ DD
If VE satisfies the basic properties of an option on the firm’s assets:
• VE ≥ max{0, VA − VB }
δ 2 VE
E
• δV
δVA ∈ [0, 1) and δVA2 > 0
• VE (VA∗ ) = 0 where VA∗ is the default boundary, then
Propositions 1 and 2:
VA − VB
VA
1
1
≤
=
σA
σE
DI ≤
VA − X
VA
1
σA
1
≤ DD
σE
≤
VA − VA?
VA
1
σA
Default point VA < VB
• VE convex in VA implies
DI ≤
1
σE ≤ DD
✓
◆
✓
◆
✓
◆
VA VB
1
1
VA X
1
VA VA ⇤
1

=

VA
VA
VA
A
E
A
A
Value of Equity
• Inverse of equity volatility is close to distance to insolvency if
creditors force insolvent firm into bankruptcy
VE
• Implies 1/ E is the distance to insolvency if creditors force an
insolvent firm into bankruptcy as soon as it is insolvent.VA - VB
V*A
σE =
dVE VA
σ . dVE
dVA VE A dVA
=
X
VE
,
VA −X
VB
X ∈ {VA∗ , VB }. σE =
VA
Value of Assets
VA
σ , 1
VA −X A σE
=
VA −X 1
.
VA
σA
DI ≈ 1/σEt
• Hereafter, use “DI” to denote σ1
E
• Why is our approximation useful?
Robust to model misspecification
Does not require any accounting data
Captures off-balance sheet leverage
Long time series available
assessing the approximation
Calibrating and Validating DI
Calibrating and Validating DI
• Calibration: What does level of DI mean in terms of credit rating?
• Validation: DI vs. Other measures of financial soundness.
Bond spreads
CDS Swap rates
Default Rates
• Is the relationship btw DI and financial soundness stable?
Calibrating DI
Using credit ratings :
• Above 4: Good and safe
• At 3: Cutoff between Investment Grade and Speculative Grade
• Below 2: Vulnerable
• Below 1: Highly vulnerable to bankruptcy or default
CCC
B+
S&P Rating
AA+
AA
AA-
A+
A
4
A-
BBB+
BBB
BBB-
3
BB+
BB
BB-
2
B
B-
CCC+
1
CCC-
CC
C-D
Median Distace to Insolvency
5
DIt by rating: all firms
4
3
2
1
0
DI and Bond Spreads (OAS)
• BoA-Merrill Lynch Corporate Bond OAS by 7 ratings, by month
• Monthly median DIt within same rating classes
• 1997-2012: Pooled data and pre Aug 2007 vs. post Aug 2007
Log DI and Log OAS
Pooled data by rating, Pre and Post 2007
Log Bond Spread DI = 1 DI = 2 DI = 3 Spread = 400bp Spread = 200bp Spread = 100bp Log Distance to Insolvency DI = 4 Further Validation: DI vs. Default Rates
Fraction of firms with DI<1
1
0.9
0.08
0.8
0.07
0.7
0.06
0.6
0.05
0.5
0.04
0.4
0.03
0.3
0.02
0.2
0.01
0.1
0
0
1926
1930
1934
1938
1942
1946
1950
1954
1958
1962
1966
1970
1974
1978
1982
1986
1990
1994
1998
2002
2006
2010
Moody's Bond Default Rate
0.09
Moody's Default Rate
Fraction of Firms with DI<1
0.1
Calibration of DI
• Above 4: Good and safe
• At 3: Cutoff between Investment Grade and Speculative Grade
• Below 2: Not Investment Grade
• Below 1: Highly vulnerable to bankruptcy or default
• Roughly Stable relationship over time
Distribution of Financial Soundness
Measurement: 1926-2012
• Measure DIt as 1/σEt monthly for each firm
• Calculate σEt = standard deviation of daily returns in month
Every NYSE, AMEX, and NASDAQ firm in CRSP
Every month, 1926 to 2012
• Construct cross-section distribution of DIt every month
Start with several hundred firms per month
End with several thousand
2012
2010
2008
2006
2004
2002
2000
1998
1996
perc10
1994
1992
1990
1988
perc25
1986
1984
1982
1980
perc50
1978
1976
1974
1972
perc75
1970
1968
1966
1964
perc90
1962
1960
1958
1956
perc95
1954
1952
1950
1948
1946
1944
1942
1940
1938
1936
1934
1932
1930
1928
1926
DI Percentiles 1926-2012
13
12
perc5
11
10
9
8
7
6
5
4
3
2
1
0
Summarizing the distribution of DIt = 1/σEt
• The cross section of DI is approximately log normal
• We can summarize it by two moments
• We will focus on two moments: median and 95th percentile
1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 J-­‐26 N-­‐29 S-­‐33 J-­‐37 M-­‐41 M-­‐45 J-­‐49 N-­‐52 S-­‐56 J-­‐60 M-­‐64 M-­‐68 J-­‐72 N-­‐75 S-­‐79 J-­‐83 M-­‐87 M-­‐91 J-­‐95 N-­‐98 S-­‐02 J-­‐06 M-­‐10 Diagnostic check for log normality
Financial soundness and recessions
Jan-10
Jan-06
Jan-02
Jan-98
Jan-94
Jan-90
Jan-86
Jan-82
Jan-78
Jan-74
Jan-70
Jan-66
Jan-62
Jan-58
Jan-54
Jan-50
Jan-46
Jan-42
Jan-38
Jan-34
Jan-30
Jan-26
DI (Log Scale)
Deep insolvency crises: median firm hits one
4
3
2
1
Jan-10
Jan-06
Jan-02
Jan-98
Jan-94
Jan-90
Jan-86
Jan-82
Jan-78
Jan-74
Jan-70
Jan-66
Jan-62
Jan-58
Jan-54
Jan-50
Jan-46
Jan-42
Jan-38
Jan-34
Jan-30
Jan-26
DI (Log Scale)
Broad insolvency crises: 95th pctl junk
4
3
2
1
Insolvency Crises & Recessions:
DI, Bond Spreads, Volatility
• Offer structural interpretation of credit spread and vol measures
Bond and CDS Spreads, volatility, Distance to Insolvency:
Linked through capital structure and valuation
⇒ All capture signals based on size of vol adjusted equity cushions
Jan-26
Jan-30
Jan-34
Jan-38
Jan-42
Jan-46
Jan-50
Jan-54
Jan-58
Jan-62
Jan-66
Jan-70
Jan-74
Jan-78
Jan-82
Jan-86
Jan-90
Jan-94
Jan-98
Jan-02
Jan-06
Jan-10
Bond Spread Percentage Points
Moody's Baa-Treasury Spread
GZ-spread
9
8
7
120
6
100
5
80
4
60
3
2
40
1
20
0
0
Median Equity Volatility Percentage Points
DI, volatility, and bond spreads
Median Equity Volatility
140
Leverage vs. Asset volatility
Aggregate vs. Idiosyncratic volatility
Decomposing Distance to Insolvency
• Decompose Distance to Insolvency into:
Leverage
Asset Volatility
• An advantage of our structural approach!
• Use unlimited liability benchmark:
1
Bt
log(DIt ) = log σ1Et = log VAtV−V
+
log
σAt
At
• Need to use equity and accounting data
COMPUSTAT data for value of liabilities VBt
Decomposition of log( σ1Et ): October 2008
perc95
perc90
perc75
perc50
perc25
perc10
perc05
10
9
Distance to Insolvency
8
7
6
Increase in Volatility
Holding Leverage Constant:
5
4
Acheives nearly entire
2008 DI contraction!
3
2
1
0
Oct-07
Oct-08
Oct-08 Alt:
07 Lvg & 08 Vol
Jan-­‐72 Jul-­‐73 Jan-­‐75 Jul-­‐76 Jan-­‐78 Jul-­‐79 Jan-­‐81 Jul-­‐82 Jan-­‐84 Jul-­‐85 Jan-­‐87 Jul-­‐88 Jan-­‐90 Jul-­‐91 Jan-­‐93 Jul-­‐94 Jan-­‐96 Jul-­‐97 Jan-­‐99 Jul-­‐00 Jan-­‐02 Jul-­‐03 Jan-­‐05 Jul-­‐06 Jan-­‐08 Jul-­‐09 Jan-­‐11 Jul-­‐12 Decomposition of log( σ1Et )
median log 1/sigmaE constant leverage median log 1/sigmaE 4 3 2 1 Decomposing Asset Volatility
• Common and idiosyncratic component of returns
• Firm i, month t, day k, CAPM within month:
ritk = αit + βit REW tk + itk
• Compare volatility of total returns to volatility of residuals
0.5
Jan-10
Jan-06
Jan-02
Jan-98
Jan-94
Jan-90
Jan-86
Jan-82
Jan-78
Jan-74
Median DI Total Volatility
Jan-70
Jan-66
Jan-62
Jan-58
Jan-54
Jan-50
Jan-46
Jan-42
Jan-38
Jan-34
Jan-30
Jan-26
2
Total and Idiosyncratic DI
Median DI Idiosyncratic volatility
1.5
1
0.5
0
Conclusions
• Insolvency Crises in three big recessions
Broad: 95% of firms junk
Deep: median firm well below junk cutoff
Not so for other recessions
• Asset volatility key driver, especially idiosyncratic volatility
⇒ Need structural models which match stylized facts above, and,
can asses how changes in the financial soundness of firms:
Can drive business cycles, and match firm behavior
in x-section of financial soundness in normal times
Black and Scholes option adjustment, 1997-2012
1/sigmaE vs option adjusted DI
10
8
6
4
2
0
−2
85
back to main slide
87
90
92
perc95
95
OA
97
00
perc50
02
OA
05
07
perc05
10
OA
12