Transcript Extending Factor Models of Equity Risk to Credit Risk and

Suspecting the Rating Agencies
Dan diBartolomeo
Northfield Information Services
January 2012
The Matter At Hand

One of the largest contributing factors to the Global Financial
Crisis of 2008-2009 was the huge number of fixed income
instruments with very high ratings (e.g. AAA) that were either
severely downgraded or went into actual default.
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All three of the major rating agencies, Moody’s, Standard and
Poor’s, and Fitch were shown to be seriously deficient in their
ratings of a variety of debt instruments, particularly complex
instruments (e.g. Credit Default Obligations or CDOs).
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The rating agencies failed again with the obligations of major
financial institutions such demonstrated by the spectacular
collapses of firms such as AIG, Bear Stearns and Lehman
Brothers.
Some Unpleasant Outcomes
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From the first quarter 2005 through
the third quarter of 2007, two thirds of
CDOs S&P had rated were
downgraded.
 44% of all CDOs were downgraded
to “speculative” or “in default”
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9.8% were downgraded to
“speculative” or “in default”
$250 Billion in major bank write offs
from January 1, 2007 through April
2008, another $1.3 Trillion estimated
from April 2008 to date
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Over the same time, 17% of sub-prime
residential mortgage securities were
downgraded
When Money Is At Stake, Cheat!
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S&P has admitted to “notching” ratings on many securitized
instruments
If an issuer wanted a rating done in a hurry, S&P would
simply assume a rating of one grade lower than whatever
S&P or Moody’s had most recently rated the debt of the
same issuer
To my mind, this is fraud
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The expectations of financial market participants is that rating
agencies actually conduct some form of credit analysis before
issuing a rating
At a cocktail party, a securitization lawyer for S&P rebuked me,
saying they had done nothing illegal, as there are no actual
requirements for any analysis
Beating the Agencies at their Own Game
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At previous QWAFAFEW events we have described an approach
to combine equity factor risk models and structural models of
credit risk to provide consistent measures of equity risk, default
risk and default correlation.
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The most important metric arising from this process is a “market
implied” expected life of a firm. We employ this as a quantitative
measure of the “sustainability” of firms
In this presentation we will show how the a simple model using
the expected life metric captured bankruptcy risk during the
Global Financial Crisis and was predictive of subsequent credit
rating changes and defaults
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We will also show that a related simple portfolio strategy would resulted
in significant alpha for US fixed income portfolios during the most
stressful portion of the GFC
Basic Contingent Claims Literature
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Merton (1974) poses the equity of a firm as a European call
option on the firm’s assets, with a strike price equal to the face
value of the firm’s debt
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Black and Cox (1976) provide a “first passage” model
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Alternatively, lenders are short a put on the firm assets
Default can occur only at debt maturity
Default can occur before debt maturity
Firm extinction is assumed if asset values hit a boundary value (i.e.
specified by bond covenants)
Leland (1994) and Leland and Toft (1996)
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Account for the tax deductibility of interest payments and costs of
bankruptcy
Estimate boundary value as where equity value is maximized subject to
bankruptcy
Reverse the Concept: Sustainability
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Instead of trying to estimate how likely it is that firm goes
bankrupt, let’s reverse the logic
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We will estimate the “market implied expected life” of firms
using contingent claims analysis
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Formally, our measure is the median of the expectation of the
distribution of the life of the firm
Makes different default probabilities for different bond issues very
natural as each maturity will lie at a different point in the survival time
distribution
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Firms with no debt can now be included since it is possible that
they get some debt in the future and default on that
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A quantitative measure of the fundamental and “social”
concept of sustainability
Our Basic Option Pricing Exercise
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Underlying is the firm’s assets with asset volatility determined
from the equity factor model
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Solve numerically for the “implied expiration date” of the option
that equates the option values to the stock price
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How volatile would a firm’s stock be if the firm had no debt?
This is the volatility of the assets
Market implied expected life of the firm
See Yaksick (1998) for numerical methods for evaluating a perpetual
American option
Include a term structure of interest rates so that as the implied
expiration date moves around, the interest rate changes
appropriately
Our Previously Published Research
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diBartolomeo, Journal of Investing, December 2010
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Used equity volatilities from Northfield US Fundamental Model
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One year horizon for risk forecast
Near horizon” model are more suitable but less history available
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Estimate monthly for all firms in Northfield US equity universe
from December 31, 1991 to March 31, 2010
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Study three samples:
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All
Financial firms
Non-financial firms
Sources of Time series variation
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Stock prices, debt levels, Northfield risk forecasts
Mix of large and small firms, 4660 <= N <= 8309
A Digression on “Too Big to Fail”
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For the full sample period of 1992 through March 31, 2010
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Non Financials:
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Financials:
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Median 14.74, Cap Weighted 18.42
Revenue Weight 17.60
Median 22.28, Cap Weighted 17.06
Revenue Weighted, 7.86
“Too Big to Fail” is really real
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Risk taking is heavily concentrated in the largest financial firms
Risk taking has been concentrated in the largest financial firms for
at least 20 years
Quantifying “Sustainability”
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MSCI KLD DSI 400 index of US large cap firms considered
socially responsible, 20 year history
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July 31, 1995
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DSI 400, Median 17, Average 17.91, Standard Deviation 9.93
S&P 500, Median 14, Average 15.40, Standard Deviation 9.28
Difference in Means is statistically significant at 95% level
March 31, 2010
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Typically about 200 firms in common with the S&P 500
DSI 400, Median 30, Average 26.39, Standard Deviation 11.45
S&P 500, Median 30, Average 24.93, Standard Deviation, 10.92
Difference in Means is statistically significant at 90% but not 95%
Testing on Disjoint Sets (DSI NOT S&P, S&P NOT DSI)
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Statistically significant difference in means for every time period tested
Results to “Sustainability” Equity Investing
(1992 through March 2010)
Table 11
Mean
Monthly
Annual
Leveraged
Compound
S&P Risk
Cumulative
Monthly
Return
Return
Standard
Deviation
Return
Equivalent
Return
Q5 Equal
1.33
713.77
9.15
10.90
7.45
Q1 Equal
1.03
790.86
3.64
11.50
12.83
Q5 Cap
0.77
251.60
6.62
4.98
4.76
Q1 Cap
0.79
414.32
3.78
7.77
8.26
S&P 5002
0.75
347.74
4.32
6.78
6.78
Combining Sustainability and MV (1992 through
March 2010, 200 Max Positions)
Mean
Monthly
Cumulative
Monthly
Standard
Deviation
Annual
Compound
Return
Annual
Sharpe
Ratio
Q1
MV
1.07
840.43
2.96
12.34
.81
Q5
MV
1.77
2901.15
6.80
19.33
.71
A Simple Start on Credit Ratings
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We combined rating levels from S&P, Moody’s and Fitch into a
unified letter scheme
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Each rating level was assigned a numerical value
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A rating of “AAA” was 10 on the numeric scale
A rating of “D” (default) was 1 on the scale
Intermediate levels of AA,A,BBB,BB,B,CCC,CC,C
A “+” added .333
A “-” subtracted .333
The scale is convenient but does not reflect any actual
differences in probability of default (PD) or economic “loss
given default” (LGD)
Numeric Rating Values Based on Spreads
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As part of our normal fixed income analysis we estimate
“option-adjusted spreads” for about 6 Million fixed income
instruments on a monthly basis
Measures the portion of bond yield not associated with time
value of money. This is premium for credit risk and illiquidity
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The median of the OAS values for set of the category members is used
Monthly history available to 2001
Bonds are broken into about 800 categories based on rating,
geographic region of issue and sector
Computational model assumes lognormal interest rates and combines
features from Fabozzi and Dattatreya (1989) and Black, Derman and
Toy (1990).
We can keep “AAA” ratings at 10, and “D” at 1 but rescale
intermediate levels inversely proportional to OAS
A Revised Numeric Scale From Spreads
60 Months Ending June 2011
Rating
Simple Numeric
OAS Spread BP
Spread Numeric
AAA
10
86
10
AA
9
89
9.96
A
8
107
9.73
BBB
7
149
9.20
BB
6
287
7.47
B
5
364
6.50
CCC
4
428
5.69
CC
3
455
5.35
C
2
494
4.86
D
1
801
1
Criminal Abuse of a Temp
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We wanted a really clean history of US bond rating changes
across all rating agencies
We sent a temp (a classmate of mine) to the Boston Public
Library to hand collect every rating change published in
Barrons from 1992 to 2008
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There are roughly 8500 events in the data set and we have
been able match about 6500 of those to entities with
publicly traded equity
The good news is that “Steve” was so good that he is now a
very valued member of our Boston tech support staff
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Information was hand entered into spreadsheets and then matched to
issuers, in a partly automated , partly manual way
It took roughly four months of tough full time effort
Criminal Abuse Of An Intern
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Our summer intern was then left to do an “event study” type
model of the rating changes for the subset of US corporate
bonds
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Dependent variable was the percentage change in the “simple”
numerical value of the credit rating
Independent variables:
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The big job is merging the “expected life” data derived from equities to
issue level bond data
It sounds easy but it is really a mess to track the related equity across
mergers, acquisitions and spin-offs
All data was standardized to make pooling across time easier
12 month percentage change in expected life as of prior month end
12 month change in the cross-sectional Z-score of expected life within
the US equity universe
“Ethan” survived too
A Modest But Encouraging Result
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We converted all data to rank values within the pooled sample
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In-sample our model had a correlation of about 40% (Rsquared = .16)
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Even with our simple model we could meaningfully predict
subsequent changes in bond ratings
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A very high degree of statistical significance on coefficients (T > 4)
R-squared was higher for subsets of lower grade bonds (i.e. NOT “A”)
These results are all conditional that a change in rating would eventually
take place since only such events existed in our data
Non-events (no rating change) were excluded from the sample by design
Perhaps our model would predict 14 of every 5 downgrades
Expanding Study to Full Data
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Universe is all US corporate bonds in the Northfield “Everything
Everywhere” model
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Study period from December 31, 2005 to June 30, 2011
Minimum maturity one year
Each bond is matched to contemporaneous expected life of
issuer
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Typical size around 18,000 bond issues
Assignments are updated annually for mergers, acquisitions
Return performance calculations exclude bonds with price
outliers at the start of the period
Things Go “Pear Shaped” In The GFC
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It should be intuitive that bonds with higher ratings should be
associated with issuers with longer expected lives
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At 12/31/2005, the correlation across categories was +.68
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Sample size of 17445 issues
At 12/31/2007 (pre bailouts), the correlation was -.35
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Break all bonds into 20 rating categories (including “+” and “-”)
Calculate average expected life for all bonds in each rating category
Correlate the average expected life and our simple numeric rating
Sample size of 22069 issues
By 12/31/2008, (post bailouts) the correlation was +.27
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Sample size of 20043 issues
A Simple Metric : Z Score of Expected Life Within
Rating Category
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At each year end starting at 2005 we convert the expected life
of issuer for each bond issue to a Z score within rating category
A negative Z score indicates that our metric suggests that the
firm is less creditworthy than the published rating
Sort universe of 22000 bond issues into quintiles by Z score
At 12/31/2006: Of the bottom quintile of 4400 bond issues,
2940 were from Wall Street firms that either went bankrupt,
were acquired or needed major government assistance
The rogues gallery included:
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Bear Stearns (534 issues), Merrill Lynch (868), Lehman Brothers (657),
Morgan Stanley (257), CIT Financial (338), Countrywide (136) and
Washington Mutual (24)
Nearly identical result for 12/31/2007
Z-score Within Rating
January 2006 Through June 2011
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US government intentions to mount the TARP bailout were announced on October 3,
2008 with most of the details filled in a couple weeks later.
At October 31, 2008, the cumulative Q1/Q5 return spread was more than 1200
basis points in less than three years on widely diverse portfolios (equal weight
across issues).
The cumulative return spread peaked in December 2008 and declined back to
almost exactly zero by June 2011.
The implicit and explicit guarantees by the US Treasury and Federal Reserve had
essentially driven the perceived creditworthiness of corporate bonds back to preGFC levels
14
Cumulative Q1/Q5 Return Spread
12
10
8
6
4
2
0
-2
-4
Other Agencies: The Lace Case
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Lace Financial is a small US rating agency specializing in
community banks, credit unions and insurance companies
Santoni and Arbia (2010) studied the effectiveness of the Lace
ratings on small US banks
116 small banks rated by Lace went under in 2009
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72% of the failed banks were rated “E” (lowest non-investment grade) at
least a year before actual failure
94% of the failed banks were rated “E” six months before the actual
failure
Clearly, the Lace ratings were effective but maybe it’s just an
issue of answering an easy question.
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Analyzing a small community bank may just be that much easier than a
complex, global entity like Citigroup or Lehman Brothers.
Let’s Start at the Beginning
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In the late 1990s, Moody’s began to provide credit ratings
of securitized corporate loans (CLO) based on a method
known as the Binomial Expansion Technique
Once a default probability had been estimated for loans in a
pool, the probabilities of potential multiple defaults within
the pool was based on simple binomial probability formulas
that assumed that defaults would be fully independent
across borrowers
To account for the obvious flaw that defaults are likely to be
correlated, Moody’s introduced an adjustment called
Diversity Scoring
In 1999, Northfield published a research paper criticizing
BET and Diversity Scoring based on a client request
Moody’s Diversity Scoring
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To account for default correlation, Diversity Scoring reduced
the assumed number of issues in a loan pool
For example, if you had 70 loans in a pool, you might count
that as 40 independent loans
Moody’s broke firms into 32 industries
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Implicitly there is an assumption that defaults are
correlated within industries, but never across industries
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2 credits in the same industry counted as 1.5
10 credits in the same industry counted as 4
Completely ignores potential for pervasive effects of recession, war
or other systemic influences
Although Moody’s largely abandoned BET in 2005, many
institutions such as AIG continued to use the method
“The Secret Formula That Destroyed Wall Street”
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Cover story in WIRED magazine, March 2009
Refers to the “Gaussian Copula” approach for estimating
default risk across a pool of loans, from Li (2000)
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Allows for closed form calculation of marginal risks as more and more
loans are added to the pool to be securities
Requires an assumption of the expected correlation of defaults
The problem is credit risky instruments have high skew in the
payoff distribution, so the joint distribution will be Gaussian
under the Central Limit Theorem only for very large numbers of
independent events
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Even a small degree of correlation calls the method into question
The Problem of Higher Order Dependence
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Imagine you want to allocate money to two hedge funds
based on traditional MPT
The two portfolio managers happen to have offices in the
same building and meet for coffee every morning
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If the coin is fair, the time series of their portfolio returns
will be zero
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During conversation, they flip a coin. If the coin comes up “heads”
they hold the identical portfolio for that day. If it comes up “tails”
they go long/short against each other
It varies daily from +1 to -1. averaging zero
Being independent implies zero correlation, but zero
correlation does not imply independence
We Go Blindly Forward with the Gaussian Copula
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Investment banks love the Gaussian copula because now you
can get joint default probabilities over any number of loans with
the estimation of a single number, the default correlation
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The rating agencies such as Moody’s and S&P go along and rate based
on this method
The problem is where to get the default correlation assumption,
since actual defaults were rare events, so statistical estimation
from historical data is questionable
Bankers used observable correlations from changes in spreads
in the credit default swap market
CDO/CDS Default Correlations
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Assessing default correlations from credit swap curves and
CDO trading was horrendously faulty
Once CDOs and CDO2 could be written on “generic ABS”
index results instead of specific pools, they were a form of
legalized gambling
The volumes in the CDO market were many times the
volume of actual underlying loans against which to hedge
credit risk, creating severe pricing distortions
The CDO/CDS markets were dominated by a few large
players such as AIG, further distorting economic pricing
relationships
Summary
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The global financial crisis has many contributing factors, but
the largest single contributor was the horrendous performance
of fixed income credit ratings from the major rating agencies
In some cases, the quality of ratings was severely upward
biased by business in considerations
In many cases the contributing factors were simply poor
quantitative analysis in which mathematical convenience was
allowed to take precedence over the conceptual rigor of the
models
The shortcomings in the analytical methods applied to the
RMBS, CDO and CDS markets were easily observed by those
who were relatively free of conflicts of interest