Search My Blog
 About Donald

Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura. Read More

 Now Available

An Introduction to Derivative Securities, Financial Markets, and Risk ManagementAdvanced Financial Risk Management, 2nd ed.

 Contact Us
Kamakura Corporation
2222 Kalakaua Avenue

Suite 1400
Honolulu HI 96815

Phone: 808.791.9888
Fax: 808.791.9898

Americas, Canada
James McKeon
Director of USA Business Solutions
Phone: 215.932.0312

Andrew Zippan
Director, North America (Canada)
Phone: 647.405.0895
Asia, Pacific
Clement Ooi
President, Asia Pacific Operations
Phone: +65.6818.6336

Australia, New Zealand
Andrew Cowton
Managing Director
Phone: +61.3.9563.6082

Europe, Middle East, Africa
Jim Moloney
Managing Director, EMEA
Phone: +

Tokyo, Japan
3-6-7 Kita-Aoyama, Level 11
Minato-ku, Tokyo, 107-0061 Japan
Toshio Murate
Phone: +03.5778.7807

Visit Us
Linked In Twitter Seeking Alpha

Careers at Kamakura
Technical Business Consultant – ASPAC
Asia Pacific Region
Business Consultant – ASPAC
Asia Pacific Region


Kamakura Risk Manager Data Expert
Europe, North America, Asia & Australia 



Kamakura Blog

Aug 21

Written by: Donald van Deventer
8/21/2013 11:20 PM 

We first analyzed default risk at Bank of America Corporation (BAC) on July 8, 2013. On that day, the one year default probability for the firm was 0.18% and the ten year annualized default probability was 0.49%. We also did an extensive analysis of the credit crisis history of consolidated Bank of America borrowings (including borrowings of Countrywide Financial and Merrill Lynch) from the Federal Reserve and the events leading up to those borrowings on May 25, 2011.

Bank of America consolidated borrowings during the credit crisis peaked at $48.1 billion, nearly double the amount of money that Lehman Brothers requested but did not get from the Federal Reserve prior to its bankruptcy filing on September 14, 2008. Today’s study incorporates Bank of America bond price data as of August 20, 2013 to analyze the potential risk and return to bondholders of  Bank of America Corporation, which recently completed a tender for $6.2 billion in various notes due in 2014.

Institutional investors around the world are required to prove to their audit committees, senior management, and regulators that their investments are in fact “investment grade.” Interest rate risk managers at major firms like Bank of America Corporation use the marginal cost of funds reflected in the bond market to centralize interest rate risk and to measure internal profitability based on this “transfer pricing yield curve.” For many investors, “investment grade” is an internal definition; for many banks and insurance companies “investment grade” is also defined by regulators. In this note we analyze the updated current levels and past history of default probabilities for Bank of America Corporation. We also measure the reward, in terms of credit spread, for taking on the default risk of Bank of America Corporation bonds. On August 20, Bank of America Corporation non-call fixed rate bonds were traded 1,002 times for $266.6 million in volume.  After eliminating outliers, we used 730 trades on 88 Bank of America Corporation bonds with a trade volume of $243 million in this study.  There were also 24 trades in the bonds non-call fixed rate bonds of Bank of America NA, the bank subsidiary, on August 20 but we leave analysis of the bonds of the bank itself for another day and focus on the bonds of the holding company.
Assuming the recovery rate in the event of default would be the same on all bond issues, a sophisticated investor who has moved beyond legacy ratings seeks to maximize revenue per basis point of default risk from each incremental investment, subject to risk limits on macro-factor exposure on a fully default-adjusted basis. We analyze the maturities where the credit spread/default probability ratio is highest for Bank of America Corporation. We also consider whether or not a reasonable U.S. bank investor would judge the firm to be “investment grade” under the June 13, 2012 rules mandated by the Dodd-Frank Act of 2010, which requires that credit rating references be eliminated.  The new rules delete references to legacy credit ratings and replace them with default probabilities as explained here.
Term Structure of Default Probabilities
Maximizing the ratio of credit spread to matched maturity default probabilities requires that default probabilities be available at a wide range of maturities. The graph below shows the current default probabilities for Bank of America Corporation ranging from one month to 10 years on an annualized basis.  The default probabilities range from 0.16% at one month to 0.08% at 1 year (down 0.10% from our July report) and 0.44% at ten years (down 0.05% from July).

We explain the source and methodology for the default probabilities below.
Summary of Recent Bond Trading Activity
The National Association of Securities Dealers launched the TRACE (Trade Reporting and Compliance Engine) in July 2002 in order to increase price transparency in the U.S. corporate debt market. The system captures information on secondary market transactions in publicly traded securities (investment grade, high yield and convertible corporate debt) representing all over-the-counter market activity in these bonds. TRACE data for Bank of America Corporation included 1,002 trades with principal amount of $266.6 million in the fixed-rate non-callable bonds of the firm on August 20, 2013. We used the 730 trades on 88 of the bonds with principal amount of $243.3 million after eliminating the most obvious outliers and observations with incomplete details among the data from TRACE.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Bank of America Corporation bonds. These curves reflect the noise in the TRACE data, as some of the trades are small odd-lot trades. The lowest curve, in dark blue, is the yield to maturity on U.S. Treasury bonds, interpolated from the Federal Reserve H15 statistical release for that day, which matches the maturity of the traded bonds of Bank of America Corporation. The second lowest curve, in the lighter blue, shows the yields that would prevail if investors shared the default probability views outlined above, assumed that recovery in the event of default would be zero, and demanded no liquidity premium above and beyond the default-adjusted risk-free yield.  The third line from the bottom (in orange) graphs the lowest yield reported by TRACE on that day on Bank of America Corporation bonds. The fourth line from the bottom (in green) displays the average yield reported by TRACE on the same day.  The highest yield is obviously the maximum yield in each Bank of America Corporation issue recorded by TRACE.

The data makes it clear that there is a sizable liquidity premium built into the yields of Bank of America Corporation above and beyond the “default-adjusted risk free curve” (the risk-free yield curve plus the matched maturity default probabilities for the firm).  The credit spreads are relatively erratic for maturities under 7 years. The credit spreads generally widen with maturity, the normal pattern for a high quality credit, with the exception of the two longest maturity bonds.

The high, low and average credit spreads at each maturity are graphed below.  Credit spreads are gradually increasing with the maturity of the bonds, with the exception of the longest maturities. We have done nothing to smooth the data reported by TRACE, which includes both large lot and small lot bond trades.

Using default probabilities in addition to credit spreads, we can analyze the number of basis points of credit spread per basis point of default risk at each maturity.  This ratio of spread to default probability is shown in the following table for Bank of America Corporation.  At almost all maturities under 4 years, the reward from holding the bonds of Bank of America Corporation, relative to the matched maturity default probability, is more than 10 basis points of credit spread reward for every basis point of default risk. The ratio of spread to default probability decreases with maturity once the maturity of the bonds exceeds 4 years, falling to a spread to default ratio between 4 and 8 times.

The credit spread to default probability ratios are shown in graphic form here.  For the reader’s convenience, we fitted a cubic polynomial that explains the average spread to default probability ratio as a function of years to maturity.  This polynomial explains 52% of the variation in the average credit spread to default probability ratio:

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended August 16, 2013 (the most recent week for which data is available), the credit default swap trading volume on Bank of America Corporation was 13 trades with $67.7 million of notional principal, a small fraction of the daily bond trading volume on August 20. The number of credit default swap contracts traded on Bank of America Corporation in the 155 weeks ended June 28, 2013 is summarized in the following table:

Bank of America ranked 12th among all reference names in weekly credit default swap trading volume during this period, which is graphed below:

On a cumulative basis, the default probabilities for Bank of America Corporation range from 0.08% at 1 year to 4.30% at 10 years, as shown in the following graph.

Over the last decade, the 1 year and 5 year default probabilities for Bank of America Corporation have varied as shown in the following graph. The one year default probability peaked at just under 20% in the first half of 2009 as Bank of America was absorbing Countrywide Financial and Merrill Lynch. The 5 year default probability (annualized) peaked at just over 5%.

The legacy credit ratings [those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO)] for Bank of America Corporation have changed six times during the decade.
The macro-economic factors driving the historical movements in the default probabilities of Bank of America Corporation include the following factors among those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

  • Unemployment rate

  • 3 month U.S. Treasury bill rates

  • 10 Year U.S. Treasury yield

  • BBB rated corporate bond yield

  • Dow Jones Industrials stock index

  • The VIX volatility index

  • Home price index

  • 6 international macro factors

These macro factors explain 89.4% of the variation in the default probability of Bank of America Corporation.
Bank of America Corporation can be compared with its peers in the same industry sector, as defined by Morgan Stanley (MS) and reported by Compustat.  For the USA “diversified financials” sector, Bank of America Corporation has the following percentile ranking for its default probabilities among its 218 peers at these maturities:

1 month 84th percentile
1 year 78th percentile
3 years 74th percentile
5 years 62nd percentile
10 years 63rd percentile

Even after the significant capital injections into Bank of America Corporation by the U.S. government and documented by the Inspector General of the Troubled Asset Relief Program on October 5, 2009, the percentile rankings of its default probabilities range from the 62nd to the 84th percentile of U.S. diversified financial firms.  A comparison of the legacy credit rating for Bank of America Corporation with predicted ratings indicates that the statistically predicted rating is two notches lower than the actual credit rating.  Both the actual and predicted rating are “investment grade” by traditional credit rating standards of Moody’s Investors Service and the Standard & Poor’s affiliate of McGraw-Hill.
Bank of America Corporation ranks in the bottom half of the diversified financial services sector from a credit risk perspective. The $45 billion of capital injected into Bank of America Corporation (initially a portion was invested via Merrill Lynch) is concrete evidence of two things: the firm was considered “too big to fail” and the firm was going to fail (see the title of the Inspector General’s report above) without such support. We believe that most analysts would predict that the U.S. government would again rescue the bank if necessary.  The Kamakura default probabilities used above do NOT make this assumption.  The probability of rescue is ignored; the Kamakura default probabilities are the probability of failure. We believe most analysts feel the probability of rescue is embedded in the current legacy ratings for Bank of America Corporation.  The statistically predicted rating does not include this probability, which is why the statistically predicted rating is two notches lower.   The default probabilities for Bank of America are much improved, but they still are far above the median for the diversified financials sector.
The bonds of Bank of America Corporation provide a fairly typical ratio of credit spread to default probability, with the short maturity reward for bearing credit risk significantly higher than the long term reward (the spread to default probability ratio).  We believe a majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade.  Bond investors who are optimistic that Bank of America Corporation’s troubles are behind it will receive the most credit spread per basis point of default risk at maturities of 4 years or less.


Background on Default Probabilities Used

The Kamakura Risk Information Services version 5.0 Jarrow-Chava reduced form default probability model makes default predictions using a sophisticated combination of financial ratios, stock price history, and macro-economic factors. The version 5.0 model was estimated over the period from 1990 to 2008, and includes the insights of the worst part of the recent credit crisis. Kamakura default probabilities are based on 1.76 million observations and more than 2000 defaults. The term structure of default is constructed by using a related series of econometric relationships estimated on this data base. An overview of the full suite of related default probability models is available here.

General Background on Reduced Form Models

For a general introduction to reduced form credit models, Hilscher, Jarrow and van Deventer (2008) is a good place to begin. Hilscher and Wilson (2013) have shown that reduced form default probabilities are more accurate than legacy credit ratings by a substantial amount. Van Deventer (2012) explains the benefits and the process for replacing legacy credit ratings with reduced form default probabilities in the credit risk management process. The theoretical basis for reduced form credit models was established by Jarrow and Turnbull (1995) and extended by Jarrow (2001). Shumway (2001) was one of the first researchers to employ logistic regression to estimate reduced form default probabilities. Chava and Jarrow (2004) applied logistic regression to a monthly database of public firms. Campbell, Hilscher and Szilagyi (2008) demonstrated that the reduced form approach to default modeling was substantially more accurate than the Merton model of risky debt. Bharath and Shumway (2008), working completely independently, reached the same conclusions. A follow-on paper by Campbell, Hilscher and Szilagyi (2011) confirmed their earlier conclusions in a paper that was awarded the Markowitz Prize for best paper in the Journal of Investment Management by a judging panel that included Prof. Robert Merton.