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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

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Kamakura Blog

Jul 25

Written by: Donald van Deventer
7/25/2013 12:55 AM 

In this note we analyze the default probabilities for United States Steel Corporation (X), and compare those to credit spreads on 189 bond trades in 6 different company bond issues on July 24, 2013.  US Steel has the highest default probabilities of any firm analyzed in this series of credit notes to date. Trading volume in US Steel bonds on July 24 totaled $33.74 million. Assuming the same recovery rate in the event of default 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 US Steel, and consider whether a reasonable investor would judge the firm to be “investment grade” under the June 2012 rules mandated by the Dodd-Frank Act of 2010.

Definition of Investment Grade

On June 13, 2012, the Office of the Comptroller of the Currency published the final rules defining whether a security is “investment grade,” in accordance with Section 939A of the Dodd-Frank Act of 2010.  The new rules delete reference 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 United States Steel Corporation. ranging from one month to 10 years on an annualized basis.  The default probabilities range from 0.19% at one month to 0.41% at 1 year and 1.30% at ten years.

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 United States Steel Corporation included 189 trades in six bonds of the firm on July 24, 2013.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of United States Steel Corporation bonds.  The lowest curve, in dark blue, is the yield to maturity on the benchmark U.S. Treasury bonds most similar in maturity to the traded bonds of United States Steel 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 United States Steel 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 United States Steel Corporation issue recorded by TRACE.

The data makes it very clear that there is a very large and fairly stable liquidity premium built into the yields of United States Steel 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 high, low and average credit spreads at each maturity are graphed below.  Credit spreads are gradually increasing with the maturity of the bonds, with only a small variation around this trend.

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 United States Steel Corporation.  At all maturities, the reward from holding the bonds of United States Steel Corporation, relative to the matched maturity default probability, is at least 3.38 basis points of credit spread reward for every basis point of default risk incurred. The ratio of spread to default probability generally declines as the maturity of the bonds lengthens.

The next graph plots the ratio of credit spread to default probability at each maturity.

For United States Steel Corporation, the spread/default probability ratios are highest for maturities under five years. The reward for bearing a basis point of default risk declines from levels of about 5 times to ratios generally in the 3 to 4 times default risk range.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended July 19, 2013 (the most recent week for which data is available), the credit default swap trading volume on United States Steel Corporation showed 32 contracts trading with a notional principal of $96.5 million. The next graph shows the weekly number of credit default swaps traded on United States Steel Corporation in the 155 weeks ended June 28, 2013.

The table below summarizes the volatile nature of credit default swap trading in United States Steel Corporation. during this three year period.

On a cumulative basis, the default probabilities for United States Steel Corporation range from 0.41% at 1 year to 12.29% at 10 years, as shown in the following graph.

Over the last 10 years, the 1 year and 5 year default probabilities for United States Steel Corporation have varied as shown in the following graph. The one year default probability peaked at just over 1.40% and the 5 year default probability, currently at 0.88% on an annualized basis, is at its highest level of the last decade.

Over the same decade, the legacy credit ratings (those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO)) for United States Steel Corporation have changed four times.

The macro-economic factors driving the historical movements in the default probabilities of United States Steel Corporation over the period from 1990 to the present include the following factors of those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

  • Real disposable income growth

  • 10 year U.S. Treasury yield

  • The VIX volatility index

  • Home prices

  • 4 international macro factors

These macro factors explain 86.7% of the variation in the default probability of United States Steel Corporation since 1990.

United States Steel Corporation can be compared with its peers in the same industry sector, as defined by Morgan Stanley and reported by Compustat.  For the USA materials sector, United States Steel Corporation has the following percentile ranking for its default probabilities among its peers at these maturities:

1 month 62nd percentile
1 year 65th percentile
3 years 65th percentile
5 years 55th percentile
10 years 56th percentile

United States Steel Corporation is in the bottom half of creditworthiness among its peers for all maturities.  A comparison of the legacy credit rating for United States Steel Corporation with predicted ratings indicates that the statistically predicted rating is 3 ratings notches above the actual legacy rating assigned to the company.


United States Steel Corporation has experienced fairly minimal variation in its default probabilities over the last decade, particularly in comparison with financial institutions. The current five year default probability is at its highest level in a decade, however. At current default probability levels, we believe that a majority of sophisticated analysts would rate United States Steel Corporation as non-investment grade by the Comptroller of the Currency definition. We believe, however, that a substantial minority of analysts would rate the company near the bottom of the investment grade scale on the basis of the relatively stable history of default risk.

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.