Corporate bond trading activity on October 21 was led by Morgan Stanley (MS), the most heavily traded bond issuer on the day. Petrobras International Finance Company S.A. (PBR) had the two most actively traded bond issues. Alpha Natural Resources (ANR) led the credit spread ranking at 2156 basis points. Cliffs Natural Resources (CLF) (CLV) bonds dominated the lowest priced bond rankings. Credit spreads continue to be squeezed at maturities beyond 12 years, giving long-maturity minded corporate treasurers a unique opportunity to go long. The credit spread to default probability ratio generally declines as default risk rises, so high quality bond issuers dominate “best value” bond trades by this criterion. Finally, substantially all fixed rate corporate bond trading is taking place at the lowest default probability levels. As default probabilities rise, trading actively drops off dramatically. We present the analysis behind these findings in what follows.
Analysis of Most Actively Traded Bond Issuers and Bond Issues
First we rank the most actively traded bond issuers in the U.S. fixed rate corporate bond market for senior debt by the notional principal of bonds traded on that issuer name. There were 3,180 issues of 987 bond issuers traded, representing an underlying principal volume of $6.2 billion. There were a total of 19,405 trades on the day, with Morgan Stanley the most heavily traded bond issuer.
Next, we rank the most actively traded bond issues in the U.S. fixed rate corporate bond market for senior debt by the notional principal of bonds traded on that issuer name. Petrobras International Finance Company S.A. led the ranking with 2 issues at the top of the chart.
The U.S. Treasury Yield Curve
In the following section, we expand our analysis to include credit spreads relative to the current U.S. Treasury curve.
This graph shows the continuous forward rates and zero coupon bond yields that are consistent with the constant maturity Treasury yields that were reported by the U.S. Department of the Treasury at 4 p.m. Eastern time. The forward rates and zero coupon bond yields are derived using Kamakura Risk Manager and the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai,Financial Risk Analytics (1996). Kamakura Corporation recently announced new research by Managing Director Robert Jarrow which confirms that the maximum smoothness forward rate approach is consistent with the no arbitrage conditions on interest rate movements derived by Heath, Jarrow and Morton . There are other yield curve smoothing methods in common use which violate the no arbitrage restrictions. Among the methods which cannot meet the “no arbitrage” standard are the Svensson, Nelson-Siegel, and Merrill Lynch exponential smoothing approaches.
World-wide Corporate Credit Conditions
Credit spreads are a function of world-wide corporate credit conditions, which are summarized in this chart of the Kamakura Troubled Company Index.
Kamakura Corporation reported today that its troubled company index was down 0.17% to 5.10%. At this level, the index is at the 96th percentile of corporate credit conditions over the period from 1990 to the present. The record low in the index, the 100th percentile, was 3.95% set on August 4, 2014. The index hit its prior record low at 4.06% on May 19, 2014.
The Kamakura troubled company index measures the percentage of more than 35,000 public firms in 61 countries that have annualized 1 month default risk over one percent. The average index value since January, 1990 is 11.66%. Since November, 2010, the Kamakura index has used the annualized one month default probability produced by the KRIS version 5.0 Jarrow-Chava reduced form default probability model , a formula that bases default predictions on 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. The countries currently covered by the index are Argentina, Australia, Austria, Bahrain, Bangladesh, Belgium, Brazil, Canada, Chile, China, Colombia, Cyprus, Denmark, Egypt, Estonia, Finland, France, Germany, Greece, Hong Kong, Iceland, India, Indonesia, Ireland, Israel, Italy, Japan, Jordan, Kuwait, Luxembourg, Malaysia, Malta, Mexico, the Netherlands, New Zealand, Norway, Oman, Pakistan, Peru, the Philippines, Poland, Portugal, Qatar, Russia, Saudi Arabia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Taiwan, Thailand, Turkey, the United Arab Emirates, the United Kingdom, the United States, and Viet Nam.
High Yield: Widest Credit Spread Rankings
This chart ranks bond issues in the fixed rate U.S. market for non-call senior debt by credit spread, starting with the highest credit spread traded on this date. Alpha Natural Resources led the rankings with a trade-weighted average credit spread of 2156 basis points.
The credit spreads are calculated by Kamakura Corporation using the matched maturity U.S. Treasury yields reported by the U.S. Department of the Treasury and the trade-weighted average yield reported by TRACE.
High Yield: Lowest Bond Price Rankings
The next chart ranks bond issues in the fixed rate U.S. market for non-call senior debt by bond price, starting with the lowest price traded on this date. One might expect the “widest spread” and “lowest price” rankings to be the same, and often they are. They can be very different, however, because a rise in interest rates can drive down bond prices of all issuers. Today, Cliffs Natural Resources (CLF) (CLV) dominates the rankings.
Analysis of Credit Spreads and Default Probabilities
We next turn to a more detailed analysis of the relationship between credit spreads and default probabilities. The default probabilities used are the Jarrow-Chava version 5.0 reduced form default probabilities from Kamakura Risk Information Services, described further at the end of this note in the Appendix.
We begin with the U.S. Dollar Cost of Funds IndexTM.
The U.S. Dollar Cost of Funds Index TM measures the trade-weighted cost of funds for the largest deposit-taking U.S. bank holding companies. The index is a credit spread, measured in percent and updated daily, over the matched maturity U.S. Treasury yield on the same day. The current bank holding companies used in determining the index are Bank of America Corporation (BAC), Citigroup Inc. (C), JPMorgan Chase & Co. (JPM), and Wells Fargo & Company (WFC). The index is an independent market-based alternative to the Libor-swap curve that has traditionally been used by many banks as an estimate of their marginal cost of funds. Kamakura Corporation is the calculation agent, and the underlying bond price data is provided by TRACE and the U.S. Department of the Treasury. Today’s on the run values for the U.S. Dollar Cost of Funds Index are shown below.
At the 5 year maturity, the U.S. Dollar Cost of Funds Index today is 1.012%, an increase of 0.002% from the prior day.
Featured Bond Issuer: Toyota Motor Credit Corporation
Today’s featured bond issuer is the Toyota Motor Corporation (TM) subsidiary Toyota Motor Credit Corporation.
This graph compares the issuer’s trade-weighted average credit spreads with the U.S. Dollar Cost of Funds Index on the same day. The chart shows that Toyota Motor Credit Corporation’s credit spreads are generally well below the credit spreads of the biggest U.S. banks underlying the U.S. Dollar Cost of Funds Index.
This graph shows the zero coupon yield curve for both the featured issuer and the U.S. Treasury.
Both curves are produced by Kamakura Risk Information Services using Kamakura Risk Manager, version 8.1. The issuer’s zero coupon yield curve was created by applying the maximum smoothness forward rate approach to zero coupon credit spreads, relative to the base U.S. Treasury curve. The underlying senior non-call fixed rate bond data for the issuer was supplied by the TRACE system and processed by Kamakura Risk Manager to minimize the trade-weighted sum of squared pricing errors. Zero coupon credit spreads are a critical input to the risk management process, with applications in counterparty credit risk, transfer pricing, stress testing, capital adequacy assessment, market risk and asset and liability management.
Credit Spreads by Years to Maturity, Legacy Ratings, and Default Probability Levels
The next graph shows the credit spread as a function of years to maturity on all corporate bond trades in the U.S. market which met the following conditions:
Coupon: Constant fixed rate until maturity
Maturity: 1 year or more
Trade volume: $5 million or more
Seniority: Senior debt
Callability: Non-call (except for “make whole” calls)
Survivor Option: Excluded
Credit spreads at the longer maturities decline slightly once the number of years to maturity exceeds 12 years.
In a recent note, we explained why it is incorrect to use the common financial relationship that says credit spreads equal the default probability times (one minus the recovery rate). In the next few graphs, the inconsistency of this simple formula with the actual data will be obvious.
The graph shows the credit spread as a function of the matched-maturity default probability on all corporate bond trades in the U.S. market which met the conditions listed above:
The next graph shows the credit spread to default probability ratio on all corporate bond trades in the U.S. market which meet the same set of conditions:
The relationship between credit spreads and default probabilities is shown in the next graph. Generally speaking, the ratio of credit spread to default probability declines as the level of default risk increases, contrary to the expectations of many.
Analysis of Trading Volumes by Legacy Credit Ratings, Years to Maturity, and Default Probabilities
We now analyze how corporate bond trading volume varied by legacy credit ratings, years to maturity and default probability level. We analyze only those bonds which meet the same criteria listed above:
Coupon: Constant fixed rate until maturity
Seniority: Senior debt
Callability: Non-call (except for “make whole” calls)
Survivor Option: Bonds with a survivor option are excluded
This graph displays the dollar volume of underlying principal traded in the U.S. corporate bond market, displayed by legacy credit ratings, on this date:
A legacy credit rating of 1 is the best credit quality. This graph gives the misleading impression that most corporate bond trading volume is in corporate names with medium credit quality. That impression is due to well-known errors in legacy credit ratings that have been documented byHilscher and Wilson and the U.S. Senate Permanent Subcommittee on Investigations. Below we plot trading volume by default probability level to see the reality of trading patterns: the heaviest trading volume is in the bonds with lowest default probabilities.
The next graph displays the number of issues traded in the U.S. corporate bond market, displayed by legacy credit ratings, on this date.
Again, the heaviest trading volume appears to be in the middle credit quality ranges, but this is misleading, as noted above and corrected below.
The following graph displays the dollar volume of underlying principal traded in the U.S. corporate bond market, displayed by years to maturity, on this date.
Trading volume at maturities of 10 years and beyond is very sparse except for a small jump in volume for maturities of 22 to 28 years.
The next graph displays the number of issues traded in the U.S. corporate bond market, displayed by years to maturity, on this date.
The pattern of trading volume by number of issues is similar to the pattern displayed by dollar volume.
This graph displays the dollar volume of underlying principal traded in the U.S. corporate bond market, displayed by matched maturity default probabilities. This graph makes it very clear that the substantial majority of trading volume is in the lowest default probability ranges, contradicting the misleading impression given by legacy ratings above.
The last graph displays the number of issues traded in the U.S. corporate bond market, displayed by matched maturity default probabilities.
This graph confirms the impression given in the prior graph. The overwhelming majority of corporate bond trades take place in the best default probability ranges.
Background on the Default Probability Models Used
The Kamakura Risk Information Services version 5.0 Jarrow-Chava reduced form default probability model (abbreviated KDP-JC5) 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. KRIS covers 35,000 firms in 61 countries, updated daily. Free trials are available at Info@Kamakuraco.com. An overview of the full suite of Kamakura default probability models is available here.
We recommend this introduction to the use of default probabilities in fixed income strategy by J.P. Morgan Asset Management.
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.
Further information is available at www.kamakuraco.com and via e-mail at email@example.com.