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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

Sep 24

Written by: Donald van Deventer
9/24/2014 4:01 AM 

Stress testing-based risk management analysis is now a critical element of financial institutions’ financial strategy. Stress testing regimes like the Federal Reserve’s 2014 Comprehensive Capital Analysis and Review require a five step process:

  1. Macro-economic factors are shifted
  2. Default probabilities of all counterparties move in response
  3. Credit spreads of all counterparties move in response
  4. Valuations of all extensions of credit then shift
  5. The institution’s own default risk, capital position, and liquidity position shift as well

This note focuses on how changes in default risk impact liquidity in the corporate bond market, perhaps the best observable proxy for measuring a financial institution’s ability to convert its assets to cash in a credit crisis.

The Analysis
This note is based on traded prices of fixed rate senior corporate bonds in the U.S. market on September 23, 2014. We exclude floating rate issues, index-linked issues, issues with a survivor option, and callable issues, leaving a transparent plain vanilla set of traded bond data. The bond trading volume and price data is provided by Kamakura Risk Information Services based on data from the TRACE system. On September 23, 2014, the total trading volume and the most heavily traded bond issuers are shown in this chart:


The largest banks in the United States generally rank very high on this list: JPMorgan Chase & Co. (JPM) is fifth and Bank of America Corporation (BAC) is sixth on this trading day.

A shift in default probabilities in response to a change in macro factors has multiple impacts: it changes credit spreads, bond prices, and bond market liquidity. The chart below plots matched-maturity credit spreads versus default probabilities. The credit spreads are calculated by Kamakura Risk Information Services using the U.S. Treasury yield data provided by the U.S. Department of the Treasury based on each bond’s trade-weighted average yields. The default probabilities are from Kamakura Risk Information Services. The model used is the reduced form Jarrow-Chava model, version 5. The chart below shows that the change in credit spreads is complex as default probabilities rise: 

In general, the ratio of the credit spread to the default probability declines dramatically as the default probability of the issuer rises, all other things being equal. The implied spread calculation from Kamakura Risk Information Services includes the impact of financial ratios and macro-economic factors. More than 60 variables are statistically significant drivers of credit spreads.

The most important impact of a change in default risk from stress testing is a change in bond market liquidity. We turn to that issue now.

The Impact of Default Probabilities on Bond Trading Volume
Most studies that relate bond market liquidity to the credit risk of the issuer use legacy credit ratings. This analytical choice is problematic for a number of reasons:

  • Legacy ratings have no explicit maturity
  • Legacy ratings have no explicit formulaic link to default probabilities
  • Legacy ratings are less accurate in assessing credit risk than modern reduced form default probabilities, as shown by Hilscher and Wilson (2013).

For these reasons, legacy ratings are a distraction in the stress testing process and we ignore them in this note. Instead, we use the KRIS reduced form default probabilities noted above and explained in the appendix. We use the default probabilities with the same maturity as each traded bond. In the next chart, we show the dollar volume of principal traded in the corporate bond market on September 23 at different levels of default risk: 

The annualized default probability ranges are from 0 to 0.10%, 0.11% to 0.20% and so on up through 1.00%. The ranges then widen to 0.20% up through 2.00%. Beyond 2.00%, we report using default probability ranges from 2.01% to 4.00%, 4.01% to 6.00%, 6.01% to 10.00%, and 10.01% through 100.00%. The chart makes it exceptionally clear that the overwhelming majority of bond trading volume takes place at very low default probability levels. There was $2.45 billion dollars of volume in bonds with default probabilities of 0.10% or less. Volume dropped to $825 million for default probabilities in the 0.11% to 0.20% range. As default probabilities rise, volume continues to drop with the exception of the $279.7 million of volume in the 1.01% to 1.20% range and the $131.4 million in volume in the 1.21% to 1.40% default probability range.

Another cut of the data displays the number of individual bond issues traded by the same default probability ranges. That data is shown in this chart: 

For bond issues with default probabilities of more than 0.50%, in no default probability category were more than 25 bond issues traded. Consider a firm with a default probability of 0.08% on September 23, 2014. Holding everything constant but the default probability, one can do a visual “stress test” of the liquidity in the firm’s bonds. A stress test of 0.50% in default risk would take the issuer to 0.58% default probability. Using the chart above, the number of issues trading drops from 1512 to 24 in the default probability range from 0.51% to 0.60%. This is a 98.4% drop in trading volume when measured by the number of issues with actual trades. If we use the prior chart, dollar volume of trading drops from $2450.2 million in the 0% to 0.10% range to $46.2 million in the 0.51% to 0.60% default probability range. Measured by dollar volume, this is a 98.1% reduction in trading volume.

The plot of the credit spread to default probability ratios above showed that, on average, the response of a change in credit spread to a rise in default risk is less than 1 to 1. On the one hand, this means that the impact on bond prices from a default probability shift is somewhat dampened. On the other hand, the clear lesson of the last two charts is that it becomes much less likely than one can sell the bond “easily.” Financial theory usually assumes frictionless markets where the volume of trading does not affect the price at which the bonds trade. Clearly, the trading volume graphed above shows that this is a highly tenuous assumption at best.

Even in a benign credit environment like that which prevailed on September 23, 2014, a 0.50% rise in default probabilities from under 0.10% to the 0.51 to 0.60% range reduces trading volume by 98%. A shift in macro-economic factors that triggers such a default probability rise is likely to have a separate and distinct (adverse) impact on trading volume above and beyond the “all other things being equal” assumptions we have made in this note. From a financial institution’s point of view, a default probability shift of this magnitude both impairs the value of credits held and dramatically reduces the ability to sell those credits. This is consistent with experience in the 2006-2010 credit crisis, in which financial markets literally disappeared for many asset classes. Allowing for this adverse impact on the liquidity of markets and the resulting liquidity risk of financial institutions is an essential element in measuring the safety and soundness of financial institutions.

Appendix: 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 An overview of the full suite of Kamakura default probability models is available here.

Using Default Probabilities in Asset Selection
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.

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