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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 28

Written by: Donald van Deventer
7/28/2013 10:55 PM 

In this note we analyze the current levels and past history of default probabilities for Time Warner Cable (TWC).  We compare those default probabilities to credit spreads on 540 bond trades in 9 different company bond issues on July 26, 2013.  Time Warner Cable has some of the lowest default probabilities of any firm analyzed in this series of credit notes to date. Trading volume in these 9 Time Warner Cable bonds on July 26 totaled $68,745,000, and the analysis in this note is based on those traded prices.

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 Time Warner Cable. We also consider whether or not 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 Time Warner Cable ranging from one month to 10 years on an annualized basis.  The default probabilities range from 0.00% at one month to 0.00% at 1 year and 0.15% at ten years.  Note that the default probabilities at the 1 month and 1 year maturity are not literally zero—they are reported as zero only because of rounding to two decimal places.

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 Time Warner Cable included 540 trades in nine bonds of the firm on July 26, 2013.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Time Warner Cable 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 Time Warner Cable. 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 Time Warner Cable. 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 Time Warner Cable issue recorded by TRACE.

The data makes it very clear that there is a very large and stable liquidity premium built into the yields of Time Warner Cable above and beyond the “default-adjusted risk free curve” (the risk-free yield curve plus the matched maturity default probabilities for the firm).  The one aberration is in the TRACE-reported spreads for the bond with slightly more than 6.5 years to maturity.

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, again at 6.5 years to maturity.

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 Time Warner Cable.  At all maturities, the reward from holding the bonds of Time Warner Cable, relative to the matched maturity default probability, is at least 20 basis points of credit spread reward for every basis point of default risk incurred. The ratio of spread to default probability is literally “off the charts” at maturities under 2 years because of the near-zero default probabilities for Time Warner Cable at those maturities.

The credit spread to default probability ratios are shown in graphic form here, with the vertical axis capped at a ratio of 50 times:

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 Time Warner Cable showed 56 contracts trading with a notional principal of $222.0 million. The next graph shows the weekly number of credit default swaps traded on Time Warner Cable in the 155 weeks ended June 28, 2013. Time Warner Cable ranked 394th of 1,144 reference names in contracts traded over this period:

The table below summarizes the key statistics of credit default swap trading in Time Warner Cable during this three year period.

On a cumulative basis, the default probabilities for Time Warner Cable range from 0.00% at 1 year (rounded to 2 decimal places) to 1.44% at 10 years, as shown in the following graph.

Over the last 4 years, the 1 year and 5 year default probabilities for Time Warner Cable have varied as shown in the following graph. The one year default probability peaked at just under 0.40% and the 5 year default probability peaked at just under 0.20% during that period.  Default probabilities did show a sharp rise earlier in the credit crisis however.

The legacy credit ratings (those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO)) for Time Warner Cable have not changed since ratings were first reported for Time Warner Cable in August 2010.

The macro-economic factors driving the historical movements in the default probabilities of Time Warner Cable include the following factors of those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

  • Nominal gross domestic product

  • 10 year U.S. Treasury yield

  • BBB rated corporate bond yields

  • The Dow Jones Industrial index

  • Commercial real estate price index

  • 7 international macro factors

These macro factors explain 96.7% of the variation in the default probability of Time Warner Cable, a very high proportion.

Time Warner Cable can be compared with its peers in the same industry sector, as defined by Morgan Stanley and reported by Compustat.  For the USA consumer discretionary-media sector, Time Warner Cable has the following percentile ranking for its default probabilities among its peers at these maturities:

1 month 3rd percentile
1 year 3rd percentile
3 years 7th percentile
5 years 2nd percentile
10 years 1st percentile

Time Warner Cable is among the least risky of the 131 firms in the USA consumer discretionary-media sector at all maturities.  A comparison of the legacy credit rating for Time Warner Cable with predicted ratings indicates that the statistically predicted rating is 1 ratings notch above the actual legacy rating assigned to the company.


After the credit crisis, Time Warner Cable has experienced minimal variation in its default probabilities.  Short-term default risk is so close to zero that default probabilities are indistinguishable from zero when rounding to two decimal places. The company currently offers more compensation in terms of credit spread per basis point than any other company yet reviewed in this series.  Legacy credit ratings for Time Warner Cable are one notch below that which one would predict using the best available statistics and default probabilities. The main risk facing Time Warner Cable is technology risk, the risk that cable technology becomes obsolete. At current default probability levels, we believe that a strong majority of sophisticated analysts would rate Time Warner Cable investment grade by the Comptroller of the Currency definition.

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.