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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

Oct 24

Written by: Donald van Deventer
10/24/2013 4:57 AM 

In this note we take a second look at the current levels and past history of default probabilities for Time Warner Cable Inc. (TWC), which declared its dividend payable in December today.  We compare those default probabilities to credit spreads on 541 bond trades in 12 different company bond issues on October 23, 2013.  Time Warner Cable Inc. continues to have some of the lowest default probabilities of any firm analyzed in this series of credit notes to date. Trading volume in these 12 Time Warner Cable Inc. bonds on October 23 totaled $92.4 million, 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 Inc. 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. Background on the Dodd-Frank Act and the implementation of the related regulations by the Office of the Comptroller of the Currency are described in the last section of this note.

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 (in green) shows the current default probabilities for Time Warner Cable Inc. ranging from one month to 10 years on an annualized basis. Default probabilities on July 26 are shown in yellow. The current default probabilities range from 0.00% at one month to 0.00% at 1 year and 0.14% at ten years, down 1 basis point from our report on July 26.  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.  We can compare the default probabilities for Time Warner Cable Inc. with its peer group in the technology, media and telecommunications sector based on data for October 23, 2013. Time Warner Cable Inc. default probabilities are shown in dark blue and lie at the bottom of the peer group:

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. We used the bond data described above in this report.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Time Warner Cable Inc. bonds.  The lowest curve, in dark blue, is interpolated U.S. Treasury yield with a maturity equal to that of the traded bonds of Time Warner Cable Inc. 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 Inc. 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 Inc. 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 Inc. 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 generally increasing with the maturity of the bonds.

We can also compare the credit spreads on Time Warner Cable Inc. bond trades with the credit spreads on other bond trades in the technology, media and telecommuncations peer group.  We note that, even though Time Warner Cable Inc. has among the lowest default probabilities in the peer group, the credit spreads are quite wide relative to peers. 

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 Inc.  At all maturities, the reward from holding the bonds of Time Warner Cable Inc., relative to the matched maturity default probability, is at least 25 basis points of credit spread reward for every basis point of default risk incurred, five basis points wider than we reported in July. The ratio of spread to default probability is almost “off the charts” at maturities under 2 years because of the near-zero default probabilities for Time Warner Cable Inc. at those maturities.

The credit spread to default probability ratios are shown in graphic form here.


The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended October 18, 2013 (the most recent week for which data is available), the credit default swap trading volume on Time Warner Cable Inc. showed 21 contracts trading with a notional principal of $101 million, less than half the trading volume we reported in July. The next graph shows the weekly number of credit default swaps traded on Time Warner Cable Inc. in the 155 weeks ended June 28, 2013. Time Warner Cable Inc. 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 Inc. during this three year period.

On a cumulative basis, the default probabilities for Time Warner Cable Inc. range from 0.00% at 1 year (rounded to 2 decimal places) to 1.35% at 10 years (shown in green), down 9 basis points since July 26 (shown in yellow).

Over the last 4 years, the 1 year and 5 year default probabilities for Time Warner Cable Inc. have varied as shown in the following graph. The one year default probability peaked at just under 0.25% and the 5 year default probability peaked at just under 0.17% 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 Inc. have not changed since ratings were first reported for Time Warner Cable Inc. in August 2010.

The macro-economic factors driving the historical movements in the default probabilities of Time Warner Cable Inc. 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 Inc., a very high proportion.

Time Warner Cable Inc. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (MS) and reported by Compustat.  For the USA consumer discretionary-media sector, Time Warner Cable Inc. has the following percentile ranking for its default probabilities among its 133 peers at these maturities:

1 month

4th percentile, up 1 percentile since July

1 year

4th percentile, up 1 percentile

3 years

6th percentile, down 1 percentile

5 years

1st percentile, 2nd lowest firm, down 1 percentile

10 years

0th percentile, the lowest firm, down 1 percentile

Time Warner Cable Inc. is among the least risky of the firms in the USA consumer discretionary-media sector at all maturities.  A comparison of the legacy credit rating for Time Warner Cable Inc. with predicted ratings indicates that the statistically predicted rating is 2 ratings notches above the actual legacy rating assigned to the company, one notch higher than we reported in July.


After the credit crisis, Time Warner Cable Inc. has experienced minimal variation in its default probabilities.  Short-term default risk continues to be 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, and this compensation has widened since July.  Legacy credit ratings for Time Warner Cable Inc. are two notches below that which one would predict using the best available statistics and default probabilities. A widening of the gap between the predicted and actual rating often indicates that a rating change is overdue. The main risk facing Time Warner Cable Inc. is technology risk, the risk that cable technology becomes obsolete. At current default probability levels, we believe that a very strong majority of sophisticated analysts would rate Time Warner Cable Inc. 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.

Background on the Dodd-Frank Act and the Definition of “Investment Grade”

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.” For many investors, “investment grade” is an internal definition; for many banks and insurance companies “investment grade” is also defined by regulators. We consider whether or not a reasonable U.S. bank investor would judge Dell Inc. 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 from U.S. government regulations.  Section 939A states the following:


(a) AGENCY REVIEW.—Not later than 1 year after the date of the enactment of this subtitle, each Federal agency shall, to the extent applicable, review—
(1) any regulation issued by such agency that requires the use of an assessment of the credit-worthiness of a security or money market instrument; and
(2) any references to or requirements in such regulations regarding credit ratings.
(b) MODIFICATIONS REQUIRED.—Each such agency shall modify any such regulations identified by the review conducted under subsection (a) to remove any reference to or requirement of reliance on credit ratings and to substitute in such regulations such standard of credit-worthiness as each respective agency shall determine as appropriate for such regulations. In making such determination, such agencies shall seek to establish, to the extent feasible, uniform standards of credit-worthiness for use by each such agency, taking into account the entities regulated by each such agency and the purposes for which such entities would rely on such standards of credit-worthiness.
(c) REPORT.—Upon conclusion of the review required under subsection (a), each Federal agency shall transmit a report to Congress containing a description of any modification of any regulation such agency made pursuant to subsection (b).

The new rules issued by the Office of the Comptroller of the Currency in accordance with Dodd-Frank are described here. The summary provided by the OCC reads as follows:

“In this rulemaking, the OCC has amended the regulatory definition of ‘investment grade’ in 12 CFR 1 and 160 by removing references to credit ratings. Under the revised regulations, to determine whether a security is ‘investment grade,’ banks must determine that the probability of default by the obligor is low and the full and timely repayment of principal and interest is expected. To comply with the new standard, banks may not rely exclusively on external credit ratings, but they may continue to use such ratings as part of their determinations. Consistent with existing rules and guidance, an institution should supplement any consideration of external ratings with due diligence processes and additional analyses that are appropriate for the institution’s risk profile and for the size and complexity of the instrument. In other words, a security rated in the top four rating categories by a nationally recognized statistical rating organization is not automatically deemed to satisfy the revised ‘investment grade’ standard.”

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.