Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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AT&T Inc. Bonds: Not a Ringing Endorsement

08/27/2013 10:11 AM

The telecommunications sector around the world is experiencing enormous disruption. This note uses the default probabilities and bond credit spreads of AT&T Inc. (T) to measure the reward-to-risk ratio on the company’s bonds.  Today’s study incorporates AT&T bond price data as of August 26, 2013. A total of 355 trades were reported on 25 fixed-rate non-call bond issues of AT&T with trade volume of $109.6 million.  After eliminating one bond issue with flawed data, we analyze the remaining 349 trades for $109.5 million in principal amount in this note.

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 the firm 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.  The new rules delete references to legacy credit ratings and replace them with default probabilities as explained here.

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. In this note, we also analyze the maturities where the credit spread/default probability ratio is highest for AT&T Inc.

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 AT&T Inc. ranging from one month to 10 years on an annualized basis.  The default probabilities range from 0.16% at one month to 0.08% at 1 year and 0.53% 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. We used the bond data mentioned above for 24 AT&T Inc. fixed rate non-call issues in this analysis.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of AT&T Inc. bonds. These curves reflect the noise in the TRACE data, as some of the trades are small odd-lot trades. The lowest curve, in dark blue, is the yield to maturity on U.S. Treasury bonds, interpolated from the Federal Reserve H15 statistical release for that day, which matches the maturity of the traded bonds of AT&T 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 AT&T 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 AT&T Inc. issue recorded by TRACE.

The data makes it clear that there is a fairly stable liquidity premium built into the yields of AT&T 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 credit spreads are relatively erratic for maturities under 5 years. The credit spreads generally widen with maturity, the normal pattern for a high quality credit, with the exception of two bonds with maturities near 28 years.  A regular reader of this series of notes may notice that the ratio of credit spread to default probability for AT&T Inc. is narrower than normal.  We document that fact in the rest of this note.

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 have done nothing to smooth the data reported by TRACE, which includes both large lot and small lot bond trades. For the reader’s convenience, we fitted a cubic polynomial that explains the average spread as a function of years to maturity.  This polynomial explains 93% of the variation in the average credit spread over the maturity term structure:

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 AT&T Inc. At almost all maturities under 3.5 years, the reward from holding the bonds of AT&T Inc., relative to the matched maturity default probability, is more than 4 basis points of credit spread reward for every basis point of default risk. The ratio of spread to default probability decreases once the maturity of the bonds exceeds 3.5 years, falling to a spread to default ratio between 2.5 and 3.5 times.  This reward to risk ratio is among the lowest of any firm analyzed in this series of bond studies.  In our recent note on Citigroup, Inc., for example, the reward-to-risk ratio was as much as ten times higher than we are finding for AT&T Inc.

The credit spread to default probability ratios are shown in graphic form here. We have again added a cubic polynomial relating the credit spread to default probability ratio to the years to maturity on the underlying bonds.  The smoothed line explains about 45% of the variation in the reward to risk ratio.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended August 16, 2013 (the most recent week for which data is available), the credit default swap trading volume on AT&T Inc. was 16 trades with $46.3 million of notional principal, a small fraction of the daily bond trading volume on August 26. The number of credit default swap contracts traded on AT&T Inc. in the 155 weeks ended June 28, 2013 is summarized in the following table:

AT&T Inc. ranked 170th among all reference names in weekly credit default swap trading volume during this period, which is graphed below:

On a cumulative basis, the default probabilities for AT&T Inc. range from 0.08% at 1 year to 5.15% at 10 years, as shown in the following graph.

Over the last decade, the 1 year and 5 year default probabilities for AT&T Inc. have varied as shown in the following graph. The one year default probability peaked at just under 0.60% in the first half of 2009 during the worst part of the credit crisis. The 5 year default probability (annualized) peaked near 0.60% in 2005.  The default probability history for AT&T Inc. is striking for two reasons.  First, the peak in default probabilities is well below that of many well-known banks and industrial firms during the credit crisis.  That’s the good news. The bad news is that the volatility of the default probabilities has not abated as the credit crisis recedes into history.  That is due to the on-going disruption in the telecommunications industry.

In a recent study by Kamakura of the 82 borrowers under the Federal Reserve’s Commercial Paper Funding Facility AT&T Inc. did not need to borrow under the facility even though its competitor Verizon Communications (VZ) did so.

In contrast to the daily movements in default probabilities graphed above, the legacy credit ratings [those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO)] for AT&T Inc. have changed only twice during the decade.

The macro-economic factors driving the historical movements in the default probabilities of AT&T Inc. have been derived using historical data beginning in January 1990.  A key assumption of such analysis, like any econometric time series study, is that the business risks of the firm being studied are relatively unchanged during this period. This assumption is complicated for AT&T Inc. and its competitors as the fundamental technology used in the telecommunications sector is undergoing a complete upheaval.  With that caveat, the historical analysis shows that AT&T Inc. default risk responds to changes in the following factors among those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

  • Change in real gross domestic product
  • Change in real disposable income
  • Change in nominal disposable income
  • Unemployment rate
  • 3 month U.S. Treasury bill rates
  • 10 year U.S. Treasury yield
  • BBB rated corporate bond yield
  • The VIX volatility index
  • Home price index
  • Commercial real estate prices
  • 1 international macro factor

These macro factors explain 70.9% of the variation in the default probability of AT&T Inc., a much lower than average percentage because technology factors have dominated in the determination of the firm’s credit risk.

AT&T 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 “telecom services” sector, AT&T Inc. has the following percentile ranking for its default probabilities among its 64 peers at these maturities:

1 month 56th percentile
1 years 31st percentile
3 years 13th percentile
5 years 11th percentile
10 years 8th percentile

The percentile ranking of AT&T Inc. default probabilities at one month is in the riskiest half of the telecom services peer group. The percentile ranking for AT&T Inc. at 10 years is in the safest decile of credit risk among telecom services firms. This reflects the market prices of the firm’s common stock and bonds, with investors betting that the firm is a long-term survivor in the telecommunications sector with declining risk as time goes on. That being said, the peer comparison with the risky telecom sector is favorable for AT&T Inc. mainly because the entire sector has higher default probabilities than the average industrial firm. Taking still another view, both the actual and statistically predicted AT&T Inc. credit ratings are “investment grade” by traditional credit rating standards of Moody’s Investors Service and the Standard & Poor’s affiliate of McGraw-Hill.


AT&T Inc. is a complex credit.  While the long-term peer group comparison places the firm in the best decile of credit risk, the entire telecommunications sector faces a constantly changing technological landscape and a higher than average level of default risk.  This is reflected in a high degree of volatility for ATT Inc. default probabilities even though they have remained well below the 1% level at which the Kamakura Troubled Company Index labels a firm as “troubled.”  In spite of this concern, we believe a strong majority of analysts would define AT&T Inc. as investment grade.  Note that our views on the quality of the credit are explicitly given in the first part of this paper where we state the default probabilities for the firm.  We discuss the “investment grade” analysis like a political poll, for the same reason polling is used in politics: “investment grade” involves complex perceptions of the analyst, parallel to perceptions of presidential candidates, even when everyone has identical information.  The percentage ranking for “investment grade” is not 100% for any firm, just as no candidate for President of the United States has received 100% of the vote.

Even though the default probabilities of AT&T are relatively low, the ratio of the credit spreads to default probabilities for the firm are very low across the board.  The attractiveness of the AT&T name and the firm’s status as an icon of American industry comes with a price.  All other things being equal, investors in the bonds of AT&T receive much less reward (in terms of credit spread) relative to the risk they are taking (in terms of default probabilities) compared to the bonds of other issuers.

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.



Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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