Verizon Communications Inc. (VZ) agreed on September 2, 2013, to buy out the Vodafone Group PLC (VOD) interest in the company's U.S. wireless business. The marketing process for a Verizon Communications Inc. bond issue estimated at $25 billion is underway at this time. In this note we compare the risk and return trade-off for the bonds of Verizon Communications Inc. with the bonds of Sprint Communications, Inc. which we analyzed yesterday. This note uses the default probabilities and bond spreads of Verizon Communications Inc., Sprint parent Sprint Corporation (S) (default probabilities only), and subsidiary Sprint Communications, Inc. (bond spreads only) to measure the relative reward-to-risk ratio on both firm's bonds. Today's study incorporates Verizon Communications Inc. bond price data as of September 9, 2013. A total of 739 trades were reported on 26 fixed-rate non-call bond issues of Verizon Communications Inc. with trading volume of $258.3 million. Trading volume for the bonds of Sprint Communications, Inc. for September 9 was down from the previous business day. We used a total of 5 fixed rate non-call bond issues on which there were 70 trades on principal value of $62.6 million. All of this data was used in this study. We leave for another day an analysis of spread on the bonds of various regional subsidiaries of Verizon Communications Inc.
A simple comparison of the yields on the bonds of both Verizon Communications Inc. and Sprint Communications, Inc. along with the U.S. Treasury curve might leave the naïve reader with the impression that the bonds of Sprint are a better investment. When we repeat the analysis on a risk-adjusted basis, however, the opposite conclusion is made quite strongly. We turn to that task now.
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 Verizon Communications 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. 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 Verizon Communications 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 Verizon Communications Inc. ranging from one month to 10 years on an annualized basis. For maturities longer than ten years, we assume that the 10-year default probability is a good estimate of default risk. The default probabilities range from 0.06% at one month to 0.04% at one year and 0.40% at ten years. These default probabilities are dramatically lower than the default probabilities reported in yesterday's analysis for the parent Sprint Corporation, and today's default probabilities for Sprint are higher still.
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 the 26 Verizon Communications Inc. fixed rate non-call bond issues mentioned above.
The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Verizon Communications 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 Verizon Communications 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 Verizon Communications 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 Verizon Communications Inc. issue recorded by TRACE.
The liquidity premium built into the yields of Verizon Communications Inc. above and beyond the "default-adjusted risk free curve" (the risk-free yield curve plus the matched maturity default probabilities for the firm) generally widens as the maturity of the underlying bonds increases.
The high, low and average credit spreads at each maturity are graphed below. Again, we see 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 92.53% 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 Verizon Communications Inc. For maturities under 3 years, the credit spread to default probability ratio is more than 10 times, compared to a ratio of less than 1.5 for Sprint Communications, Inc. The ratio of spread to default probability decreases beyond that, generally ranging between 5 and 7 times. This compares to a spread to default probability ratio for Sprint Communications, Inc. that is less than one. This reward to risk ratio offers above average risk-adjusted returns relative to the other firms analyzed in this series of bond notes.
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 76.6% 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 30, 2013 (the most recent week for which data is available), the credit default swap trading volume on Verizon Communications Inc. was 19 trades with $86.1 million of notional principal, a small fraction of the daily bond trading volume on September 9. The number of credit default swap contracts traded on Verizon Communications Inc. in the 155 weeks ended June 28, 2013, is summarized in the following table:
Verizon Communications Inc. ranked 161st 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 Verizon Communications Inc. range from 0.04% at 1 year to 3.89% at 10 years, less than 1/10th of the ten year cumulative default risk that we reported yesterday for Sprint Corporation.
Over the last decade, the 1 year and 5 year default probabilities for Verizon Communications Inc. have been volatile, but neither the 1 year default probability nor the 5 year default probability have exceeded 0.60% in the last decade. This is 1/100th of the peak level we reported for Sprint Corporation yesterday.
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) for Verizon Communications Inc. have changed only three times during the decade, somewhat more slowly than the median 815 days since the last rating change for rated companies found in a recent study by Kamakura Corporation.
The macro-economic factors driving the historical movements in the default probabilities of Verizon Communications 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. With that caveat, the historical analysis shows that Verizon Communications 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
- 3 month U.S. Treasury bill rates
- The yield on BBB-rated corporate bonds
- The Dow Jones stock price index
- The VIX volatility index
- Home price index
- Commercial real estate prices
- 2 international macro factors
These macro factors explain 70.4% of the variation in the default probability of Verizon Communications Inc.
Verizon Communications 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, Verizon Communications Inc. has the following percentile ranking for its default probabilities among its 63 peers at these maturities:
1 month 43rd percentile
1 year 17th percentile
3 years 11th percentile
5 years 5th percentile
10 years 5th percentile
The percentile ranking of Verizon Communications Inc. default probabilities at one year through three years is in the safest quarter of the peer group. The percentile ranking for Verizon Communications Inc. at 5 and 10 years is in the safest 1/20th of the peer group. Taking still another view, both the actual and statistically predicted Verizon Communications 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. The statistically predicted rating is one notch above the legacy rating.
We believe the overwhelming majority of analysts would rate Verizon Communications Inc. as investment grade. By any credit metric, it is a far safer credit risk than Sprint Communications, Inc. From a bond risk and return point of view, Verizon Communications Inc. bonds offer a ratio of credit spread to default risk that is more than 5 times as high as the same ratio on the bonds of Sprint Communications.
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 database. 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.
Additional disclosure: Kamakura Corporation has business relationships with a number of firms mentioned in this article.