Donald R. Van Deventer, Ph.D.

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


Wal-Mart Stores Inc.: Bonds on Aisle 9

09/24/2013 09:27 AM

This note focuses on the risk and return on the bonds of Wal-Mart Stores Inc. (WMT) in light of the analysis of Safeway Inc. (SWY) bonds analyzed yesterday. Today’s note incorporates Wal-Mart Stores Inc. bond price data as of September 23, 2013. A total of 199 trades were reported on 25 fixed-rate non-call bond issues of Wal-Mart Stores Inc. with trading volume of $53.1 million. All of this data was used in this study.  We find a much different risk and return pattern for Wal-Mart than we found yesterday for Safeway Inc.

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 Wal-Mart Stores 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 Wal-Mart Stores 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 Wal-Mart Stores Inc. ranging from one month to 10 years on an annualized basis. For maturities longer than ten years, we assume that the ten year default probability is a good estimate of default risk. The default probabilities range from 0.00% at one month (0.00385% before rounding) to 0.00% at 1 year (0.002062% before rounding) and 0.10% at ten years.

We also 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 all of the bond data mentioned above for the 25 Wal-Mart Stores 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 Wal-Mart Stores 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 Wal-Mart Stores Inc. The next 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 orange line graphs the lowest yield reported by TRACE on that day on Wal-Mart Stores Inc. bonds. The green line displays the average yield reported by TRACE on the same day.  The red line is the maximum yield in each Wal-Mart Stores Inc. issue recorded by TRACE.

The graph shows an increasing “liquidity premium” for holding the bonds of Wal-Mart Stores Inc.  We explore this premium in detail below.

The high, low and average credit spreads at each maturity are graphed below.  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 96.72% 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.  The ratio of credit spread to default probability for Wal-Mart Stores Inc. for maturities under 1 year is not plotted since default probabilities are so small (less than 0.004%).  The credit spread to default probability ratio is more than 24 for maturities less than 2 years. For maturities beyond that, the ratio is generally between 9 and 11, a very high ratio for a credit of this quality. This ratio of spread to default probability is shown in the following table for Wal-Mart Stores Inc.:

The credit spread to default probability ratios are shown in graphic form here. Again, the short term ratios are not plotted because the default probabilities are so close to zero.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended September 13, 2013 (the most recent week for which data is available), the credit default swap trading volume on Wal-Mart Stores Inc. was 53 trades for $208 million of notional principal.  Wal-Mart Stores Inc. was the 173rd most heavily traded name by notional principal in the CDS marketplace that week. The number of credit default swap contracts traded on Wal-Mart Stores Inc. in the 155 weeks ended June 28, 2013 is summarized in the following table:

Wal-Mart Stores Inc. ranked 380th 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 Wal-Mart Stores Inc. range from 0.00% (after rounding) at 1 year to 0.96% at 10 years, a very small cumulative probability of default compared to many firms analyzed in this series of bond studies.

Over the last decade, the 1 year and 5 year default probabilities for Wal-Mart Stores Inc. have never exceeded 0.14% at any time, even during the heart of the 2006-2011 credit crisis.

In contrast to the daily movements in default probabilities graphed above, we turn to the legacy credit ratings for Wal-Mart Stores Inc., those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO). These legacy ratings have not changed even once during the decade, compared to 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 Wal-Mart Stores 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 Wal-Mart Stores Inc. default risk responds to changes in four domestic risk factors and seven international risk factors (because of the firm’s world-wide product sourcing) among the 26 factors listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review. These macro factors explain 74.8% of the variation in the default probability of Wal-Mart Stores Inc.:

  • Nominal disposable income
  • 3 month U.S. Treasury bill yield
  • 10 year U.S. Treasury yield
  • Dow Jones stock price index
  • 7 international risk factors

Wal-Mart Stores 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 “food and staples retailing” sector, Wal-Mart Stores Inc. has the following percentile ranking for its default probabilities among its 35 peers at these maturities:

1 month 29th percentile
1 year 20th percentile
3 years 6th percentile (3rd lowest)
5 years 3rd percentile (2nd lowest)
10 years 3rd percentile (2nd lowest)

The percentile ranking of Wal-Mart Stores Inc. default probabilities is higher than one might expect in the short run simply because all firms in this sector are benefitting enormously from credit conditions that Kamakura Corporation currently ranks at the 93rd percentile (with 100 representing the best credit conditions since 1990). Taking still another view, the actual and statistically predicted Wal-Mart Stores Inc. credit ratings both show a rating strongly in “investment grade” territory.  The statistically predicted rating is four notches below the legacy rating.


We believe that an overwhelming majority of analysts would rate Wal-Mart Stores Inc. as investment grade.  That is true even though we believe that the legacy ratings of the firm represent a four notch “over-rating,” due largely to the stickiness of ratings for iconic names with a stellar legacy ratings history.  Indeed, most of the retailing sector in the United States offers exceptionally low short term default probabilities because business conditions are so good at the current time.  Wal-Mart offers considerable value to bond investors, more so than almost all of its peers, for two reasons.  First, its long term default probabilities are the second lowest in the retailing sector, ranking only after CostCo (COST).  Second, the reward to bond holders per basis point of default risk is well above average and there is none of the event risk discussed in yesterday’s post on Safeway Inc.

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 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