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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Wal-Mart Stores Bonds: An Updated Market View

01/23/2014 07:44 AM

This note is an update of the bond market view of Wal-Mart Stores Inc. (WMT) that we published September 23, 2013. Today’s note incorporates Wal-Mart Stores Inc. bond price data as of January 22, 2014. A total of 205 trades were reported on 23 fixed-rate non-call bond issues of Wal-Mart Stores Inc. with trading volume of $60.9 million. All of this data was used in this study.

Conclusion: We find that Wal-Mart Stores Inc. bond offer investors a rare combination: both low default risk and an above average reward-to-risk ratio as measured by the ratio of credit spread to matched-maturity default probability.

Wal-Mart Bond Analysis

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.  The default probabilities used are described in detail in the daily default probability analysis posted by Kamakura Corporation. The full text of the Dodd-Frank legislation as it concerns the definition of “investment grade” is summarized at the end of our analysis of Citigroup (C) bonds published December 9, 2013.

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 current default probabilities (plotted in green) range from 0.01% at one month (up from 0.00385% on September 23, shown in yellow) to 0.00% at 1 year (0.003577% before rounding) and 0.10% at ten years (unchanged from September 23).

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 23 Wal-Mart Stores Inc. fixed rate non-call bond issues mentioned above.

The graph below shows 6 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 dots graph the lowest yield reported by TRACE on that day on Wal-Mart Stores Inc. bonds. The green dots display the trade-weighted average yield reported by TRACE on the same day.  The red dots represent the maximum yield in each Wal-Mart Stores Inc. issue recorded by TRACE. The black dots and connecting line are derived from fitting a trade-weighted cubic polynomial to Wal-Mart Stores Inc. credit spreads.

The graph shows a generally 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 trade-weighted cubic polynomial that explains the average spread as a function of years to maturity.  This polynomial explains 74.12% of the variation in the average credit spread over the credit spread 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 average credit spread to default probability ratio is more than 10 for maturities less than 2 years. For maturities beyond that, the ratio is generally between 4 and 10, a higher than average 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 spread to default probability ratios have dropped by 1-2 percentage points since our September 23, 2013 analysis, which is reproduced here.

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 January 17, 2014 (the most recent week for which data is available), the credit default swap trading volume on Wal-Mart Stores Inc. was 21 trades for $71 million of notional principal.  The weekly number of credit default swap contracts traded on Wal-Mart Stores Inc. in the 181 weeks ended December 27, 2013 ranged from 1 to 134 contracts with an average of 21.0 contracts traded per week.  There were no trades during three weeks of this period. The weekly notional value of contracts traded varied from $2 million to $809 million with an average of $145.8 million.  Note that roughly 75% of trading in the credit default swap market is between dealers.

The weekly number of contracts traded in the 181 weeks ended December 27, 2013 is shown here for Wal-Mart Stores Inc.

The weekly notional principal of credit default swaps traded on Wal-Mart Stores Inc. in the 181 weeks ended December 27, 2013 is shown here:

On a cumulative basis, the current default probabilities (shown in green) for Wal-Mart Stores Inc. range from 0.00% (after rounding) at 1 year to 1.04% at 10 years, up 0.08% from September 23 (shown in yellow).

Over the last decade, the 1 year (in blue) and 5 year default probabilities (in yellow) for Wal-Mart Stores Inc. have never exceeded 0.14% at any time, even during the heart of the 2006-2011 credit crisis. Note, however, that the five year default probabilities have been rising for some time.

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 five risk factors among the 28 factors listed by the Federal Reserve in its 2014 Comprehensive Capital Analysis and Review. These macro factors explain 44.5% of the variation in the default probability of Wal-Mart Stores Inc.:

  • Nominal gross domestic product
  • 3 month U.S. Treasury bill yield
  • 10 year U.S. Treasury yield
  • BBB-rated corporate bond yields
  • 1 year change in home prices

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 33 peers at these maturities:

1 month 33rd percentile, up 4 percentage points since September
1 year 27th percentile, up 7 percentage points
3 years 9th percentile, up 3 percentage points
5 years 6th percentile, up 3 percentage points
10 years 3rd percentile, unchanged and the 2nd lowest of the peer group

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 98th 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, however.


Before reaching any conclusions about the “investment grade” status of Wal-Mart Stores Inc., we first look at more data from the bond market.  We exclusively use data from January 22, 2014.  We first look at a comparison of credit spreads on traded Wal-Mart Stores Inc. bonds versus traded bonds in the same “retail” sector:

Wal-Mart trades well below the median of the peer group, although the number of bonds traded for the peer group is small.  We next look at the comparison of matched-maturity default probabilities for Wal-Mart versus the same peer group for bonds traded January 22:

It is hard to draw conclusions from this graph because of the small number of traded bonds.  Accordingly we turn to the larger data set of traded bonds among firms with a legacy rating consistent with the older definition of “investment grade.”  This graph shows that Wal-Mart is trading at the bottom range (i.e. the best levels) of investment grade firms:

Matched-maturity default probabilities are also very low compared to the matched-maturity default probabilities on investment grade bonds traded January 22:

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.

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.

Author’s Note

Regular readers of these notes are aware that we generally do not list the major news headlines relevant to the firm in question. We believe that other authors on SeekingAlpha, Yahoo, at The New York Times, The Financial Times, and the Wall Street Journal do a fine job of this.  Our omission of those headlines is intentional.  Similarly, to argue that a specific news event is more important than all other news events in the outlook for the firm is something we again believe is inappropriate for this author.  Our focus is on current bond prices, credit spreads, and default probabilities, key statistics that we feel are critical for both fixed income and equity investors.



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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