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Corporate Bond Default Loss Risk Quantification Made Simple

corporate bond example
Corporate Bond Default Loss Risk Quantification Made Simple
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corporate bond exampleIn my previous article, I presented nine dynamics of corporate bond default loss risk. In this article, I will use some of the data in my previous article to derive what default loss risk percentages should be applied in evaluating specific bonds (i.e., bonds with different credit ratings, years to maturity or call, and lien [seniority/subordination] positioning). Near the end of this article, I will present a default loss risk quantification system that is both simple and relatively accurate.

To see a list of high yielding CDs go here.

Fixing the Data Anomalies

You may remember the following data from my previous article. You may also remember me saying: “There are some data anomalies in the table that you should ignore. For instance, AAA bonds are not less likely to default after year 13; and Caa-C bonds are not totally immune from default in years 18-20. Anomalies like these occur because of limited sample sizes.”

Corp Bonds Part 3 Article - Chart 1

Below is an enhanced version of the above table. In this enhanced version, the data has been normalized so data that was, seemingly, anomalously high or low is no longer anomalously high or low. I used a variety of techniques and best judgment to normalize the data. The end result cannot be and is not perfect; but each piece of data now makes sense in context of all other pieces of data, and the revised data is strongly similar, on average, to the original data―both overall and within each credit rating bucket.

Corp Bonds Part 3 Article - Chart 2

You may be wondering why we are using data based on Moody’s data versus data based on S&P data. Although S&P rates more corporate bonds, Moody’s available explanation of the methodology used to bucket and calculate related data is far stronger. In using Moody’s data as the basis, we have much greater confidence that the data represents exactly what we think it represents.

A Cumulative View

The tables above reflect default chances within individual years. The table below presents the normalized data on a cumulative basis. As you can see in the table, an Aaa-rated bond with 1 year to maturity or call has a 0.01% chance of defaulting over its remaining life, a Baa-rated bond with 10 years to maturity or call has a 4.8% chance of defaulting over its remaining life, and a Caa-to-C-rated bond with 20 years to maturity or call has an 81.93% chance of defaulting over its remaining life. We need this data to construct our default loss risk quantification system.

Corp Bonds Part 3 Article - Chart 3

Average Life-Expectancy

When, for example, you purchase a 10-year non-callable Baa-rated bond, on average, you do not own a 10-year bond. Instead, you own a 9.8-year bond. This is because the bond may default prior to maturity. The following table is based on the normalized data above. It shows the average life-expectancy of a bond given its credit rating and years to maturity or call. In creating this table, I needed to consider (1) the percentage chance that the bond will make it to maturity or call, (2) the years to maturity or call, (3) the percentage chance that the bond will not make it to maturity or call, and (4) the default percentages for each year of the bond’s potential life. In doing the math, I assumed that all defaults occur at mid-year of the default year; so the figures are not exact. An exact calculation was not possible.

Corp Bonds Part 3 Article - Chart 4

In evaluating a bond in comparison to other investments, view it as if it has a maturity or call date that matches one of the average life-expectancies listed above. Better yet, when applicable, use the weighted-average of two figures. For example, your bond may be non-callable and have 9.25 years to maturity. In this case, you can take 75% times the 9-year figure and 25% times the 10-year figure and add the two results together. Your bond will probably make it all the way to maturity or call, but it may not. The average experience is the best experience to use in comparisons.

Default Rates in Terms of Average Life-Expectancy

The data in the table below shows the amount of default loss risk per year of average life-expectancy. If, theoretically, you bought a trillion 10-year non-callable Baa-rated bonds, on average, your bonds would have a life of 9.8 years. Your bonds would return full par value 95.2% of the time. The other 4.8% of the time they would default. The table below reflects this 4.8% spread out evenly over the average years of ownership. As you can see in the table, assuming a 100% loss upon default (which we will not do), on average, you would lose 0.49% of par value per year due to defaults. We now not only know the average life-expectancy for each bond type, we also know the average annualized default loss risk for each bond type.

Corp Bonds Part 3 Article - Chart 5

Defaulted Debt Loss Rates

As explained in my previous article, you usually do not lose 100% of par value when a bond defaults. Below is a table showing defaulted debt loss rates by lien [seniority/subordination] positioning. The data is dollar-weighted versus issuer-weighted. All other things equal, it is best to use dollar-weighted data versus issuer-weighted data because dollar-weighted data reflects the fact that you are more likely to own larger issues than smaller issues. Also, in this case, using the dollar-weighted data is more conservative than using the issuer-weighted data because the dollar-weighted figures are higher overall.

Corp Bonds Part 3 Article - Chart 6

A Simple Default Loss Risk Quantification System

The easiest way to show how the default loss risk quantification system works is by example. Pretend you are thinking of purchasing a 10-year non-callable Baa2-rated senior unsecured bond. (Senior unsecured bonds are the most common type of corporate bond.) Pretend that the annual yield-to-maturity (YTM) for this bond is 5%. Using the tables above, you can see that, for investment comparison purposes, you should view the bond as having a maturity of 9.8 years. Also using the tables above, you can see that, over the course of the average life-expectancy of 9.8 years, the bond has an average default rate of 0.49% per year; and you can see that senior unsecured bonds have a defaulted debt loss rate (the opposite of recovery rate) of 62.2%.

0.49% x 62.2% = 0.305% and 5% – 0.305% = 4.695%

0.305% is your annualized default loss risk. 4.695% is your default-loss-risk-adjusted YTM. You should never evaluate a corporate bond without adjusting for default loss risk. If the bond you are evaluating is rated Baa1 versus Baa2, you can use the A-rated average default rate per life-expectancy year of 0.24% and Baa-rated figure of 0.49% to estimate the Baa1 rate.

0.24% * 1/3 = 0.08%, 0.49% * 2/3 = 0.33%, and 0.08% + 0.33% = 0.41%

Since there are three credit quality grade steps from Baa2 to A2 (i.e., Baa1, A3, and A2) and Baa1 is the first of these steps, 0.24% gets a weighting of 1/3 and 0.49% gets a weighting of 2/3. Baa1 is closer to Baa2 than it is to A2, and the weightings reflect this. A more accurate way of estimating the Baa1 rate is by creating a graph with the data from Aaa to Caa-C for 10-years-to-maturity with a trend line. You can quickly create such a graph in Excel; but, sometimes, none of the trend lines offered by Excel provide a good answer, so you need to hand draw the trend line. In this case, none of the trend lines offered by Excel provide a good answer; but it matters very little because the correct trend line is nearly a straight line between the A and Baa data points. A trend line technique can be used to get more accurate average life-expectancy and non-whole-year (e.g., 9.25, 11.4, 6.7…) figures too.

The results provided by the system described above are subject to adjustments. For instance, a bond may be rated Baa2; but Moody’s (or another rating service) says it has positive outlook. (Negative outlooks are significantly more common than positive outlooks.) Also, your research and analysis may indicate that the bond should be rated lower or higher. Also, the specific terms and conditions of the bond may warrant using a different defaulted debt loss rate.

Although I included Caa-C bonds in this analysis, the system above is not granular enough to evaluate bonds rated below B2 well. (Caa-C includes non-defaulted bonds with ratings of Caa1, Caa2, Caa3, Ca, and C.) Regardless, it is best to leave investing in lower-rated junk bonds to professional bond specialists, as determining the value of lower-rated junk bonds is particularly difficult. If you are not a professional bond specialist and one of your bonds falls to a rating below B2, it may be good for you to continue to own the bond; but buying bonds currently rated below B2 is a different matter.

Conclusion

Currently, if you will only be holding a bond for a couple of years or less, the system above is not for you. Not without adjustment. As shown in my previous article, default rates and defaulted debt loss rates vary greatly over time. It appears as if default rates and defaulted debt loss rates will be low for the next couple of years. Beyond the next couple of years, it is much more difficult to predict what default rates and defaulted debt loss rates will be. No one knows when the next wave of heavy default losses will occur. When evaluating bonds for longer-term ownership, it is good to ignore current conditions and focus, instead, on historical default loss rates.

(Comments are desired, but I do not guarantee their publication. If your comment[s] indicates that you did not read and genuinely consider the all of the article’s contents, I may not publish it; or I may remove it. You do not need to agree; but do not be derogatory. The comment section is meant for legitimate questions or concerns and well-intended discussion.)

About Kurt Shrout

Kurt has a BA and MA in Communication and over 20 years of business experience, almost always serving as a project or program manager, director, or consultant or as an analyst. He lived and worked in many different locations in the U.S., London, England, and Hong Kong. He has experience in at least 18 different industries and 31 different enterprises.

Although he was only 49, he essentially retired in 2008 and began spending a lot more time studying investing. His articles are largely written as a public service. They provide investors with a rare totally unbiased view of the investing landscape and often include unique analysis. You can read more of his articles by clicking here.

 

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