Fridson Monthly: Do default models explain spreads?

This commentary is written by Martin Fridson, a high-yield market veteran who is chief investment officer of Lehmann Livian Fridson Advisors LLC as well as a contributing analyst to Leveraged Commentary & Data.

In "What's the best financial ratio for HY analysis?" we documented a much weaker connection between standard financial ratios and high-yield bonds' risk premiums (spreads-versus-Treasurys) than many practitioners suppose. We want to be fair, however, to the proposition that high-yield issue pricing is driven by risks that can be quantified through rigorous, fundamentally based credit analysis. In other words, that analysts are spending their time wisely in creating financial spreadsheets with the goal of identifying the subset of bonds that are trading out of line with their fundamentals. Another motivation for this study is that if financial ratios do not truly have a bearing on high-yield spreads, investors should cast a skeptical eye on the "comparables" presented by underwriters in marketing a new issue with the intention of making the offering appear attractive.

MORE FRIDSON ON FINANCE: Tide may be turning on BB and CCC & Lower high-yield price moves

A valid response to our previous finding of a low correlation between financial ratios and spreads is that the spreads reflect factors other than the default risk captured by financial ratios. In particular, the variance in spreads arises partly from bonds' differing maturities and seniorities as well as differences in tradability (secondary market liquidity). Practitioners commonly relate liquidity to issue size and also to the total amount outstanding for all of the issuer's outstanding bonds.

To address the legitimate concern about non-default-risk components of spread, we designed our experiment as described below. Our concept was to isolate the default risk component by creating a test sample of bonds as uniform as feasible, with respect to seniority, liquidity and maturity. Once we normalized for those factors, we were able to test the extent to which rigorously constructed default risk models captured the spread variance among the issues in our sample. Details of our experimental design follow.

Normalizing for intervening factors

Our first step in creating a test sample was to minimize the impact of differences in the loss-given-default component of default risk by excluding from consideration all issues within the Jan. 31, 2022, ICE BofA US High Yield Index other than those classified as senior unsecured. To normalize for differences in liquidity, we drew our test sample from the ICE BofA US High Yield Index's largest issuers, as measured by the total face amount outstanding of all issues listed under a given ticker. To normalize for maturity differences, we began with the largest issuer and granted it representation in our sample if it had a bond maturing in 2028. That year was chosen based on the average maturity within the ICE BofA US High Yield Index, which was 6.39 years on our observation date. We then applied the following protocol:

* If the issuer had no bond outstanding in 2028, we selected an issue maturing in 2027 or 2029, if available.

* If the issuer had no bond maturing in the 2027-2009 range, we skipped it and proceeded to the next largest issuer.

* If the issuer had more than one qualifying issue, we selected the one with the largest face amount outstanding. We then moved on to the next largest issuer.

We proceeded in this manner until we collected a preliminary sample of 50 issues. From the preliminary sample, we eliminated nine bonds for which one or more of the four data items described in the next section were unavailable. Our test sample consequently consisted of 41 bonds of 41 unique issuers, matched exactly for seniority and as nearly as feasible for maturity and liquidity.

Data collection

Option-adjusted spread (OAS)

First, we collected the observation-date option-adjusted spread, or OAS, for each issue in our 50-bond preliminary sample. The pricing source was ICE Indices LLC. OAS was our dependent, or response, variable. We next collected data for three independent, or explanatory, variables:

Bloomberg One-Year Default Probability (DRSK)

Source: Bloomberg

Bloomberg describes its methodology as follows:

DRSK is a hybrid model in that it combines a statistical approach with a structural model. We use a logistic regression to estimate the probability of default events based on factors that best capture credit risk. But the factors are not purely relevant accounting ratios — one of the key factors is the distance to default, or DD, derived from a hybrid Merton-Black-Cox structural model.

(See note 1.)

DRSK's component factors are:

* Distance to default.

* Flag indicating that the issuer is a bank, if applicable.

* Return on assets.

* Non-performing loans, if applicable.

* Total operation cash flows/interest expenses.

Because DRSK is a percentage probability of default, the higher the score, the greater the default risk. DRSK is therefore expected to correlate positively with OAS.

Altman Z-score (AZS)

Source: Bloomberg

The Altman Z-score, or AZS, model employs the following financial ratios:

* Working capital/total assets.

* Retained earnings/total assets.

* Earnings before interest and taxes/total assets.

* Market value of equity/total liabilities.

* Sales/total assets.

Note that default may occur without the issuer entering bankruptcy proceedings, but investors consider default without bankruptcy a relevant risk. In this light, one might automatically expect AZS to be less closely correlated than DRSK with spreads.

AZS is scaled such that a score of less than 1.3 indicates likelihood of bankruptcy within two years, while a score of greater than 3 indicates non-likelihood of bankruptcy. That is, the higher the score, the lower the risk of default, so AZS is expected to correlate negatively with OAS.

Composite Rating

Source: ICE Indices LLC

The Composite Rating applies to issue ratings, as opposed to company ratings. It is derived from the ratings assigned by the major agencies, which address both default probability and loss given default, the combination of which constitutes default risk. The capture of both components of default risk contrasts with DRSK's focus on probability of default and AZS' on the probability of bankruptcy. Agency ratings take into account both financial ratios and such factors as assessments of business prospects, management capability and willingness, as opposed to ability, to meet financial obligations.

We converted the sample issues' Composite Ratings to numerical scores from lowest default risk (BB1=1) to highest default risk represented within our final sample (CC=10). (See note 2.) Based on this scaling, the higher the score, the greater the default risk, so Composite Rating is expected to correlate positively with OAS.

Sample description

Our description of the test sample in the table below emphasizes medians in view of the high impact on means of gross outliers in a population of just 41 issues. The top portion of the table provides insight into the liquidity of the 41 bonds that constitute our test sample, to the extent that liquidity is determined by amount outstanding. Amount outstanding per issue ranged from $1.2 billion to $3.5 billion. The median of about $1.5 billion compares with a mean of $725 million for the ICE BofA US High Yield Index as a whole. For amount outstanding per issuer, our sample's median of $4.350 billion compares with a mean of $1.598 billion for the total index.

The lower portion of the table provides medians and ranges for OAS and the three default risk models that potentially explain its variance. Note the wide OAS range, attributable largely to the sample's two lowest-rated issues, a CC at +4,073 basis points and a CCC3 at +1,208 bps. The median of +308 bps is much closer to the sample's low of +163 bps. DRSK similarly displays a wide range, skewed by highly risky outliers. The median of 0.3335% probability of default within one year lies much closer to the low of 0.0002% than the high of 12.63%. AZS' distribution is less skewed by outliers, with the median of 1.34 lying close to the midway point between the high of 5.39 and the low of -2.10. Of the 41 bonds in the sample, 26, or 63%, are deemed likely to default by virtue of AZS below 1.8. Composite Ratings range from the top of the speculative-grade range (BB1) to CC, just two steps up from Default (D). By letter grade, the distribution of issues is 19 BBs, 17 Bs, 5 CCCs and one CC. The median Composite Rating is B1.

Results

The table below details the explanatory variables' correlations (R) with OAS and also with one another. Keep in mind, absolute value rather than sign (+/-) is the key to understanding these results. As noted above, AZS is scaled in such a way that it is expected to correlate negatively with OAS. Therefore, an AZS correlation with OAS of, for example, -0.40 would indicate as strong a correlation as 0.40 for DRSK or for rating.

The top line conveys the table's key findings, namely, the explanatory variables' correlations (R) with individual issues' high-yield spreads, measured by OAS. DRSK shows a somewhat stronger correlation (0.28) than AZS (-0.14), but neither attains an absolute value of 0.30, below which correlations are considered weak. The observed correlations mean that as measured by R², DRSK and AZS explain just 7.8% and 2.0%, respectively, of the variance that remains in high-yield OAS after seniority, maturity and liquidity are taken out of the picture.

By contrast, Composite Rating's correlation of 0.61 is in the 0.3 to 0.7 range, considered moderate. Composite Ratings explain 37.2% of the OAS variance after normalization for seniority, maturity and liquidity. Even though many practitioners take pains to discredit credit ratings whenever they have the chance, this finding suggests that ratings have considerably more to do with high-yield risk premiums than sophisticated but purely quantitative models of default or bankruptcy probability, much less simplistic comparisons of issuers by any single financial ratio. Clearly, portfolio managers should not be swayed by a sell-side trader seeking to induce a trade who facilely argues, "It's silly that Bond X is trading wider than Bond Y even though its EBITDA coverage is higher." Indeed, the most appropriate response might be to hang up the phone.

The particularly loose fit between AZS and OAS is dramatized by one example from the underlying data. As it happens, the median AZS of 1.34 is associated with a CC bond that has an OAS of +4,073 bps. Just a bit higher, in the context of the full AZS range, at +1.46, is a BB2 bond with an OAS of +194 bps.

Investors can further glean from the table above that although DRSK and AZS are both quantitatively sophisticated models of the likelihood that an issuer will fail to meet its obligations, the two have only a moderate -0.42 correlation with each other. AZS has a very weak -0.13 correlation with the variable shown to be best at explaining OAS variance, i.e., Composite Rating. DRSK fares considerably better in that respect, with a moderate R of 0.48. Even so, one must ask why it would make sense to rely on a metric that resembles the one with the greatest explanatory power rather than the higher-R² metric itself.

The table below is structured like the preceding one but eliminates two outliers. They are the two lowest-rated bonds in our test sample, CCC3 Endo DAC 6% due June 30, 2028, and CC Diamond Sports Group 6.625% due Aug. 15, 2027. Those two issues have by far the widest spreads of the 41 bonds in the test sample, +4,073 bps and +1,208 bps, respectively. The next widest OAS in the group is +767 bps. The ENDP issue also stands out with a DRSK of 12.63; the next highest in the sample is 3.56. Excluding gross outliers from a correlation analysis may present a truer, or at least more useful, picture.

Based on just the 39 non-outliers in the test sample, DRSK's correlation rises to a moderate 0.47, from a weak 0.28 in the previous analysis. AZS remains deep in the weak zone at -0.17, strengthened only a bit from -0.14. Composite Rating moves to the strong correlation range at 0.74, from a moderate 0.61. DRSK and AZS continue to show a weak correlation (-0.22) with each other, despite addressing more or less the same question. DRSK's correlation with the best explainer of spreads, Composite Rating, remains in the moderate zone at 0.38, although down from 0.48 in the matrix derived from all 41 issues. AZS, on the other hand, shows essentially no correlation with Composite Rating (0.01), an even weaker reading than the -0.13 found in the previous test.

Interpretation

Analysts commonly conceive of a bond's total spread as a function of default probability, loss given default, and lesser tradability, or secondary market liquidity, than Treasury bonds. We have, in addition, documented a maturity factor. (See "Spread curve slope — positive? negative? both!") Even when maturity; liquidity, as measured by amount outstanding; and loss given default, as indicated by seniority within the capital structure, are largely removed from the picture, however, rigorously constructed measures of default probability explain little of the variance in spreads among high-yield bonds. Agency ratings, despite frequently being derided by practitioners, do a far better job of explaining the residual spread variance.

We attribute ratings' superior explanatory power to the agencies' consideration of qualitative factors not captured by metrics such as the Bloomberg One-Year Default Probability and the Altman Z-score. To be clear, we do not dispute those two metrics' empirically demonstrated accuracy in predicting default or bankruptcy. Rather, we infer from our results that high-yield bond spreads reflect factors beyond the four abovementioned ones. Ratings capture more of the total picture, but even when outliers are excluded, the R² for Composite Rating, at 54.8%, leaves almost half of the residual spread variance unexplained.

That result is no discredit to the agencies, which explicitly state that ratings are not intended to address market pricing but rather to focus on default risk and possibly covenant strength, a factor not previously discussed in this study. Spreads may also reflect such non-rating factors as which industries are in or out of favor with investors, oversupply or scarcity value of certain types of issues, and displeasure with private equity sponsors that are considered egregiously unfriendly to investors. In addition, spreads on certain bonds on certain dates may genuinely be misvalued.

One potential objection to our conclusions is that our empirical findings could be period-specific. It is conceivable that with the ICE BofA US High Yield Index's OAS at, say, +800 bps rather than its Jan. 31, 2022, level of +363 bps, DRSK and AZS would show higher correlations with OAS than we found. In our judgment, conducting our analysis in a different period probably would not have changed our basic conclusions. Given that we have been transparent in our experimental design, however, readers who suspect that period-specificity materially influenced our results can test that hypothesis by replicating our experiment on a different date.

Practitioners might also conjecture that our finding of superior explanatory power for ratings, vis-à-vis quantitative models, results from a self-fulfilling characteristic of ratings' influence over spreads. That is, institutional investors and mutual funds, but not another important class of high-yield valuation determiners, hedge funds, are typically constrained to some extent in their ability to buy or retain issues rated below certain thresholds, even if they believe some of those bonds are underrated.

We have found this effect tends to be overstated, as investment guidelines are generally more flexible than represented by practitioners who make this sort of argument. Still, without doing further analysis we cannot absolutely refute the conjecture that at least at the margin, bonds trade where they do because of their ratings. If that is so, a strong correlation between ratings and spreads should be expected, rather than surprising. Proponents of the self-fulfilling hypothesis are welcome to present evidence in support of it, rather than merely assert it. We may ourselves take up the topic in the future.

Conclusion

According to a common formulation of analysts, a high-yield bond's spread-versus-Treasuries consists of the sum of premiums for default probability, loss given default, and illiquidity. We find, however, that when loss given default and illiquidity are removed as much as possible from the equation, quantitative models of default probability explain little of the remaining variance in spreads. Agency ratings, despite frequently being denigrated by practitioners, display much greater explanatory power with respect to spreads, after normalizing for seniority and illiquidity. Nearly half of that residual spread, however, is attributable to factors that ratings are not intended to address.

A key implication of our findings is that high-yield investors should be wary of, and perhaps ignore altogether, simplistic claims about relative value that merely invoke one particular financial ratio. This is so even if some otherwise well-informed analysts describe the cited ratio, e.g., total debt/EBITDA, free cash flow, as the "gold standard" for measuring credit risk.

Research assistance by Tinglan Li and Christopher Robinson.

ICE BofA Index System data is used by permission. Copyright © 2022 ICE Data Services. The use of the above in no way implies that ICE Data Services or any of its affiliates endorses the views or interpretation or the use of such information or acts as any endorsement of Lehmann Livian Fridson Advisors LLC's use of such information. The information is provided "as is" and none of ICE Data Services or any of its affiliates warrants the accuracy or completeness of the information.

Notes

1. Mario Bondioli, Martin Goldberg, Nan Hu, Chengrui Li, Olfa Maalaoui, and Harvey Stein, The Bloomberg Corporate Default Risk Model (DRSK) for Public Firms, Quantitative Risk Analytics, Bloomberg LP, March 2021, p. 9.
2. Default risk does not increase in a linear fashion as ratings descend. Therefore, a refinement of our methodology would assign scores to the rating categories based on their historical default rates. (Because our sample includes only senior unsecured bonds and the vast majority of issues are rated CCC or lower by the time they default, such a scheme would not require further refinement for loss given default.) We have not found this sort of exercise especially productive in the past, but researchers seeking to build on the present research could pursue the idea.