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 S&P Global Market Intelligence.

Risk vs. spread
We have never emphasized historical yield spreads in our valuation work. The mere fact that the U.S. high-yield spread exceeds its historical average does not prove that the asset class is cheap. If risk is greater than average, then the risk premium should be greater than average. What matters is whether the spread is greater than it ought to be, in light of the current risk level, as measured by the factors that explain the spread's variance over time. This is the reasoning behind our high-yield Fair Value econometric model, as described in "Fair Value update and methodology review" (LCD News, Jan. 24, 2018).

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Present market conditions, however, put forward a reason to compare the ICE BofA US High Yield Index's current option-adjusted spread, or OAS, with its historical average. The Federal Reserve's unprecedentedly aggressive intervention in the credit markets is overpowering traditional valuation drivers. Under these conditions, the very categories "rich" and "cheap" are superseded by "what the central bank wants the risk premium to be."

Still, there are certain questions one would ideally like to answer about present spreads:

• Is it possible to quantify the impact of Federal Reserve intervention on the high-yield spread? Put another way, what would the spread currently be if not for that intervention?

• At a minimum, is it possible to establish whether investors are currently being compensated at all for the fact that the U.S. economy is in recession? (We consider it a safe bet that the National Bureau of Economic Research will ultimately determine that the recession that began in February 2020 did not end as early as July 2020, given the 11.1% headline unemployment rate reported for June 2020.)

Before attempting to answer these two questions, we must address major problems with the customary method of calculating the historical average high-yield spread.

Flaws in traditional average-spread calculation
The usual method of calculating the historical average high-yield spread versus Treasuries is simply to collect all observations since inception (monthly, typically) and divide by the number of observations. As an alternative to that calculation of the mean, some analysts focus on the median of the sample. There are just a few small problems with these approaches.

To begin with, much statistical analysis that involves averages contains the hidden assumption that the observation sample is normally distributed. In his online book "Introduction to Normal Distributions" (note 1), David M. Land lists several characteristics of a normal distribution, including the following (we quote verbatim):

• Normal distributions are symmetric around their mean.
• The mean, median, and mode of a normal distribution are equal.
• Normal distributions are denser in the center and less dense in the tails.

The visual realization of these points is the familiar bell-shaped curve:

Contrast this image with a histogram of the monthly OAS history, from the December 1996 introduction of that metric into the ICE BofA US High Yield Index series through the end of 2019:

"Symmetry" is certainly not an adjective that this graphic brings to mind. The distribution's mode (represented by the tallest bar), the mean and the median all fall in different 100-basis-point bins. Such characteristics constitute warnings to exercise care in drawing analytical conclusions about an average derived from this distribution.

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Statistical theory aside, a very practical problem with the conventionally calculated historical average high-yield spread arises from the fact that it does not represent what is historically "normal" in a nontechnical sense. The nature of this difficulty is captured by an old joke: "I have one foot in a bucket of boiling water and the other foot in a bucket of ice water. On average, I feel fine."

High-yield spreads are far wider during recessions than during nonrecessionary periods. The average is an intermediate point between those economic-condition-dependent levels, rather than an indication of where spreads are under mythical "typical" conditions. It sheds no light to compare the spread at a given time to what the spread theoretically would be in a nonexistent state of the world, i.e., when the economy is neither in nor out of recession.

Identifying genuinely useful reference points
To avoid spurious comparisons of current and historical spreads, we divide the 277-month history into a nonrecession subsample of 251 months and a recessionary history of 26 months. We treat the recessionary months of February–June 2020 as part of the holdout sample, instead of including it in the test sample, even though including it would raise the test sample's count to the canonical minimum of 30 required for a scientific sample (note 2). Inclusion is precluded by our objective of estimating the impact of extraordinary Federal Reserve intervention on spreads in the current, recessionary period.

The table below confirms that nonrecessionary and recessionary periods are distinct regimes, with widely different mean and median spreads. For the record, the respective means of 500 and 1,070 bps are statistically different at the 99.9% confidence level. Some readers may be less than thunderstruck, however, by the difference between the nonrecessionary mean of 500 bps and the 553 mean for all months. Is it really essential, in that light, to benchmark spreads in non-recessionary periods against a strictly nonrecessionary mean?

Another page remains to be turned, however. Subdividing the spread history into its nonrecession and recession components is not sufficient to identify valid reference points for assessing the spread at a point in time. In a substantial number of months, the high-yield spread has been skewed by an exceptionally widespread on a very large industry in the high-yield index. This has happened from time to time when severe drops in crude oil prices have ballooned energy's OAS to levels far greater than the overall index's. Similarly, the telecommunications subindex widened dramatically, relative to the overall high-yield index, around the most recent turn of the century, when a wave of highly speculative underwriting culminated in the "tech wreck." Nonrecessionary spreads outside of these unusual episodes are materially tighter than in the nonrecessionary periods as a whole.

To refine further our calculation of historical average spreads in both the nonrecessionary and recessionary periods, we removed months in which either the energy or the telecommunications subindex's OAS exceeded the ICE BofA US High Yield Index's OAS by 250 bps or more. The maximum excesses over the all-industry spreads were 876 bps for Energy (January 2016) and 1,677 bps for telecommunications (June 2002). In those months, energy and telecommunications single-handedly inflated the overall high-yield spread by 102 bps and 184 bps, respectively. For months in which the threshold of a 250-bps excess was met, energy's largest share of the total index's market value was 16.14% (July 2018). For telecommunications, it was 19.78% (January 2001).

This refinement in our calculations reduces the nonrecessionary mean to 464 bps, versus the raw figure of 553 bps for all months. At 89 bps, the difference between the two figures should persuade readers who were initially skeptical about the value of refining the raw number. Note as well the substantial narrowing of the mean-median differential from 553 – 487 = 66 bps to 464 – 434 = 30 bps as a result of our various refinements. That narrowing makes the distribution more closely resemble the desired bell-shaped curve.

Adjusting for industry skewing increases the recessionary subsample's mean to 1,165 bps from 1,070 bps before that adjustment. This is the result of eliminating the entire 2001 recession from the subsample. The telecommunications OAS exceeded the ICE BofA US High Yield Index's by 250 bps or more in all eight months of that economic downturn. As noted above, we also exclude the 2020 recession from our test sample to reserve that period for our holdout sample. What remains is solely the extremely severe Great Recession of January 2008-June 2009.

Assessing the Federal Reserve's impact
Let us address first the easier of the two questions we posed at the beginning of this piece. We can confirm that as of July 10, high-yield investors are receiving some compensation for being in a recession, even if the high-yield spread is far less than it would be absent the Federal Reserve's extraordinary support of the credit markets. At 614 bps, the ICE BofA US High Yield Index's July 10 OAS exceeds the nonrecessionary, ex-energy and telecom skewing mean of 464 bps by 150 bps. That divergence slightly exceeds one standard deviation (146 bps). The prevailing risk premium, in short, is well above the historical average for nonrecessionary periods, properly calculated.

On the other hand, the July 10 high-yield spread is 551 bps below the mean for recessionary periods, properly calculated, i.e., 1,165 bps. That differential is greater than one standard deviation (455 bps). By this reckoning, the Federal Reserve's unprecedentedly aggressive intervention is suppressing the high-yield risk premium to an almost alarming extent.

Unfortunately, putting such a precise number on the Federal Reserve's impact is far from cut-and-dried. As already noted, our analysis limits the recession subsample to the Great Recession. It is debatable whether the current recession is as severe, less severe or more severe than that one. (The above-referenced unemployment rate is not the sole determinant.) One could also argue that the median, which is 102 bps lower than the mean, at 1,063 bps, is a better reference point for recessions because the mean is skewed by a few months of astronomical spreads within a small sample of months. (The monthly peak was 1,978 bps in November 2008.) A final complication is that in April 2008, shortly after the beginning of the Great Recession, the high-yield OAS dipped to 648 bps, just 34 bps greater than the July 10 level. Quantitative easing, an intervention much less powerful than the Federal Reserve's recent actions, did not commence until November 2018.

For all these reasons, a definitive answer to question No. 1 above remains elusive. We feel comfortable, however, with the answer to question No. 2 provided by the forgoing analysis. This piece also contributes to the debate by substantially improving upon calculations of the high-yield market's historical average spread, a reference point for attempting to pin down the impact of the current Federal Reserve intervention.

Research assistance by Lu Jiang and Zhiyuan Mei.

ICE BofA Index System data is used by permission. Copyright © 2020 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. http://onlinestatbook.com/2/normal_distribution/intro.html#:~:text=The%20mean%2C%20median%2C%20and%20mode,the%20standard%20deviation%20(%CF%83).

2. https://www.researchgate.net/post/What_is_the_rationale_behind_the_magic_number_30_in_statistics

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