**The potential economic impacts of the novel coronavirus have been likened to the Great Depression and a more severe version of the 2008 Great Financial Crisis. US dollar-denominated corporate bond spreads have widened in recent weeks, but even so: do they adequately compensate investors for the increased credit risks they are running?**

**Alan Cubbon develops a quantitative framework that provides one way for this question to be tackled. A number of assumptions are made regarding the market at a future date, but these can be varied to see how sensitive the final results are to these inputs.**

Let’s imagine that we’re interested in investing in 5-year corporate bonds over a horizon of the next twelve months. We can obtain from the market the current average yields and spreads of bonds grouped according to their broad rating categories of AAA, AA and so on down to CCC – C. For the sake of simplicity let’s assume these yields and spreads will stay flat and unchanged over our investment horizon.

In the table below of market values from the end of April the yield for a 5-year Treasury bond of 0.29% is taken from the US Treasury website. The Treasury spreads are derived from JP Morgan indices using median values across bonds with maturities close to 5 years. For investment grade spreads I used the JP Morgan US Liquid Index (JULI); for high yield bonds the spreads are based on JPM’s Global High Yield Bond Index, using dollar-denominated bonds issued by US-based companies. For B and CCC-rated bonds the spread values should be taken as illustrative, as the range of values is quite wide, which is unsurprising given market conditions. For all other ratings the ranges are much tighter, with the median values close to the averages.

**US Treasury yields (%) and corporate bond spreads (bp) as of 30 ^{th} June**

5y UST | AAA | AA | A | BBB | BB | B | CCC-C |

0.29% | 39 | 67 | 80 | 163 | 481 | 638 | 1051 |

**Sources**: Spreads based on data from JP Morgan. Govt. bond yield from the US Treasury, https://www.treasury.gov.

So, as of 30^{th} April if we buy an average 5-year A-rated bond for example, we get a spread of 80 basis points. If at our horizon a year later the bond is still rated A, then given our assumption on flat and unchanging spreads, we know we’ll get a return of 1.09%. However, if the bond has been upgraded to AA in the course of the year then its spread has narrowed by 13 bp and our return goes up to 1.61%. On the other hand, if the bond has been downgraded to BBB then its spread has widened by 83 bp and our return is -2.16%. And we can calculate the returns for all other possible final ratings. We can also calculate the return we get if the bond defaults by making another assumption about a bond’s recovery rate. I’ve initially assumed a rate of 35%, representing the present value of future repayments. I’ve also assumed that on average a defaulted bond would still receive half its annual initial yield as a proxy for its coupon. If we now assign probabilities to our AA bond being in each rating state at the end of the year, including default, then we can calculate the expected return of that bond. And of course we can do this for a bond of any initial rating. With a little bit of algebra we can also calculate how far spreads would have to widen out, to “breakeven” levels, before we’d have been better off holding a Treasury bond of the same maturity.

The probabilities of a bond with initial rating of X ending up with a rating of Y a year later make up rating transition matrices that are widely published by the main rating agencies. These matrices may be based on historical transition rates; or they may be forward-looking, based on the agency’s own economic forecasts.

I found on the internet two transition matrices published by Moody’s. They’re quite old but they nicely suit our purposes of depicting different regimes. One was a long-term average matrix based on transitions from 1920 to 1996; the other was the transition matrix experienced in the credit crunch year of 2008. I compressed these to eight-state matrices by averaging over AA+, AA and AA- to come up with values for a broad AA category, etc., and ignored transitions to “withdrawn rating”. The CCC category also covers CC and C-rated bonds. The charts and tables below show the spot and breakeven spreads for each credit rating, plugging each transition matrix into the framework described above. This allows us to compare the curves in “normal” times with when the credit market is extremely stressed: such as in the 2008 crisis, and as may well be the case again for this year.

** ****Spot and breakeven spread curves**

**Sources**: Transition matrices based on Moody’s data.

For me, two things stand out. The first is the low impact on the high-quality end of the spread curves of substituting the long-term average transition matrix with the 2008 crisis version. If our portfolio consists of a single AAA-rated bond, and that bond is unluckily downgraded, then of course our performance will take a hit. But if we hold a diverse portfolio of bonds, such that the transitions we experience are in line with the expectations in the matrix, then we could expect our performance in a 2008-like scenario to be not much different from any other year.

The second thing that stands out is the contrast at the very high-yield end of the curve. Based on the input spreads and 2008 rating transition matrix, CCC spreads actually need to *tighten* before we’d be better off than simply holding Treasury bonds. How does 2008 compare to today? The effects of COVID-19 on the markets are of course still unfolding, but several commentators are predicting that default rates could well be worse in 2020 or 2021 than in 2008.

Therefore: either high yield spreads are too low, or these forecasts of default rates are overblown, right? How to make sense of this? Recall that I chose to use the median spreads for each rating category. If instead I’d calculated the average spreads, based on weighting each bond equally, I’d have obtained significantly higher values: a CCC spread of 1835 bp instead of 1081 bp. This average is skewed by several bonds with very high spreads, many of which are issued by companies in the energy sector. The curves using these spreads with the same transition matrices as before are shown in the chart below, together with the equally-weighted average spread levels for each rating.

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**The curves based on average spreads**

AAA | AA | A | BBB | BB | B | CCC-C | |

Median spreads, bp | 39 | 67 | 80 | 163 | 481 | 638 | 1051 |

Average spreads, bp | 40 | 64 | 94 | 190 | 509 | 750 | 1835 |

**Source**: Spreads based on data from JP Morgan.

So if your portfolio more closely reflected the equally-weighted market, including the high-spread bonds, then even with the 2008 transition matrix you’d still have a positive, though small, cushion at the high yield end. The world makes more sense again. By taking the median spread I was effectively screening out the effect of these bonds: and it could be the case that I was being overly pessimistic in using a transition matrix that had not been similarly adjusted. But I wanted to make a point. Which is: if you’re a high-yield portfolio manager you should look carefully at the spreads you’re receiving against a backdrop of appropriate transition expectations. There’s not a great deal of room to play in.

Because of the uncertainties around these spread values and default rates some sensitivity analysis is in order. Staying with average spreads, the table below shows the breakeven spread cushions for CCC-rated bonds for different combinations of default and recovery rates. The values along the top of the box represent percentage changes to the 2008 annual default rate of 25.5% for CCCs. All other transition probabilities have been scaled proportionately from the original 2008 matrix. The box is around the value found in the scenario shown in the right-hand chart above.

**CCC breakeven spread cushions based on different recovery and default rates**

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As discussed above there is a wide range of spreads across CCC bonds, even with a similar maturity close to 5 years. The table below shows the CCC cushions using different starting spot spreads, all other input values unchanged from the scenario above using the average spread values.

** ****CCC breakeven spread cushions based on different spot values**

The purpose of this blog is not to portray any type of credit as attractive or otherwise: it’s simply to argue that it is useful to have a quantitative framework such that the merits of credit can be explored. The different transition matrices also provide a historical context against which our current situation can be compared. High spreads could appear attractive, but the increased default risks could mean that benefiting fully from those spreads is unlikely.

In addition to the risks of downgrade or default there are other ways in which high spreads, such as index providers may publish, can fail to translate into equivalent returns. To list a few:

- Market volatility can intrude. Investors may not be able to achieve the spreads quoted by index providers if it takes time to use an investor’s cash injection to purchase bonds for their portfolio, and during that time spreads periodically fall.
- A bond’s yield and spread values are calculated with an in-built assumption that all cashflows can be reinvested at that yield for the remaining life of the bond. In practice, with typical upward sloping term structures for both yields and spreads, available reinvestment rates for shorter periods can be significantly lower.
- Index providers often quote yields and spreads at mid, and rarely include transaction costs when calculating index returns. These costs can of course can be especially high when transacting in less liquid high-yield bonds. The most diligent index-follower can easily end up under-performing as a result.
- How accurately do the spreads reflect your portfolio? It’s clearly desirable to the calculations that the spot spreads are as accurate as possible, but as mentioned this is not always straightforward. Index providers have to strike a balance between including lots of bonds to achieve diversity, and ensuring those bonds are sufficiently liquid. In stressed markets that balance shifts. Even if you can accurately observe the current spread of a bond, you can’t know for sure how an upgrade or downgrade would impact the spread for that individual bond. Such “noise” can be reduced by applying the framework to a diverse portfolio of bonds, but even then care needs to be taken. For example, is the portfolio overly skewed to one sector, such as energy? As highlighted earlier this sector has its own particular set of issues, and is behaving differently from the rest of the market.

If I seem to be suddenly undermining the usefulness of the framework described above then that’s not my intention. In fact quite the contrary. The heightened risks in credit, especially at the high yield end of the spectrum, surely means that any simple tools which allow those risks to be explored are today more valuable than ever.