Recent Posts

Wednesday, November 25, 2015

Primer: What Is The Fair Value Of A Credit Spread?

The valuation of corporate bonds is difficult because the fair value of a corporate bond is driven by two sets of prices: the default risk free curve (usually defined by the bonds of the central government of that currency), and the spread of the corporate bond over that curve. When we look at investment grade corporate bonds, we are usually interested in the movements of the spread; the movement of the risk-free curve is the domain of interest rate analysts. For bonds trading with low spreads, the spread is equal to the expected annualized default loss rate for the bond plus some form of a liquidity premium.

It should be noted that the valuation of corporate bonds is a complicated business; I am only interested in discussing the fundamentals which are applied to generic bonds. Some example complications are given below.
  • Many corporate bonds are callable, which means that the issuer can pay them off ahead of their nominal maturity date (based on pre-defined conditions, such as the need to pay a premium). This is an option embedded within the bond structure, which affects pricing. The fact that corporate bonds tended to be callable led to a total return underperformance of government bonds during the post-1980 bond bull market. This makes it hard to judge the relative attractiveness of corporate bonds based on historical index performance.
  • Taxes can affect pricing, most notably in the U.S. municipal market. Since these bonds are not taxable for local investors, they are willing to buy the bonds at yields less than Treasury bonds. This makes municipal bonds utterly unattractive to investors without such a tax incentive, such as foreign investors. As a result, the municipal market is largely isolated and prone to mis-pricing.

Furthermore, bonds that are seen as having a high probability of default will trade on a quite different basis than I am assuming here. For an issuer that is likely to default, its bonds trade near their expected recovery rate in a default scenario. This means that all of the bonds that are at the same level of seniority may have the same price, regardless of their maturity. Since a bond with a short maturity has a low interest rate sensitivity, the bond yield for a shorter maturity bond has to be much higher than a longer maturity bond if both are trading well below par. This creates the distinctive “inverted yield curve,” which is characteristic of distressed issuers (and which is mistakenly applied to government bonds when the government yield curve mildly inverts ahead of a recession).

Fair Value As A Risk Premium

We could imagine a situation is that we could have a generic 10-year corporate bond trading with a yield of 5.50% (issued by the Acme Corporation), while the 10-year Treasury yield is 4%; both bonds have no embedded options, and are assumed to be trading at par ($100). The 150 basis point (1.5%) yield advantage of the corporate bond is its spread.

The fair value of the spread can be defined as:
(Fair Value) = (Annualised expected default loss) + (liquidity premium).
Unfortunately, the right hand side of the equation consists of two terms, neither of which can be directly measured. In practice, we need to model of the terms, and then the other can be inferred from observed market prices.

If we temporarily assume that the liquidity premium is zero, and the observed market yield for the Acme bond is equal to fair value, we see that the annualised expected default loss is 1.5%. This could correspond to any number of scenarios, such as:
  • each year (over the next 10 years), there is a 1.5% chance that there will be default in which the salvage value of the bond is $0 (that is, 100% credit losses);
  • each year (over the next 10 years), there is a 3% chance that there will be a default in which the salvage value of the bond is $50 (that is, 50% credit losses).
In other words, there can be a low probability of high losses, or a higher probability of mild losses. Since a common exercise is to use corporate spreads to infer implied default probabilities, this shows why analysts need to fix an assumed recovery rate to generate the default probability. The typical assumption is to round off  historical default recovery rates.

(An advanced reader will note that I am discussing what is known as “risk neutral probabilities,” in my discussion. If someone is averse to taking risks, the fact that there is uncertainty in the payments will raise the required spread on the corporate bond in order for it to be equally attractive as a default risk free bond. Given the uncertainties involved, it is hard to worry about this detail. The only implication is that “true” default probabilities are slightly lower than what is implied by these calculations, but the probabilities involved are generally quite low to begin with.)

For bonds that are at the weaker end of the investment grade spectrum, we can get away with assuming that the “liquidity premium” is zero, and we can just assume that the spread is proportional to the probability of default. However, this is not helpful for high grade bonds which are bankruptcy remote. (Notable examples include German Pfandbriefe, Canadian provincial bonds, or bonds with guarantees by the central government, such as Ginnie Mae bonds in the United State, or Canada Mortgage Bonds in Canada.) For these high-grade bonds, the spreads are typically not very high (often 20-40 basis points), but even so, the spread is much higher than what the historical default experience would suggest is reasonable. For these bonds, one could probably assume that the entire spread consists of the “liquidity premium,” and we could round the expected probability of default to zero.

Why is this liquidity premium non-zero?
  • Wider bid-offer spreads makes these bonds less attractive than government benchmarks.
  • Since these markets are typically not backstopped by central bank operations, there is no guarantee of market liquidity. Under this interpretation, the liquidity premium is not really the expected loss based on default by the issuer, rather it is the expected loss as the result of having an inability to deal in the bonds during the crisis.
  • Financing costs matter – see below.
Assuming that you agree with my characterisation of the liquidity premium, one way of extracting it from market data is to assume that the default rate is zero for certain high grade components of the market, and then the default risk explains the premium of other bonds over that high grade benchmark.


It is possible to calculate the spread of a corporate bond versus the swap curve, instead of the government curve. In fact, the calculation is easier, as the government bond curve is poorly defined, as government bonds can be relatively cheap or expensive versus a fitted curve. Although such a spread is reasonable to work with, we technically should not use it to infer a default probability.

The reason for this is that the spread of a corporate bond versus the swap curve represent an apples-to-oranges comparison. A corporate bond investment requires an investment of capital, as does the purchase of a Treasury bond. Conversely, a standard swap starts out with a Net Present Value of $0, and so it does not represent a capitalised purchase of anything.

(Note: The use of Credit Default Swaps (CDS) makes it easier to infer default probabilities (since their payoff is based solely upon the event of default). However, relating CDS spreads to corporate bond spreads requires discussion of funding costs, and is beyond the scope of this article.)

Alternative View: Funding Costs

A more sophisticated method to look at corporate bond valuation is to look at the cost of funding a position in the bonds. Although this is of great practical importance, it does not answer the question of what the fair value of the corporate spread should be.

Let us imagine that there is a 10-year corporate bond that trades 150 basis points above the 10-year swap rate, yet it is possible to borrow against the bond short term at LIBOR + 20 basis points. Such a situation would be extremely attractive to many market participants. They would:
  • Buy the bond, and enter into an interest rate swap where they pay the fixed rate, and receive LIBOR. The net effect of the package is to create a synthetic floating-rate bond that pays LIBOR + 150 basis points.
  • Borrow as much as possible at LIBOR+20 basis points to fund the position.
Since this would be a popular trade, the spread on the corporate bond would be reduced by the buying pressure, while the funding cost increased.

We can alternatively describe the fair value of a corporate bond as follows:
(Fair value spread) = (Expected financing spread over the lifetime of the bond).
Using this formulation, we can see why regulatory changes that affect the ability of market participants to fund corporate bond positions matter a lot for corporate bond valuation. Anything that raises funding costs will feed through into corporate spreads.

A reasonable person would say that this crazy. Even though the funding cost for three months is currently LIBOR + 20 basis points, that tells us nothing about the future funding costs for the remaining 9¾ years of the bond’s lifetime. The 150 basis point spread on the bond may reflect a reasonable expectation that future funding costs will be higher.

That reasonable person would be right, but that does not really matter. As anyone familiar with Hyman Minsky’s writings would realise, the markets have a tendency to extrapolate current funding conditions into the future as far as the eye can see. This is why the business cycle is unlikely to be abolished any time soon.

Viewing corporate bonds spreads as being reflective of funding costs is realistic, and is useful if you are discussing technical factors within the spread market (particularly for bankruptcy-remote high grade issuers). However, default risks are the fundamental factor that should be driving funding cost differentials.


A corporate bond spread should compensate investors for the default risk associated with the bond. However, for high-grade bonds, bankruptcy odds are so low that spreads reflect technical factors – such as liquidity premia, and funding cost differentials.

(c) Brian Romanchuk 2015

No comments:

Post a Comment

Note: Posts are manually moderated, with a varying delay. Some disappear.

The comment section here is largely dead. My Substack or Twitter are better places to have a conversation.

Given that this is largely a backup way to reach me, I am going to reject posts that annoy me. Please post lengthy essays elsewhere.