Corporate bond default spread risk

Duffee, G.R., 1996b. Estimating the Price of Default Risk. Federal Reserve Board, Washington, DC. Duffee, G.R., 1998. The relation between treasury yields and corporate bond yield spreads. J. Financ. 53 (6), 2225-2241. 

The credit rating of a company is a major determinant of the yield that will be payable by that company s bonds. The yield spread of a corporate bond over the risk-free bond yield is known as the default premium. In practice, the default premium is composed of two elements, the compensation element specific to the company and the element related to market risk. This is because, in an environment where the default of one company was completely unrelated to the default of other companies, the return from a portfolio of corporate bonds would equal that of the risk-free bond. The gains from bonds of companies that did not default compensated for the loss from those that did default. The additional part of the default premium, the risk premium, is the compensation for risk exposure that cannot be diversified away in a portfolio, known as systematic or non-diversifiable risk. Observation of the market tells us that in certain circumstances, the default patterns of companies are related for example, in a recession there are more corporate defaults, and this fact is reflected in the risk premium. 

A credit default swap (CDS) price provides fundamental credit risk information of a specific reference entity or asset. As explained before, asset swaps are used to transform the cash flows of a corporate bond for interest rate hedging purpose. Since the asset swaps are priced at a spread over the interbank rate, the ASW spread is the credit risk of the same one. However, market evidence shows that credit default swaps trade at a different level to asset swaps due to technical... 

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

We have stated that the yield premium required on a corporate bond accounts for the default risk exposure of such a bond. The level of yield spread is determined by the expected default loss of the bond and it is assumed that investors can assess the level of the default risk. This makes it possible to calculate the level of the theoretical default spread. 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

For lower- and non-rated bonds, the observed effect is the opposite to that of an investment-grade corporate. Over time the probability of default decreases therefore, the theoretical default spread decreases over time. This means that the spread on a long-dated bond will be lower than that of a short-dated bond because if the issuer has not defaulted on the long-dated bond in the first few years of its existence, it will then be viewed as a lower risk credit, although the investor may well continue to earn the same yield spread. 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

Like Black and Cox s work, the authors find spreads similar to the market spreads. Moreover, they find a correlation between credit spread and interest rate. In fact, they illustrate that firms with similar default risk can have a different credit spread according to the industry. The evidence is that a different correlation between industry and economic environment affects the yield spread on corporate bonds. Then, the duration of a corporate bond changes following its credit risk. For high-yield bonds, the interest-rate sensitivity increases as the time to maturity decreases. 

There are two main types of credit risk that a bond portfolio or position is exposed to. They are credit default risk and credit spread risk. Credit default risk is defined as the risk that the issuer will be unable to make timely payments of interest and principal. Typically, investors rely on the ratings agencies—Fitch Ratings, Moody s Investors Service, Inc., and Standard 8c Poor s Corporation—who publish their opinions in the form of ratings. 

Another indicator of credit risk is the credit risk premium the spread between the yields on corporate bonds and those of government bonds in the same currency. This spread is the compensation required by investors for holding bonds that are not default-free. The size of the credit premium changes with the market s perception of the financial health of individual companies and sectors and of the economy in general. The variability of the premium is illustrated in FIGURES 10.2 and 10.3 on the following page, which show the spreads between the U.S.-dollar-swap and Treasury yield curves in, respectively, February 2001 and February 2004. 

Asset-swap pricing is commonly applied to credit-default swaps, especially by risk management departments seeking to price the transactions held on credit traders book. A par asset swap typically combines an interest rate swap with the sale of an asset, such as a fixed-rate corporate bond, at par and with no interest accrued. The coupon on the bond is paid in return for LIBOR plus, if necessary, a spread, known as the asset-swap spread. This spread is the price of the asset swap. It is a function of the credit risk of the underlying asset. That makes it suitable as the basis for the price payable on a credit default swap written on that asset. 

Thus the OAS is an indication of the value of the option element of the hond as well as the premium required by investors in return for accepting the default risk of the corporate bond. When OAS is measured as a spread between two bonds of similar default risk, the yield difference between the bonds reflects the value of the option element only. This is rare and the market convention is measure OAS over the equivalent benchmark government bond. OAS is used in the analysis of corporate bonds that incorporate call or put provisions, as well as mortgage-backed securities with prepayment risk. For both applications, the spread is calculated as the number of basis points over the yield of the government bond that would equate the price of both bonds. 

Using the spot rate structure at Table 12.1, the price of this bond is calculated to be 98.21. This would be the bonds fair value if it were liquid and default free. Assume, however, that the bond is a corporate bond and carries an element of default risk, and is priced at 97.00. What spread over the risk-free price does this indicate We require the spread over the implied forward rate that would result in a discounted price of 97.00. Using iteration, this is found to be 67.6 basis points. The calculation is... 

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