Bond Default Risk

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. 

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Vol. 543 C. Benkert, Default Risk in Bond and Credit Derivatives Markets. IX, 135 pages. 2004. 

Vol. 582 J. Andritzky, Sovereign Default Risks Valuation Implications of Debt Crises and Bond Restructurings. 

In an asset-swap contract, the investor assumes the credit risk of the bond. In case the bond defaults, the investor will continue to pay the swap, without... 

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. 

Generally, the theoretical default spread is almost exactly proportional to the default probability, assuming a constant default probability. Generally, however, the default probability is not constant over time, nor do we expect it to be. In Figure 8.3, we show the theoretical default spread for triple-B-rated bonds of various maturities, where the default probability rises from 0.2% to 1 % over time. The longer dated bonds, therefore, have a higher aimual default risk and so their theoretical default spread is higher. Note that after around 20 years the expected default probability is constant at 1%, so the required yield premium is also fairly constant. 

Portfolio managers must also take account of a further relationship between default risk and interest-rate risk. That is, if two corporate bonds have the same duration but one bond has a higher default probability, it essentially has a shorter duration because there is a greater chance that it will experience premature cash flows, in the event of default. 

This means that an investor who holds bonds that carry an element of default risk should in theory take this default risk into consideration when calculating the duration of his or her portfolio. In practical terms this only has an effect with unrated or junk bonds, which have default probabilities much greater than 1%. Figure 8.5 shows how the theoretical duration of a bond decreases as its assumed default probability increases. 

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. 

The credit spread is defined as the difference between the risky rate of a defaul-table bond and the risk-free rate of a default-free bond. In this case, with bonds priced at par, between coupon and risk-free rate, the pricing is performed like a valuation of a straight bond, including the default risk adjustment. The price is given by Equation (8.25) ... 

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. 

Kovalov, P., Linetsky, V., 2008. Valuing convertible bonds with stock price, volatility, interest rate, and default risk. Working Paper No. 2008-02, EDIC Center for Financial Research. 

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. 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

The default risk component of a swap spread will be smaller than for a comparable bond credit spread. The reasons are straightforward. First, since only net interest payments are exchanged rather than both principal and coupon interest payments, the total cash flow at risk is lower. Second, the probability of default depends jointly on the probability of the counterparty defaulting and whether or not the swap has a positive value. See John C. Hull, Introduction to Futures and Options Markets, Third Edition (Upper Saddle River, NJ Prentice Hall, 1998). 

In the situation where the risk of a technical default risk is higher for credit default swaps than cash bonds. This results in protection sellers demanding a higher premium. For example, default swaps may be triggered by events that do not constitute a full default on the corresponding cash asset. 

A much easier method of generating leverage in a credit portfolio is through credit default swaps (CDS). They let investors take on or lay off default risk in an unfunded manner. Selling default protection enables one to receive the premium associated with the additional credit risk without the need to buy a bond of that entity, and in the process creates enormous leverage, especially for higher rated credits. The increased liquidity and the compression of bid/offer spreads have added to the attractiveness of this market. 

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. 

All bond instruments are characterized by the promise to pay a stream of future cash flows. The term structure of interest rates and associated discount function is crucial to the valuation of any debt security and underpins any valuation framework. Armed with the term structure, we can value any bond, assuming it is liquid and default-free, by breaking it down into a set of cash flows and valuing each cash flow with the appropriate discount factor. Further characteristics of any bond, such as an element of default risk or embedded option, are valued incrementally over its discounted cash flow valuation. 

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... 

We conclude this chapter with an illustration of the OAS technique. Consider a five-year semiannual corporate bond with a coupon of 8 percent. The bond incorporates a call feature that allows the issuer to call it after two years and is currently priced at 104.25. This is equivalent to a yield-to-maturity of 6.979 percent. We wish to measure the value of the call feature to the issuer, and we can do this using the OAS technique. Assume that a five-year Treasury security also exists with a coupon of 8 percent and is priced at 109.11, a yield of 5.797 percent. The higher yield reflects the market-required premium due to the corporate bond s default risk and call feature. 

To determine the correct rate to use, consider the corresponding price of the conventional bond when the share price is 63.47 at period fg. The price of the bond is calculated on the basis that on maturity the bond will be redeemed irrespective of what happens to the share price. Therefore, the appropriate interest rate to use when discounting a conventional bond is the credit-adjusted rate, as this is a corporate bond carrying credit risk—it is not default-risk free. However, this does not apply at a different share... 

When ratings agencies were first set up, the primary focus of credit analysis was on the default risk of the bond, or the probability that the investor would not receive the interest payments and the principal repayment as they fell due. Although this is still important, credit analysts these days... 

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