Maturities, corporate bonds

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. 

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. 

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 . 

Therefore, the valuation of corporate bonds needs to consider the put option value in which the payoff at maturity is given by Equation (8.11) ... 

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 different types of bonds in the European market reflect the different types of issuers and their respective requirements. Some bonds are safer investments than others. The advantage of bonds to an investor is that they represent a fixed source of current income, with an assurance of repayment of the loan on maturity. Bonds issued by developed country governments are deemed to be guaranteed investments in that the final repayment is virtually certain. For a corporate bond, in the event of default of the issuing entity, bondholders rank above shareholders for compensation payments. There is lower risk associated with bonds compared to shares as an investment, and therefore almost invariably a lower return in the long term. 

The most actively traded government securities for various maturities are called benchmark issues. Yields on these issues serve as reference interest rates which are used extensively for pricing other securities. Exhibit 1.2 is a Bloomberg screen of the benchmark bonds issued by the government of the Netherlands. European government bonds will be discussed in Chapter 5. As an illustration of a corporate bond. Exhibit 1.3 shows a Bloomberg Security Description screen for 4.875% coupon bond issued by Pirelli SPA that matures on 21 October 2008. 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

In the pre-euro days, traders were usually organized by currency. Now, sector specialization is the rule. For most issues, buy or sell indications are initially indicated on a spread basis. The spread can be either over the swap curve or over a specified government benchmark. A corporate bond issue keeps the same benchmark for its entire life they roll down the curve together. This is in contrast to the United States, where the convention is to quote a corporate bond s spread over the nearest on-the-run (most recently issued) 2-, 5-, 10-, or 30-year maturity Treasury bond. 

The gilts market is primarily a plain vanilla market, and the majority of gilt issues are conventional fixed interest bonds. Conventional gilts have a fixed coupon and maturity date. By volume they made up 82% of the market in June 2002. Coupon is paid on a semi-annual basis. The coupon rate is set in line with market interest rates at the time of issue, so the range of coupons in existence reflects the fluctuations in market interest rates. Unlike many government and corporate bond markets, gilts can be traded in the smallest unit of currency and sometimes nominal amounts change hands in amounts quoted down to one penny ( 0.01) nominal size. 

Each corporate bond will only be exposed to one of these factors, with an exposure that will typically increase with the bond s maturity. A rule of thumb is that it will be comparable to the bond s exposure to the shift factor. The spread risk of almost all AAA, AA, and A rated bonds will be less than their interest rate risk, and it is only for BBB rated bonds and in some very specific market sectors such as Energy and Telecoms that spread risk starts exceeding benchmark risk. Spread risk is by far the dominant source of systematic risk for high-yield instruments. 

We selected a universe of corporate bonds with maturities (on 31 May 2001) between two and six years from the iBoxx Euro Corporate Nonfinancial Index. We chose a cut-off at two years to ensure the bonds would still be in the index at the end of the 1-year test period. This produced 97 nonfinancial corporate bonds, which we aggregated into their own index. 

Exhibit 27.1 clearly shows that in most cases government bonds earn lower returns with at least the same volatility as corporate bonds from the same maturity segment (e.g., for Treasury 1-3 years). Generally, corporate bonds are thus dominant versus government bonds with... 

The risk averse investor with an investment horizon of three years (row 3) allocates his capital according to the weights in 8% corporate bonds with AA rating, 15% in A, 70% in BBB, and 8% in Treasury bonds (columns 2 to 5). His optimal term structure consists of 52% bonds with a 1-3Y maturity, 6% with 3-7 year, 5% with a 7-10 year, and 37% with a 10 year+ maturity (row 3, columns 6 to 9). 

Mitchell, K. 1991. The Call, Sinking Fund, and Term-to-Maturity Features of Corporate Bonds An Empirical Investigation. Journal of Financial and Quantitative Analysis 26, June, 201-222. 

Non-interest-beanng securities are also referred to as discounted securities. Unlike regular corporate bonds, which pay periodic interest (i.e., pay a coupon), interest is earned on these bonds by their appreciation in price over time. That is, these securities originally sell for less than their maturity or face value. All other factors being constant, the price approaches the face value as the time to maturity approaches zero. Note that this is not the same thing as a coupon bond that is selling at a discount. 

Most corporate bonds, as well as municipals and Treasury notes and bonds, pay interest on a semiannual basis. To find the interest paid during the year, multiply the par value (face or maturity value) of the bond by the annual coupon rate. This amount is then divided by 2 to determine the amount of interest paid every 6 months. It is important to know that corporate securities use a 180-day coupon period—a commercial year of 360 days or 30 days per month, whereas government securities use an exact year of 365 days (366 days for a leap year). In addition, corporate securities are delivered 5 business days after the sale, whereas government securities are delivered the same day or the day after the sale. Prices for these securities are calculated as of the delivery date. Finally, if a bond is sold between coupon dates, it will have accrued interest since the last coupon date. This accrued interest must be added to the quoted price to determine the actual amount that the investor is required to pay. 

MATURITY t RISK-FREE YIELD r CORPORATE BOND YIELD r+y RISK SPREAD y CUMULATIVE PROBABILITY OE DEEAULT ANNUAL PROBABILITY OE DEEAULT... 

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... 

A key benefit of securitization notes is the ability to tailor risk—return profiles. For example, if there is a lack of assets of any specific credit rating, these can be created via securitization. Securitized notes frequently offer better risk—reward performance than corporate bonds of the same rating and maturity. While this might seem peculiar (why should one AA-rated bond perform better in terms of credit performance than another just because it is asset-backed ), this often occurs because the originator holds the first-loss piece in the structure. 

Corporate bonds, as the name indicates, are issued by corporations. Corporate bond values often track the health of the company that issued them even more than they are affected by movements in interest rates. Investors in corporate bonds often evaluate balance sheets, products, management, competitive environment, and even the company s stock performance. There are four different corporate market sectors industrials (cyclicals), airlines/transportation, public utilities, and banking/finance. Maturities fall into four categories short term (up to 4 years), intermediate term (5-12 years), long term (13-40 years), and "absurd term" (41-100 years). 

To understand why the rate of return is fixed even though bond prices tend to fluctuate, consider for a moment the mechanics of a typical corporate bond. Let s say an investor has bonds from a large auto manufacturer. The Jace amount of the bonds, or the dollar value of each "loan," is 1,000. The coupon rate is the amount of interest the bond will pay the investor each year, and is stated in terms of a percentage of the face amount. Therefore a 1,000 bond paying 100 per year in interest has a 10 percent coupon rate ( 100/ 1,000). The maturity date is the date in the future when the investor will get her original 1,000 back. Said another way, this is the date the company will pay the face amount of the bond to the owner. 

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