I. Introduction to Bonds

University of California, Merced ECO 163-Economics of Investments Chapter 10 Lecture otes I. Introduction to Bonds Professor Jason Lee A. Definitions Definition: A bond obligates the issuer to make specified payments to the holder over a specified period of time. Definition: The face value (par value) of the bond is the payment made to the bondholder at the maturity date of the bond. Definition: The coupon (C) is the annual interest payment made to the bondholder. The coupon rate (c) is the coupon payment divided by the face value of the bond. c = C/FV Definition: A zero-coupon bond is a bond that is issued that makes no coupon payments. It is sold at a discount of the face value. The return comes from the difference between the purchase price and the face value. B. Treasury Notes and Bonds Definition: Treasury otes are U.S. government bonds issued with maturities of 1 to 10 years. Definition: Treasury Bonds are U.S. government bonds issued with maturities of 10 to 30 years. Both treasury notes and treasury bonds make semi-annual coupon payments. For example if the coupon rate is 6.25% on a $1000 face value bond then the bond will pay annual interest of $62.50 in 2 payments of $31.25. Bond prices are quoted as a percentage of the face value (typically $1000). For example, if the ask-price of a bond is quoted as 111.81 then an investor could purchase the bond for 111.81% of face value (111.81% x $1000 = $1118.10). The quoted purchase price of a bond does not include accrued interest. When an investor purchases a bond, they must also pay the seller any interest that was earned on the bond since the last coupon payment. The accrued interest is added to the purchase price of the bond. Accrued Interest = Annual Coupon Payment 2 x Days since last coupon payment 182 Example: Suppose the coupon rate is 8% and it has been 30 days since the last coupon

payment. The purchaser of the bond will have to pay the seller an additional payment of $40 $6.59 = x 2 30 182 C. Corporate Bonds Corporate bonds are less liquid that U.S. government bonds. There are various types of corporate bonds which we will focus on. 1. Callable Bonds Definition: Callable bonds are bonds that may be repurchased by the issuer of the bond at a specified call price before the maturity date. Callable bonds are typically issued during periods when interest rates are high. Firms which need to borrow during such periods would like to have the option of being able to retire the bonds should interest rates fall later. Holders of callable bonds face a risk that their bonds could be called away at any time prior to maturity and that they would then have to re-invest their proceeds in a period when interest rates are low. They must therefore be compensated for this risk. Callable bonds will pay higher coupon rates than non-callable bonds. 2. Convertible Bonds Definition: Convertible bonds are bonds which give the bondholder the option to exchange a bond for a specified number of shares of common stock in the firm. If the stock appreciates, the holders of convertible bonds would benefit. Because of the potential gains to holders of convertible bonds, convertible bonds will offer a lower coupon rate than non-convertible bonds. 3. Put Bonds Definition: Put bonds are bonds that gives the holder of the bond the option of extending the maturity date of the bond. Why would an investor wish to extend the maturity date? Suppose that a bond has a coupon rate of 8% and is nearing its maturity. If the current market coupon rates are less than 8% then the bondholder would want to extend the maturity date of the bond. 4. Floating-Rate Bonds Definition: Floating-rate bonds are bonds with coupon rates that are tied to the some specified market rate (such as the rate paid on treasury-bills). For example, a floating rate bond may pay the treasury bill interest rate plus 2%. The coupon payment will therefore be variable.

D. Preferred Stock While preferred stock is usually considered as equity it does have features which make it similar to bonds. Definition: Preferred stock is a stock that promised to pay a specified stream of dividends. If the holder of preferred stock never sells the stock then it is in effect a perpetuity (the holder will receive dividend payment forever). Unlike bonds however, a company may suspend the dividend payment to preferred stockholders at any time. However, if the dividend is unpaid then the dividend payments will accumulate. Common shareholders will not receive any dividends until the preferred shareholders are repaid in full. In cases of bankruptcy, preferred shareholders claims come before common shareholders (however preferred shareholders claims are below bondholders). Due to tax considerations, most preferred stock are hold by other corporations. E. International Bonds International bonds are divided into 2 categories: Foreign bonds and Eurobonds. Definition: Foreign bonds are issued by a borrower from a country other than the one in which the bond is sold. The bond is denominated in the currency of the country where it is sold. Example: A German bond that is dollar-denominated and sold in the U.S. is a foreign bond. Definition: Eurobonds are bonds that are denominated in one currency, usually the issuer s, but are sold in other countries. Example: A U.S. firm that issues a dollar-denominated bond in the U.K. would be a Eurobond. II. Bond Pricing How do investors determine how much to pay for a bond? Because bonds promise to pay specified amounts in the future, the price of a bond should equal the value of these future payments. However, we must take into account that dollars in the future are worth less than a dollar today. Given a choice between receiving $100 today vs. receiving $100 next year, an investor will always choose the $100 today since they can always deposit the money in a bank account and have more than $100 next year. To adjust future dollars into today s dollars we use the present value formula.

PV FV = (1+ n Where PV = present value; FV = future value; i = annual interest rate and n = number of years (periods). The price of a bond should equal the present discounted value of future dividend streams plus the present discounted value of the face value (par-value) of the bond to be paid at maturity. C C P= + (1+ (1+ 2 C + (1+ 3 C +... + (1+ n FV + (1+ n We can simplify this expression to get 1 1 P= C i i(1+ n FV + (1+ n Example: Suppose a bond pays an 8% coupon rate semi-annually. The bond has 30 years to maturity (thus there will be 60 semi-annual payments) and the face-value (par-value) of the bond is $1000. Suppose that the annual interest rate is 10%. Find the price of this bond. Since the coupon payments are made semi-annually, we need to find the semi-annual interest rate. To find the interest rate for any period we simply divide the annual interest rate by the number of periods per year. Since there are 2 semi-annual periods in a year, we will divide the annual interest rate by 2. The semi-annual interest rate is 5%. Thus: C = $40; i = 0.05; n = 60; FV = $1000 1 1 $1000 P = $40 + 60 60 0.05 = $810.71 0.05(1.05) (1.05) Suppose that the annual interest rate was instead 8% (semi-annual rate was 4%). Assume that all the other variables are the same. Calculate the price of this bond. For this example: C = $40; i = 0.04; n = 60; FV = $1000 1 1 = $40 0.04 0.04(1.04) $1000 + (1.04) P = 60 60 $1000 Key Point: There is a negative relationship between interest rates and bond prices.

As we saw in the example, changes in interest rates will result in changes in price. Fluctuations in interest rates will therefore represent a main source of risk in holding bonds. There is a risk that interest rates could increase which would lower the price of bonds. Key Point: Long-term bonds will fluctuate more from a change in interest rates than short-term bonds. Since treasury bills have a short time to maturity, they are considered safe due to the low interest rate risk. III. Bond Yields The yield on bonds is one measure of the rate of return for holding a bond. Bond yields generally include the interest payments as well as any change in the price of the bond over time (capital gain). There are various measures of bond yields. We will focus on two measures/ A. Yield to Maturity (YTM) Definition: The yield-to-maturity (YTM) is the discount rate that makes the present value of the bond s payment equal to its price. In other words, given the price of the bond, the maturity date, the face value and the coupon rate, the YTM will tell us the implied return if the bond was held to maturity. Example: Suppose that you purchase a 30 year $1000 face value 8% coupon bond that makes semi-annual payments for $1276.76. What is the YTM of this bond? In the example you are given P = $1276.76; FV = $1000; n = 60 and C = $40. The interest rate ( is unknown. 1 1 $1276.76= $40 i i(1+ 60 $1000 + 60 (1+ Such calculations would be difficult by hand and are generally made using EXCEL or a financial calculator. Solving we find that ( = 0.03 (which is a semi-annual YTM rate). The annualized yield (bond equivalent yield) can be found by taking the semi-annual rate and multiplying by the number of semi-annual periods in a year (2) to get 0.06. An alternative yield measure called the effective annual yield takes into account the possibility of compound interest (coupon payments are re-invested over time). The general formula for effective annual yield is (1 + semi-annual YTM) 2 1. In our example the effective annual yield would equal (1.03) 2 1 = 6.09% YTM is a proxy measure for the average annual return for a bond if it was held until maturity.

B. Current Yield Another measure of bond yield is the current yield. Definition: The current yield is the bond s annual coupon payment divided by the bond price. The current yield gives the annual return of a bond regardless of the maturity of the bond. C/P = current yield. Example: Suppose that you purchase a 30 year $1000 face value 8% coupon bond that makes semi-annual payments for $1276.76. What is the current yield of this bond? C/P = $80/$1276.76 = 6.27%. Note that in the previous examples when the bond price was above the face value the current yield will be greater than the YTM. This should make some intuitive sense because if you hold the bond until maturity (as the YTM would imply) you will suffer a capital loss since the purchase price of $1276.76 is greater than the face value of the bond of $1000. Since the current yield does not take into account the maturity of the bond it ignores the potential capital loss. Thus the current yield will be higher than the YTM. Key Point: For premium bonds (bonds selling above their face value) the current yield will be greater than YTM. For discount bonds (bonds selling less than face value) the current yield will be less than YTM. IV. Bond Prices Over Time A. YTM vs. Holding Period Return If market interest rates change over time, the holding period return (HPR) will be affected due to the change in the bond price over time. Interest rate fluctuations may cause the HPR to be significantly different than the initial YTM of the bond when it was initially sold. As we saw in the last section, the YTM is the average rate of return of the bond if it is held until maturity. The YTM of a bond is known for certain since the interest payments, face value and maturity date are known. The holding period return (HPR) is the rate of return over a specific investment holding period. The HPR will depend on the price of the bond at the end of the holding period. However, since the future price of the bond will depend on what the interest rate will be in the future it is unknown. If the bond price is unknown then HPR will not be known today. P P = P 1 0 HPR + 0 C P 0

Where P 1 is the price of the bond at the end of the investment period; P 0 is the purchase price of the bond; C = coupon payment. Example: Suppose that a 30 year coupon bond had the following characteristics: Annual coupon (C) = $80 Face Value (FV) = $1000 Price (P) = $1000 YTM = 8% Suppose that interest rates fall over the course of the year which causes the price of the bond to increase to P 1 = $1050 next year. Calculate the one year HPR for this bond. $1050 $1000 $80 HPR = + = 13% $1000 $1000 Note that the HPR is significantly higher than the YTM of 8% when the bond was first purchased since the HPR takes into account the appreciation in bond price due to the interest rate change. If the investor were to sell the bond next year he would earn a 13% return. Key Point: If interest rates increase, the HPR will be less than the initial YTM. If interest rates were to decrease then HPR will be greater than the initial YTM. B. Zero-Coupon Bonds and Treasury Strips Definition: Zero coupon bonds are bonds that do not pay a coupon. Pay the face value of the bond at the maturity date. Investors return comes from the appreciation in the bond price. Definition: U.S. Treasury strips are created by an investment bank which breaks down ( strips ) a bond into a series of independent securities which are sold at a discount. Example: An investment bank could purchase $1,000,000 5 year Treasury note that pays a coupon rate of 10%. The bank will receive 10 semi-annual payments of $100,00 and a payment of $1,000,000 at the end of 5 years. The bank could create 11 different zero-coupon bond issues and can sell the claim on each payment. Bond issue #1: zero-coupon bond that will pay $100,000 in 6 months. Bond issue #2: zero-coupon bond that will pay $100,000 in 12 months. --- Bond issue #10: zero-coupon bond that will pay $100,000 in 60 months. Bond issue #11: zero-coupon bond that will pay $1,000,000 in 60 months. The price of a discount bond will increase as time passes since at maturity the bond will pay the face value.

To illustrate: Suppose the price of a $1000 face value discount bond with 30 years to maturity and an interest rate of 10% will equal P = $1000/(1.10) 30 = $57.31 Suppose the price of a $1000 face value discount bond with 20 years to maturity and an interest rate of 10% will equal P = $1000/(1.10) 20 = $148.64 The Internal Revenue Service (IRS) treats the appreciation of price of a discount bond as an implicit interest payment and taxes the investor on the implied interest. For example, a 30 year $1000 face value discount bond with an interest rate of 10% would sell for $57.31. If the interest rate remained unchanged, next year the same bond will be worth $63.04 since P = $1000/(1.10) 29 = $63.04. The gain in price ($63.04 - $57.31 = $5.73) will be treated at implied interest and will be subject to a tax. V. Default Risk A. Bond Ratings While government bonds are generally treated an free of default risk this is not true for corporate bonds. In a corporation declares bankruptcy, bondholders will not receive all of their promised payments. Since there is always some risk of default for corporate bonds the actual return for corporate bonds is now known for certain. Bond default risk measures are provided by rating agencies. The main agencies are 1. Moody s Investor Services 2. Standard and Poor s Corporation 3. Fitch Investor Services Ratings are assigned letter grades with AAA being the highest and D the lowest. Bonds that are rated BBB (S&P and Fitch) or Baa (Moody s) are considered investment grade bonds. Lower rated bonds are classified as speculative grade or junk bonds (high-yield). B. Bond Indentures While bond ratings are a way to measure the level of default risk, bond indentures are a way to minimize the risk of default for bondholders. Definition: A bond indenture is a contract between the issuer and the bondholder which specifies a set of provisions that are designed to protect the bondholder from default.

Common types of bond indentures are 1. Sinking Fund One problem that may increase the risk of default is that the bond issuers are required to repay the bondholder the face value of the bond at maturity. If the issuer issued a large number of bonds with the same maturity then there s a risk that the issuer will not have enough cash on hand to repay all the bonds at maturity. One way to ensure that the issuer has adequate cash flow to meet its obligation is to try to spread the burden of repayment over a number of years instead of all at once. Definition: A sinking fund is a contract provision which allows the issuer to periodically repurchase some of the outstanding bonds prior to maturity in the open market. By retiring some of the bond issues ahead of maturity, the issuer will have to make less of a payment at the maturity date. There are special sinking fund provisions which allow for the repurchase of the bond at a special call price (some bondholders will see their issues called before maturity). The issues which get repurchased are chosen randomly. 2. Subordination of Further Debt Another risk faced by bondholders is the risk that after they purchase a firm s bonds, the firm will borrow even more money. A firm that accumulates more and more debt face a higher risk of default. Definition: Subordination clauses place restrictions on additional borrowing by firms. Additionally such provisions state that senior bondholders will be paid first over subsequent (subordinated or junior) bondholders in the event of a bankruptcy. 3. Dividend Restrictions Provisions may also be written into the bond contract which limits the amount of dividends a firm can pay out. Bondholders would prefer that a firm keep cash in reserve in order to pay down its future debt obligations rather to have that cash distributed to its shareholders. 4. Collateral Definition: Collateral are assets that are promised to lenders should the borrower default. Definition: Debenture bonds are bonds that are not secured by any collateral Bonds with collateral provisions written into its contract are generally considered safer than debenture bonds. The reason is that since the bondholders with collateral provisions are promised physical assets (which can be sold) even if the firm declares bankruptcy they are

somewhat protected from default risk. Holders of debenture bonds on the other hand may not receive any assets should the firm goes bankrupt and thus face a higher default risk. Since debenture bondholders face a higher default risk, they receive a higher yield than holders of collaterized bonds. C. YTM and Default Risk Recall that YTM is the average rate of return if the bond is held to maturity. The YTM represented a best-case scenario which assumes that the bond issuer doesn t default between now and the maturity date. The fact that there is always a risk of default in holding corporate bonds implies that the actual yield must be different than the YTM. To compensate the bondholder for the possibility of default, corporate bonds must offer a default premium. Definition: Default premium is the difference in yield between a corporate bond and an identical government bond. The greater the risk of default of a corporate bond the higher the default premium. D. Credit Default Swaps (CDS) Definition: A credit default swap (CDS) is an insurance policy on the default risk of a corporate bond or loan. Suppose you were a bondholder and wanted to minimize your risk that the bond you just purchased will default. You could purchase a credit default swap on the bond issue for a premium. If the firm were to declare bankruptcy and default on its debt, the issuer of the CDS will repay the value of the bond. As a result, the bondholder is now guaranteed repayment of the bond either by the firm or the issuer of the CDS. One of the reasons for the popularity of the CDS was that it allowed a bondholder to be able to transform any risky bond into a safe bond. For example, a bondholder could purchase a relative risky BBB-rated bond but then simultaneously purchase a CDS on that bond. The bondholder is now guaranteed repayment on the principal and thus the formerly risky BBB rated bond is now the equivalent of an AAA rated bond due to the purchase of the insurance policy. However, the popularity of CDS was one of the contributing factors to the near collapse of the financial system during the financial crisis 2007-2009. One of the largest issuers of credit default swaps, AIG, had issued over $400 billion worth of CDS contracts mostly on sub-prime mortgages and other highly speculative loans which were becoming worthless.

Banks had purchased a large amount of CDS in order to protect themselves from what they knew were highly speculative investments. Bank managers believed that by purchasing insurance via CDS they were protected from any default risk. However, with bonds and loans defaulting simultaneously it would prove impossible for AIG to be able to repay all of its obligations. A default by AIG would have resulted in banks having to be forced to write down hundreds of billions dollars worth of bonds and loans. To prevent a chain reaction of defaults in the banking system, AIG was bailed out by the federal government.