CHAPTER 10Bond Prices and YieldsInterest rates go up and bond prices go down. But which bonds go up themost and which go up the least? Interest rates go down and bond prices goup. But which bonds go down the most and which go down the least? Forbond portfolio managers, these are very important questions about interestrate risk. An understanding of interest rate risk rests on an understanding ofthe relationship between bond prices and yieldsIn the preceding chapter on interest rates, we introduced the subject of bond yields. As wepromised there, we now return to this subject and discuss bond prices and yields in some detail. Wefirst describe how bond yields are determined and how they are interpreted. We then go on toexamine what happens to bond prices as yields change. Finally, once we have a good understandingof the relation between bond prices and yields, we examine some of the fundamental tools of bondrisk analysis used by fixed-income portfolio managers.10.1 Bond BasicsA bond essentially is a security that offers the investor a series of fixed interest paymentsduring its life, along with a fixed payment of principal when it matures. So long as the bond issuerdoes not default, the schedule of payments does not change. When originally issued, bonds normallyhave maturities ranging from 2 years to 30 years, but bonds with maturities of 50 or 100 years alsoexist. Bonds issued with maturities of less than 10 years are usually called notes. A very small numberof bond issues have no stated maturity, and these are referred to as perpetuities or consols.2 Chapter 10Straight BondsThe most common type of bond is the so-called straight bond. By definition, a straight bondis an IOU that obligates the issuer to pay to the bondholder a fixed sum of money at the bond'smaturity along with constant, periodic interest payments during the life of the bond. The fixed sumpaid at maturity is referred to as bond principal, par value, stated value, or face value. The periodicinterest payments are called coupons. Perhaps the best example of straight bonds are U.S. Treasurybonds issued by the federal government to finance the national debt. However, business corporationsand municipal governments also routinely issue debt in the form of straight bonds.In addition to a straight bond component, many bonds have additional special features. Thesefeatures are sometimes designed to enhance a bond’s appeal to investors. For example, convertiblebonds have a conversion feature that grants bondholders the right to convert their bonds into sharesof common stock of the issuing corporation. As another example, “putable” bonds have a put featurethat grants bondholders the right to sell their bonds back to the issuer at a special put price.These and other special features are attached to many bond issues, but we defer discussionof special bond features until later chapters. For now, it is only important to know that when a bondis issued with one or more special features, strictly speaking it is no longer a straight bond. However,bonds with attached special features will normally have a straight bond component, namely, theperiodic coupon payments and fixed principal payment at maturity. For this reason, straight bondsare important as the basic unit of bond analysis.The prototypical example of a straight bond pays a series of constant semiannual coupons,along with a face value of $1,000 payable at maturity. This example is used in this chapter becauseBond Prices and Yields 3it is common and realistic. For example, most corporate bonds are sold with a face value of $1,000per bond, and most bonds (in the United States at least) pay constant semiannual coupons.(marg. def. coupon rate A bond’s annual coupon divided by its price. Also calledcoupon yield or nominal yield)Coupon Rate and Current YieldA familiarity with bond yield measures is important for understanding the financialcharacteristics of bonds. As we briefly discussed in Chapter 3, two basic yield measures for a bondare its coupon rate and current yield.A bond's coupon rate is defined as its annual coupon amount divided by its par value or, inother words, its annual coupon expressed as a percentage of face value:Coupon rate = Annual coupon / Par value [1]For example, suppose a $1,000 par value bond pays semiannual coupons of $40. The annual couponis then $80, and stated as a percentage of par value the bond's coupon rate is $80 / $1,000 = 8%. Acoupon rate is often referred to as the coupon yield or the nominal yield. Notice that the word“nominal” here has nothing to do with inflation.(marg. def. current yield A bond’s annual coupon divided by its market price.)A bond's current yield is its annual coupon payment divided by its current market price:Current yield = Annual coupon / Bond price [2]For example, suppose a $1,000 par value bond paying an $80 annual coupon has a price of $1,032.25.The current yield is $80 / $1,032.25 = 7.75%. Similarly, a price of $969.75 implies a current yield of$80 / $969.75 = 8.25%. Notice that whenever there is a change in the bond's price, the coupon rate4 Chapter 10remains constant. However, a bond's current yield is inversely related to its price, and changeswhenever the bond's price changes.CHECK THIS10.1a What is a straight bond?10.1b What is a bond’s coupon rate? Its current yield?(marg. def. yield to maturity (YTM) The discount rate that equates a bond’s pricewith the present value of its future cash flows. Also called promised yield or justyield.)10.2 Straight Bond Prices and Yield to MaturityThe single most important yield measure for a bond is its yield to maturity, commonlyabbreviated as YTM. By definition, a bond’s yield to maturity is the discount rate that equates thebond’s price with the computed present value of its future cash flows. A bond's yield to maturity issometimes called its promised yield, but, more commonly, the yield to maturity of a bond is simplyreferred to as its yield. In general, if the term yield is being used with no qualification, it means yieldto maturity.Straight Bond PricesFor straight bonds, the following standard formula is used to calculate a bond’s price givenits yield:Bond Prices and Yields 5Bond price 'CYTM1 &1(1% YTM/2)2M%FV(1% YTM/2)2M[3]where C = annual coupon, the sum of two semi-annual couponsFV = face valueM = maturity in yearsYTM = yield to maturityIn this formula, the coupon used is the annual coupon, which is the sum of the two semiannualcoupons. As