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Chapter 11

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Administrative Studies
ADMS 3531
Dale Domian

Chapter 11: Bond Prices and Yields 11.1 Bond Basics Straight Bonds ­ Straight bond - is an IOU that obligates the issuer of the bond to pay the holder of the bond: ­ A fixed sum of money (called the principal, par value, or face value) at the bond’s maturity and sometimes ­ Constant, periodic interest payments (called coupons) during the life of the bond. ­ Treasury bonds are straight bonds. ­ Special features may be attached: o Convertible bonds o Callable bonds o Putable bonds Coupon Rate and Current Yield ­ Two basic yield measures for a bond are its coupon rate and its current yield. ­ Coupon Rate – a bond’s annual coupon divided by its par value. Also called coupon yield or nominal yield Coupon rate= Annual coupon Par value ­ Current yield – a bond’s annual coupon divided by its market price Annual coupon Current yield= Bond price 11.2 Straight Bonds and Yield to Maturity ­ Yield to Maturity (YTM) – is the discount rate that equates today’s bond price with the present value of the future cash flows of the bond. o Sometimes called its promised yield ­ The price of a bond is found by adding together the present value of the bond’s coupon payments and the present value of the bond’s face value. Straight Bond Prices   C  1  FV Bond Price= 1− 2M  + 2M YTM 1+ YTM 1+ YTM  ( 2)  ( 2) present value of the bond’s coupon payments present value of the bond’s face value ­ C represents the annual coupon payments (in $) ­ FV is the face value of the bond (in $) ­ M is the maturity of the bond, measured in years ­ YTM is the yield to maturity Example: ­ What is the price of a straight bond with: $1,000 face value, coupon rate of 8%, YTM of 7%, and a maturity of 20 years?   C  1  FV Bond PriceYTM − 1+YTM 2M+ 1+YTM 2M  ( 2)  ( 2)   Bond Price =0 − 1 2×2+ 10002×20 0.07 (1+0.072)  (1+0.072) = (1,142.857×0.747428) + 252.5725 = $1,106.78. Premium and Discount Bonds ­ Bonds are given names according to the relationship between the bond’s selling price and its par value. Premium bonds price> par value YTM < coupon rate Discount bonds price< par valueYTM > coupon rate Par bonds price = par YTM = coupon value rate ­ In general, when the coupon rate and YTM are held constant: o For premium bonds: the longer the term to maturity, the greater the premium over par value. o For discount bonds: the longer the term to maturity, the greater the discount from par value. Relationships Among Yield Measures ­ For premium bonds: o coupon rate > current yield > YTM ­ For discount bonds: o coupon rate < current yield < YTM ­ For par value bonds: o coupon rate = current yield = YTM Example: ­ Suppose we know the current price of a bond, its coupon rate, and its time to maturity. How do we calculate the YTM? ­ We can use the straight bond formula, trying different yields until we come across the one that produces the current price of the bond.   $110= $80 1− 1 + $1,000 YTM  YTM 2× YTM 2×8 YTM = 6.3843%  (1+ 2)  (1+ 2) A Note on Bond Price Quotes ­ If you buy a bond between coupon dates, you will receive the next coupon payment (and might have to pay taxes on it). ­ However, when you buy the bond between coupon payments, you must compensate the seller for any accrued interest. ­ The convention in bond price quotes is to ignore accrued interest. o Clean Price – the price of a bond net of accrued interest; this is the price that is typically quoted o This results in what is commonly called a clean price (i.e., a quoted price net of accrued interest). o Sometimes, this price is also known as a flat price. ­ The price the buyer actually pays is called the dirty price. o Dirty Price – the price of a bond including accrued interest, also known as the full or invoice price o This is because accrued interest is added to the clean price. o Note: The price the buyer actually pays is sometimes known as the full price, or invoice price. 11.3 More on Yields Yield To Call ­ Most bonds are callable bonds –a bond is callable if the issuer can buy it back before it matures ­ A callable bond gives the issuer the option to buy back the bond at a specified call price anytime after an initial call protection period. o Call price – the price the issuer of a callable bond must pay to buy it back o Call protection period (call deferment period) – the period during which a callable bond cannot be called ­ Therefore, for callable bonds, YTM may not be useful. ­ Yield to call (YTC)– is a yield measure that assumes a bond will be called at its earliest possible call date. ­ The formula to price a callable bond is:   C  1  CP Callable Bond Price= 1− 2T+ 2T YTC  (1+ YTC )  (1+ YTC )  2  2 ­ C is the annual coupon (in $) ­ CP is the call price of the bond ­ T is the time (in years) to the earliest possible call date ­ YTC is the yield to call, with semi-annual coupons. o As with straight bonds, we can solve for the YTC, if we know the price of a callable bond. 11.4 Interest Rate Risk and Malkiel’s Theorems  Holders of bonds face interest rate risk.  Interest rate risk - is the possibility that changes in interest rates will result in losses in the bond’s value.  Realized Yield - the yield actually earned or “realized” on a bond  Realized yield is almost never exactly equal to the yield to maturity, or promised yield. Malkiel’s Theorems 1. Bond prices and bond yields move in opposite directions. a. As a bond’s yield increases, its price decreases. b. Conversely, as a bond’s yield decreases, its price increases. 2. For a given change in a bond’s YTM, the longer the term to maturity of the bond, the greater the magnitude of the change in the bond’s price. 3. For a given change in a bond’s YTM, the size of the change in the bond’s p
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