CHAPTER TWENTYYIELD TO MATURITYBond C coupon pays $50/year;Slide 4Slide 5Slide 6Slide 7Slide 8SPOT RATESlide 10DISCOUNT FACTORSSlide 12FORWARD RATESlide 14Slide 15Slide 16Slide 17Slide 18Slide 19FORWARD RATES AND DISCOUNT FACTORSYIELD CURVESSlide 22Slide 23Slide 24TERM STRUCTURE THEORIESSlide 26TERM STRUCTURE THEORY: Unbiased ExpectationsSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33TERM STRUCTURE THEORY: Liquidity PreferenceTERM STRUCTURE THEORY: Liquidity PreferenceSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43TERM STRUCTURE THEORY: Market SegmentationSlide 45TERM STRUCTURE THEORY: Preferred HabitatTERM STRUCTURE THEORY: Preferred HabitatSlide 48TERM STRUCTURE THEORY: Preferred Habitat1CHAPTER TWENTYFUNDAMENTALS OF BOND VALUATION2YIELD TO MATURITY•CALCULATING YIELD TO MATURITY EXAMPLE–Imagine three risk-free returns based on three Treasury bonds:Bond A,B are pure discount types;mature in one year3Bond C coupon pays $50/year;matures in two years4YIELD TO MATURITYBond Market Prices:Bond A $934.58Bond B $857.34Bond C $946.93WHAT IS THE YIELD-TO-MATURITY OF THE THREE BONDS?5YIELD TO MATURITY•YIELD-TO-MATURITY (YTM)–Definition: the single interest rate* that would enable investor to obtain all payments promised by the security.–very similar to the internal rate of return (IRR) measure* with interest compounded at some specified interval6YIELD TO MATURITY•CALCULATING YTM:–BOND A–Solving for rA(1 + rA) x $934.58 = $1000 rA= 7%7YIELD TO MATURITY•CALCULATING YTM:–BOND B–Solving for rB(1 + rB) x $857.34 = $1000 rB = 8%8YIELD TO MATURITY•CALCULATING YTM:–BOND C–Solving for rC(1 + rC)+{[(1+ rC)x$946.93]-$50 = $1000 rC = 7.975%9SPOT RATE•DEFINITION: Measured at a given point in time as the YTM on a pure discount security10SPOT RATE•SPOT RATE EQUATION:where Pt = the current market price of a pure discount bond maturing in t years; Mt = the maturity value st = the spot rate tttsMP111DISCOUNT FACTORS•EQUATION:Let dt = the discount factor ttsd1112DISCOUNT FACTORS•EVALUATING A RISK FREE BOND:–EQUATIONwhere ct = the promised cash payments n = the number of paymentsntttcdPV113FORWARD RATE•DEFINITION: the interest rate today that will be paid on money to be –borrowed at some specific future date and –to be repaid at a specific more distant future date14FORWARD RATE•EXAMPLE OF A FORWARD RATELet us assume that $1 paid in one year at a spot rate of 7% has9346$.07.11PV15FORWARD RATE•EXAMPLE OF A FORWARD RATELet us assume that $1 paid in two years at a spot rate of 7% has a 8573$.)07.1()1(12,1fPV%01.92,1f16FORWARD RATEf1,2 is the forward rate from year 1 to year 217FORWARD RATE•To show the link between the spot rate in year 1 and the spot rate in year 2 and the forward rate from year 1 to year 2 2212,1)1(1$)1(11$ssf18FORWARD RATEsuch thator)1()1(1212,1ssf222,11)1()1)(1( sfs 19FORWARD RATE•More generally for the link between years t-1 and t:•or11,2,1)1()1()1(ttttssfttttttsfs )1()1()1(,11120FORWARD RATES AND DISCOUNT FACTORS•ASSUMPTION:–given a set of spot rates, it is possible to determine a market discount function–equation)1()1(1,111 tttttfsd21YIELD CURVES•DEFINITION: a graph that shows the YTM for Treasury securities of various terms (maturities) on a particular date22YIELD CURVES•TREASURY SECURITIES PRICES–priced in accord with the existing set of spot rates and–associated discount factors23YIELD CURVES•SPOT RATES FOR TREASURIES–One year is less than two year;–Two year is less than three-year, etc.24YIELD CURVES•YIELD CURVES AND TERM STRUCTURE–yield curve provides an estimate of•the current TERM STRUCTURE OF INTEREST RATES•yields change daily as YTM changes25TERM STRUCTURE THEORIES•THE FOUR THEORIES1.THE UNBIASED EXPECTATION THEORY2. THE LIQUIDITY PREFERENCE THEORY3. MARKET SEGMENTATION THEORY4. PREFERRED HABITAT THEORY26TERM STRUCTURE THEORIES•THEORY 1: UNBIASED EXPECTATIONS–Basic Theory: the forward rate represents the average opinion of the expected future spot rate for the period in question–in other words, the forward rate is an unbiased estimate of the future spot rate.27TERM STRUCTURE THEORY: Unbiased Expectations•THEORY 1: UNBIASED EXPECTATIONS–A Set of Rising Spot Rates•the market believes spot rates will rise in the future–the expected future spot rate equals the forward rate–in equilibriumes1,2 = f1,2where es1,2 = the expected future spot f1,2 = the forward rate28TERM STRUCTURE THEORY: Unbiased Expectations•THE THEORY STATES:–The longer the term, the higher the spot rate, and–If investors expect higher rates ,•then the yield curve is upward sloping•and vice-versa29TERM STRUCTURE THEORY: Unbiased Expectations•CHANGING SPOT RATES AND INFLATION–Why do investors expect rates to rise or fall in the future?•spot rates = nominal rates–because we know that the nominal rate is the real rate plus the expected rate of inflation30TERM STRUCTURE THEORY: Unbiased Expectations•CHANGING SPOT RATES AND INFLATION–Why do investors expect rates to rise or fall in the future?•if either the spot or the nominal rate is expected to change in the future, the spot rate will change31TERM STRUCTURE THEORY: Unbiased Expectations•CHANGING SPOT RATES AND INFLATION–Why do investors expect rates to rise or fall in the future?•if either the spot or the nominal rate is expected to change in the future, the spot rate will change32TERM STRUCTURE THEORY: Unbiased Expectations–Current conditions influence the shape of the yield curve, such that•if deflation expected, the term structure and yield curve are downward sloping•if inflation expected, the term structure and yield curve are upward sloping33TERM STRUCTURE THEORY: Unbiased Expectations•PROBLEMS WITH THIS THEORY:–upward-sloping yield curves occur more frequently–the majority of the time, investors expect spot rates to rise–not realistic position34TERM STRUCTURE THEORY: Liquidity Preference •BASIC NOTION OF THE THEORY–investors primarily interested in purchasing short-term securities to reduce interest rate risk35TERM STRUCTURE THEORY: Liquidity Preference•BASIC NOTION OF THE THEORY–Price Risk•maturity strategy is more risky than a rollover strategy•to convince investors to buy longer-term securities, borrowers
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