《货币银行学》课程授课教案（英文讲义）Chapter 05 Bonds, Bond Prices, and the Determination of Interest Rates

Chapter5Bonds,BondPricesand theDeterminationof InterestRatesChapter 5Bonds,Bond Prices and theDeterminationofInterestRatesProblems and Solutions1Consider a U.S. Treasury Bill with 270 days to maturity.If the annual yield is3.8 percent, what is the price?$100Answer: P-(1+0.038)9/2 = $97.242.Which of these$100facevaluebondswill haveahigher yield to maturity?Why?6 percent coupon bond selling for s85a.b.7percent coupon bond sellingfor $10o8 percent coupon bond selling for $115c.Answer:$6$100a. $85=i= 24.71%1+i1+i$7$100b. $100=i= 7%1+i1+i$8$100c.$115i=6.1%1+i1+iOption(a.)hasthehighestyieldtomaturity3.You are considering purchasing a consol that promises annual payments of s4a.If the current interest rate is 5 percent, what is the price of the consol?b.You are concerned that the interest rate may rise to 6 percent. Compute thepercentage change in the price of the consol and the percentage change in theinterestrate.ComparethemYour investment horizon is one year.You purchase the consol when thec.interestrateis5percentandsell it ayearlater,followingariseintheinterestrate to 6 percent. What is your holding period return?Answer:Instructor'sManualt/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Problems and Solutions 1. Consider a U.S. Treasury Bill with 270 days to maturity. If the annual yield is 3.8 percent, what is the price? Answer: $97.24 (1 0.038) $100 9 /12 = + P = 2. Which of these $100 face value bonds will have a higher yield to maturity? Why? a. 6 percent coupon bond selling for $85 b. 7 percent coupon bond selling for $100 c. 8 percent coupon bond selling for $115 Answer: a. 24.71% 1 $100 1 $6 $85 = + + + = i i i b. 7% 1 $100 1 $7 $100 = + + + = i i i c. 6.1% 1 $100 1 $8 $115 = + + + = i i i Option (a.) has the highest yield to maturity. 3. You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 5 percent, what is the price of the consol? b. You are concerned that the interest rate may rise to 6 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Answer:

Chapter5Bonds,BondPricesandtheDeterminationofInterestRates$4a.P:=$800.05$4b. newP:$66.670.06P falls by 16.7%; i rises by 20%$4$66.67$8011.7%1$80$804.Inarecent issueofTheWall StreetJournal.locatethepricesand yieldsonU.STreasury issues.For onebond selling above par and one sellingbelowpar(assuming they both exist), compute the current yield and compare it to thecoupon rate and the ask yield printed in the paper.Answer:(FromtheApril5,2004WallStreetJournal)a.$100,4%notematuringFeb2014:askprice=$98.26,askyield=4.15%Current yield = $4/$98.26 = 4.1%PricePar value:coupon rate>current yield>ask yield5.There is considerable concern that the government of Transaxia, an emergingeconomy in Eastern Europe, will default on its debt.Some years ago it issued 8percent coupon bonds that now have one year to maturity.Looking at the market,you find that the yield on these bonds is 24 percent.If the current risk-freeinterest rate is 5percent, and assuming that investors do not demand a riskpremium for holding Transaxian bonds, what is the probability that theTransaxians will default?Answer:$108Yield =0.24Price=$87.10PriceExpectedValuePrice = ExpectedPV = $87.10 =ExpectedValue=$91.461.05ExpectedValue=$91.46=ProbabilityofPayoff*$108-→ProbofPayoff=84.7%Instructor'sManualt/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets a. $80 0.05 $4 P = = b. $66.67 0.06 $4 newP = = P falls by 16.7%; i rises by 20% c. 11.7% $80 $66.67 $80 $80 $4 + = 4. In a recent issue of The Wall Street Journal, locate the prices and yields on U.S. Treasury issues. For one bond selling above par and one selling below par (assuming they both exist), compute the current yield and compare it to the coupon rate and the ask yield printed in the paper. Answer: (From the April 5, 2004 Wall Street Journal) a. $100, 4% note maturing Feb 2014: ask price=$98.26, ask yield=4.15% Current yield = $4/$98.26 = 4.1% PricePar value: coupon rate>current yield>ask yield 5. There is considerable concern that the government of Transaxia, an emerging economy in Eastern Europe, will default on its debt. Some years ago it issued 8 percent coupon bonds that now have one year to maturity. Looking at the market, you find that the yield on these bonds is 24 percent. If the current risk-free interest rate is 5 percent, and assuming that investors do not demand a risk premium for holding Transaxian bonds, what is the probability that the Transaxians will default? Answer: $91.46 1.05 Pr $87.10 1 Pr $87.10 Pr $108 0.24 = = = = = = = ExpectedValue ExpectedValue ice ExpectedPV ice ice Yield Expected Value = $91.46 = Probability of Payoff * $108 →Prob of Payoff=84.7%

Chapter5 Bonds, Bond Prices and the Determination of Interest RatesProbability of Default =100% - 84.7%=15.3%The Transxians do, in fact, default.As a result, investors become more attuned6.to the chances that other small emerging-market economies may default, andimmediatelymovetoreducetheirexposuretothem.Describetheconsequencesof this increase in risk aversion for the prices of both low-risk bonds and riskieremerging-marketbonds.Answer:Investors willwant to shift theirmoney into relatively low-risk bmds.Thedemand for emerging-market bonds shifts left, which causes prices to fall and yieldsto rise.The demand for low-risk bonds shifts right, increasing prices and reducingyields.7.A 10-year zero-coupon bond has a yield of 6 percent. Through a series ofunfortunate circumstances, expected inflation rises from 2 percent to 3 percent.a.Compute the change in the price ofthe bondb.Suppose that expected inflation is still 2 percent, but the probability that it willmove to 3 percent has risen.Describe the consequences for the price of thebond.Answer:a. Price (with 2% expected inflation)=100/(1.06)i0= $55.84Price (with 3% expected inflation)=100/(1.07)"0= $50.83The price has fallen by $5.01b. There is increased inflation risk.Investors will require compensation fortaking on additional risk, so the pricewill fall and theyield will rise.8. Assume that forecasts for the U.S. economy have taken a sudden turn for theworse.Everyonehad expected healthygrowthof3-4percent inthecomingyear.but now a recession is predicted, with output contracting by as much as 2 percent.Officials expect unemployment to rise and corporate profits to plummet.Describe the consequences for prices and interest rates for both government andprivate-sector bonds.Consider both the supply and demand effects. Use graphsto supportyouranswerAnswer:Corporations will be more likely to default during the impending recession,so the perceived riskiness of corporate bonds relative to government bonds hasincreased and demandfor corporate bonds will shift left.It will also becomemoredifficult for corporations to borrow, shifting the supply of corporate bonds to the left.This combination could cause prices of corporate bonds to increase or decrease.(See figure 6.6)Instructor'sManualt/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets Probability of Default = 100% - 84.7% = 15.3% 6. The Transxians do, in fact, default. As a result, investors become more attuned to the chances that other small emerging-market economies may default, and immediately move to reduce their exposure to them. Describe the consequences of this increase in risk aversion for the prices of both low-risk bonds and riskier emerging-market bonds. Answer: Investors will want to shift their money into relatively low-risk bonds. The demand for emerging-market bonds shifts left, which causes prices to fall and yields to rise. The demand for low-risk bonds shifts right, increasing prices and reducing yields. 7. A 10-year zero-coupon bond has a yield of 6 percent. Through a series of unfortunate circumstances, expected inflation rises from 2 percent to 3 percent. a. Compute the change in the price of the bond. b. Suppose that expected inflation is still 2 percent, but the probability that it will move to 3 percent has risen. Describe the consequences for the price of the bond. Answer: a. Price (with 2% expected inflation) = 100/(1.06)10 = $55.84 Price (with 3% expected inflation) = 100/(1.07)10 = $50.83 The price has fallen by $5.01 b. There is increased inflation risk. Investors will require compensation for taking on additional risk, so the price will fall and the yield will rise. 8. Assume that forecasts for the U.S. economy have taken a sudden turn for the worse. Everyone had expected healthy growth of 3-4 percent in the coming year, but now a recession is predicted, with output contracting by as much as 2 percent. Officials expect unemployment to rise and corporate profits to plummet. Describe the consequences for prices and interest rates for both government and private-sector bonds. Consider both the supply and demand effects. Use graphs to support your answer. Answer: Corporations will be more likely to default during the impending recession, so the perceived riskiness of corporate bonds relative to government bonds has increased and demand for corporate bonds will shift left. It will also become more difficult for corporations to borrow, shifting the supply of corporate bonds to the left. This combination could cause prices of corporate bonds to increase or decrease. (See figure 6.6)

Chapter 5 Bonds, Bond Prices and the Determination of Interest RatesBecause the perceived riskiness of corporate bonds has increased, demand forlow-risk government bonds will increase, which will cause prices of governmentbonds to rise and prices to fall.(See figure 6.4)9.What impact woulda stock-market collapse have on bonds?Why?Answer:Theperceivedriskinessofbondsrelativetostockswouldfall and investorswould shift their money into bonds.Demand for bonds would shift right, causingprices to rise and yields to fall.10. The government proposes cutting taxes on investment by implementing a creditfor investment in information technology equipment.Theproposalwouldreduce government tax revenues.Describe the likely impact on the bond market.Answer:Firms would have an incentiveto increase their investments, they wouldborrow more, shifting the supply of corporate bonds to the right, which woulddecrease prices and raise yields.Because government tax revenues have fallen, the government will need toborrow more.This will shift the supply of government bonds to the right, decreasingprices and raising yields.11. Other musicians, among them Rod Stewart, James Brown, and Dusty Springfield,haveissuedbondssimilartothosecreatedbyDavidBowie(asdescribedinthearticle in the chapter).What is likely to make such bond issues successful?Answer:Because the success of these artists is uncorrelated with any financialmarkets, investors see these bonds as an opportunity to reduce their overall riskthrough diversification.12.Usesupplyanddemand in thebond markettoexplain eachof thefollowingnewsheadlines.Showinadiagramwhatshiftsandexplainwhya.“Treasury prices fell for the sixth time in seven sessions as investors maderoom for new debt issues."b.Government bonds continued their month-long rise as data indicated thatthe U.S. economy is still progressing, but at a moderate pace."c."U.S. Treasurys rise sharply as stocks take dive."d.“Treasury prices are rising on expected future rate cut."e.“Illiquidity is crippling bond world."Answer.a. The supply of bonds has increased, causing prices to fallInstructor'sManual t/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets Because the perceived riskiness of corporate bonds has increased, demand for low-risk government bonds will increase, which will cause prices of government bonds to rise and prices to fall. (See figure 6.4) 9. What impact would a stock-market collapse have on bonds? Why? Answer: The perceived riskiness of bonds relative to stocks would fall and investors would shift their money into bonds. Demand for bonds would shift right, causing prices to rise and yields to fall. 10. The government proposes cutting taxes on investment by implementing a credit for investment in information technology equipment. The proposal would reduce government tax revenues. Describe the likely impact on the bond market. Answer: Firms would have an incentive to increase their investments; they would borrow more, shifting the supply of corporate bonds to the right, which would decrease prices and raise yields. Because government tax revenues have fallen, the government will need to borrow more. This will shift the supply of government bonds to the right, decreasing prices and raising yields. 11. Other musicians, among them Rod Stewart, James Brown, and Dusty Springfield, have issued bonds similar to those created by David Bowie (as described in the article in the chapter). What is likely to make such bond issues successful? Answer: Because the success of these artists is uncorrelated with any financial markets, investors see these bonds as an opportunity to reduce their overall risk through diversification. 12. Use supply and demand in the bond market to explain each of the following news headlines. Show in a diagram what shifts and explain why. a. “Treasury prices fell for the sixth time in seven sessions as investors made room for new debt issues.” b. “Government bonds continued their month-long rise as data indicated that the U.S. economy is still progressing, but at a moderate pace.” c. “U.S. Treasurys rise sharply as stocks take dive.” d. “Treasury prices are rising on expected future rate cut.” e. “Illiquidity is crippling bond world.” Answer. a. The supply of bonds has increased, causing prices to fall

Chapter5Bonds,BondPrices and theDetermination of InterestRatesSPrice of BondsPoP,DQuantityof Bondsb. People's wealth has increased, shifting demand to the right.Firms have moreinvestment opportunities, which shifts supply to the right.IIfpricesarerising,itmust mean that the shift of demand is stronger than the shift of supplyPrice of BondsSS1P,PoDQuantity of Bondsc. The perceived riskiness of stocks has risen and investors have shifted theirresourcesintolow-risk Treasurys.Demand has shiftedright, increasingpricesand decreasing yields.UPrice of BondsP,PoIncreased Demand forBondsD,DoQuantity of BondsThis shifts demand tod.Investorsexpectinterestratestofall (andpricestorise).the right (see diagramfor part c)e. If bonds are viewed as illiquid, demand shifts left, causing prices to fall andinterestratestorise.Instructor'sManualt/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets S0 S1 D E0 E1 P0 P1 Quantity of Bonds Price of Bonds S0 S1 D E0 E1 P0 P1 Quantity of Bonds Price of Bonds b. People’s wealth has increased, shifting demand to the right. Firms have more investment opportunities, which shifts supply to the right. If prices are rising, it must mean that the shift of demand is stronger than the shift of supply. S1 S0 D0 D1 E1 E0 P1 Quantity of Bonds Price of Bonds P0 S1 S0 D0 D1 E1 E0 P1 Quantity of Bonds Price of Bonds P0 c. The perceived riskiness of stocks has risen and investors have shifted their resources into low-risk Treasurys. Demand has shifted right, increasing prices and decreasing yields. S D1 D0 E1 E0 P1 P0 Quantity of Bonds Price of Bonds Increased Demand for Bonds S D1 D0 E1 E0 P1 P0 Quantity of Bonds Price of Bonds Increased Demand for Bonds d. Investors expect interest rates to fall (and prices to rise). This shifts demand to the right (see diagram for part c). e. If bonds are viewed as illiquid, demand shifts left, causing prices to fall and interest rates to rise

Chapter 5 Bonds, Bond Prices and the Determination of Interest RatesPrice of BondsPoP,Decreased Demand forBondsDQuantity of Bonds13. As you read the morning paper, you come across an ad for a bond mutual fund,afundthatpoolstheinvestmentsfromalargenumberofpeopleandthenpurchases bonds, giving the individuals “shares" in the fund.The companyclaims the fund has had a return of 13/ percent over the last year.But youremember that interest rates have been pretty low, 5 percent at most.A quickcheck of the numbers in the business section you're holding tells you that yourrecollection is correct.Explainthelogicbehind themutual fund's claim inthead.Answer: There are two possible explanations for the high return.The first is thatthe mutual fund is so much higher than the risk-free rate it must mean that they areinvesting in relatively risky bonds (and are being compensated for taking on thisrisk with higher returns).The second is that the fund was holding bonds during aperiod when interest rates were falling, so the holding period return far exceededtheinterest rate.Rememberthatwhen interestratesfall,theprices of bondsrisegiving the owner a capital gain.If interest rates are nowlow,then the likelihood isthat they will rise, causing a capital loss to the owners. Chances are that the highreturn is a consequence of the interest rate decline, so not onlywill it notberepeated, it is likely to be followed by a low or even negative return when interestrates rise.14. Your Financial World: Interest-Only Mortgages describes the monthlypayments a person would have to make under various circumstances. Showhow to derive the results in parts a-c if you borrow $400,000 at an annualinterestrateof6percent:a.An interest-only mortgage requires a payment of $1,947 a monthb.A 30-year, fixed-rate mortgage requires 360 equal payments of s$2,357c.A25-year fixed-rate mortgage requires 300 equal payments $2,538Note:To answer these questions you will need to compute the monthlycompound interest rate and use the formulas in the Appendix 4Answer:1)=0.0048676a. im =(1.0612Instructor'sManualt/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets S D1 D0 E1 P E0 0 P1 Quantity of Bonds Price of Bonds Decreased Demand for Bonds S D1 D0 E1 P E0 0 P1 Quantity of Bonds Price of Bonds Decreased Demand for Bonds 13. As you read the morning paper, you come across an ad for a bond mutual fund, a fund that pools the investments from a large number of people and then purchases bonds, giving the individuals “shares” in the fund. The company claims the fund has had a return of 13½ percent over the last year. But you remember that interest rates have been pretty low, 5 percent at most. A quick check of the numbers in the business section you’re holding tells you that your recollection is correct. Explain the logic behind the mutual fund’s claim in the ad. Answer: There are two possible explanations for the high return. The first is that the mutual fund is so much higher than the risk-free rate it must mean that they are investing in relatively risky bonds (and are being compensated for taking on this risk with higher returns). The second is that the fund was holding bonds during a period when interest rates were falling, so the holding period return far exceeded the interest rate. Remember that when interest rates fall, the prices of bonds rise giving the owner a capital gain. If interest rates are now low, then the likelihood is that they will rise, causing a capital loss to the owners. Chances are that the high return is a consequence of the interest rate decline, so not only will it not be repeated, it is likely to be followed by a low or even negative return when interest rates rise. 14. Your Financial World: Interest-Only Mortgages describes the monthly payments a person would have to make under various circumstances. Show how to derive the results in parts a-c if you borrow $400,000 at an annual interest rate of 6 percent: a. An interest-only mortgage requires a payment of $1,947 a month. b. A 30-year, fixed-rate mortgage requires 360 equal payments of $2,357. c. A 25-year fixed-rate mortgage requires 300 equal payments $2,538. Note: To answer these questions you will need to compute the monthly compound interest rate and use the formulas in the Appendix 4. Answer: a. (1.06 1) 0.0048676 12 1 = = m i

Chapter5Bonds,BondPricesandtheDeterminationofInterestRates$400,000*0.0048676=$1947$400,000*0.0048676b. C-$23571(11.0048676 360)$400,000*0.0048676=$2538c. C=1(11.0048676300 15. At the dinner table, your father is extolling the benefits of investing in bondsHe insists that as a conservative investor he will make only investments thatare safe, and what could be safer than a bond, especially a U.S. Treasury bond?What accounts for his view of bonds? Explain why you think it is right orwrong.Answer: Like most people, your father believes that the government guarantee meansthat he will get his investment back.He's right that the U.S. Treasury is extremelyunlikely to default, so there is virtually no default risk.But he's wrong aboutinterest-rateand inflationrisk.Thevalueof thebond will fluctuatewhenthe interestrate changes (moving inversely) and the purchasing power of the coupon andprincipal repayment will fluctuate with inflation.So, the bond is not risk freeInstructor's Manual t/aCecchetti:Money,Banking,andFinancial Markets

Chapter 5 Bonds, Bond Prices and the Determination of Interest Rates Instructor’s Manual t/a Cecchetti: Money, Banking, and Financial Markets $400,000*0.0048676=$1947 b. $2357 ) 1.0048676 1 (1 $400,000*0.0048676 360 C = = c. $2538 ) 1.0048676 1 (1 $400,000*0.0048676 300 C = = 15. At the dinner table, your father is extolling the benefits of investing in bonds. He insists that as a conservative investor he will make only investments that are safe, and what could be safer than a bond, especially a U.S. Treasury bond? What accounts for his view of bonds? Explain why you think it is right or wrong. Answer: Like most people, your father believes that the government guarantee means that he will get his investment back. He’s right that the U.S. Treasury is extremely unlikely to default, so there is virtually no default risk. But he’s wrong about interest-rate and inflation risk. The value of the bond will fluctuate when the interest rate changes (moving inversely) and the purchasing power of the coupon and principal repayment will fluctuate with inflation. So, the bond is not risk free