Solution Manual for Financial Markets and Institutions, 9th Edition

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Online Instructor’s ManualForFinancial Markets and InstitutionsNinthEditionFrederic S. MishkinColumbiaUniversityStanley EakinsEast Carolina University

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Table of ContentsI.Introduction............................................................................................................................11. Why Study Financial Markets and Institutions?......................................................................22. Overview of the Financial System...........................................................................................5II.Fundamentals of Financial Markets......................................................................................83. What Do Interest Rates Mean and What Is Their Role inValuation?.....................................94. Why Do Interest Rates Change?............................................................................................155. How Do Risk and Term Structure Affect Interest Rates?.....................................................236. Are Financial Markets Efficient?..........................................................................................30III.Fundamentals of Financial Institutions..................................................................................337. Why Do Financial Institutions Exist?....................................................................................348. Why Do Financial Crises Occur and Why Are They So Damaging tothe Economy?........................................................................................................................40IV.Central Banking andthe Conduct of Monetary Policy.........................................................459. Central Banksand the Federal Reserve System....................................................................4610. Conduct of Monetary Policy.................................................................................................50V.FinancialMarkets.....................................................................................................................5711. The Money Markets............................................................................................................5812. The Bond Market..................................................................................................................6413. The Stock Market...............................................................................................................7014. The Mortgage Markets.......................................................................................................7615. The Foreign Exchange Market.............................................................................................8616. TheInternational Financial System......................................................................................92VI.The Financial Institutions Industry........................................................................................9717.Banking and the Management of Financial Institutions.......................................................9818. Financial Regulation...........................................................................................................10619. Banking Industry: Structure and Competition....................................................................11320. The Mutual Fund Industry..................................................................................................11621. Insurance Companies and Pension Funds..........................................................................12322. Investment Banks, Security Brokers and Dealers, and Venture Capital Firms..................128VII.The Management of Financial Institutions..........................................................................13223. Risk Management in Financial Institutions........................................................................13324. Hedgingwith Financial Derivatives...................................................................................143Chapters on the Web25. Financial Crises inEmerging Market Economies..............................................................15326. SavingsAssociations and Credit Unions............................................................................15627. Finance Companies............................................................................................................159

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Part IIntroduction

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Chapter 1Why Study Financial Marketsand Institutions?Why Study Financial Markets?Debt Markets and Interest RatesThe Stock MarketThe Foreign Exchange MarketWhy Study Financial Institutions?Structure of the Financial SystemFinancial CrisesCentral Banks and the Conduct of Monetary PolicyThe International Financial SystemBanks and Other Financial InstitutionsFinancial InnovationManaging Risk in Financial InstitutionsApplied Managerial PerspectiveHow We Will Study Financial Markets and InstitutionsExploring the WebCollecting and Graphing DataWeb ExerciseConcluding Remarks◼Overview and Teaching TipsBefore embarking on a study of financial markets and institutions, the student must be convinced that thissubject is worth studying. Chapter 1 pursues this goal by showing the student that financial markets andinstitutions is an exciting field because it focuses on phenomena that affect everyday life. An additionalpurpose of Chapter 1 is to provide an overview for the entire book, previewing the topics that will becovered in later chapters. The chapter also provides the students with a guide as to how they will be studyingfinancial markets and institutions with a unifying, analytic framework and an applied managerial perspective.In teaching this chapter, the most important goal should be to get the student excited about the material. I havefound that talking about the data presented in the figures helps achieve this goal by showing the students thatthe subject matter of financial markets and institutions has real-world implications that they should care about.In addition, it is important to emphasize to the students thatthe course will have an applied managerial

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Chapter 1: Why Study Financial Markets and Institutions?3perspective, which they will find useful latter in their careers. Going through the web exercise is also a way ofencouraging the students to use the web to further their understanding of financial markets and institutions.◼Answers to End-of-Chapter Questions1.Well performing financial markets tend to allocate funds to its more efficient use, thereby allowingthe best investment opportunities to be undertaken. The improvement in the allocation of fundsresults in a more efficient economy, which stimulates economic growth (and thereby povertyreduction).2.Businesses would cut investment spending because the cost of financing this spending is now higher,and consumers would be less likely to purchase a house or a car because the cost of financing theirpurchase is higher.3.A change in interest rates affects the cost of acquiring funds for financial institution as well aschanges the income on assets such as loans, both of which affect profits. In addition, changes ininterest rates affect the price of assets such as stock and bonds that the financial institution ownswhich can lead to profits or losses.4.While it is true that there are many interest rates in the economy, like the interest rate paid by acorporate bond or the interest rate charged to a homeowner, it is also true that all of these interestrates tend to move together. Evidence shows that movements in different interest rates over time arein large part explained by the same events, and thereby allow economists to refer to “the” interest ratewhen trying to determine its movements.5.The lower price for a firm’s shares means that it can raise a smaller amount of funds, and so investmentin plant and equipment will fall.6.A bond is a debt instrument, which entitles the owner to receive periodic amounts of money(predetermined by the characteristics of the bond) until its maturity date. A common stock, however,represents a share of ownership in the institution that has issued the stock. In addition to its definition,it is not the same to hold bonds or stock of a given corporation, since regulations state thatstockholders are residual claimants (i.e. the corporation has to pay all bondholders before payingstockholders).7.It makes foreign goods more expensive and so British consumers will buy less foreign goods andmore domestic goods.8.It makes British goods more expensive relative to American goods. American businesses will find iteasier to sell their goods in the United States and abroad, and the demand for their products will rise.9.Changes in foreign exchange rates change the value of assets held by financial institutions and thuslead to gains and losses on these assets. Also changes in foreign exchange rates affect the profitsmade by traders in foreign exchange who work for financial institutions.10.In the mid to late 1970s and the late 1980s and early 1990s, the value of the dollar was low, makingtravel abroad relatively more expensive; that would have been a good time to vacation in the UnitedStates and see the Grand Canyon. As the dollar’s value rose in the early 1980s, travel abroad becamerelatively cheaper, making it a good time to visit the Tower of London.

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4Mishkin/Eakins•Financial Markets and Institutions,EighthEdition11.In general people do not lend large amounts of money to one another because ofseveral informationproblems. In particular, people do not know about the capacity of other people of repaying theirdebts, or the effort they will provide to repay their debts. Financial intermediaries, in particularcommercial banks, tend to solve these problems by acquiring information about potential borrowersand writing and enforcing contracts that encourage lenders to repay their debt and/or maintain thevalue of the collateral.12.Savings and loan associations, mutual savings banks, credit unions, insurance companies, mutualfunds, pension funds, and finance companies.13.The latest financial crisis in the US and Europe occurred in 2007–2009. At the beginning it hitmostly the US financial system, but it then quickly moved to Europe, since financial markets arehighly interconnected. One specific way in which these markets were related, is that some financialintermediaries in Europe held securities backed by mortgages originated in the US, and when thesesecurities lost their a considerable part of their value, the balance sheet of European financialintermediaries were adversely affected.14.The profitability of financial institutions is affected by changes in interest rates, stock prices, andforeign exchange rates; fluctuations in these variables expose these institutions to risk.15.Because the Federal Reserve affects interest rates, inflation, and business cycles, all of which havean important impact on the profitability of financial institutions.◼Quantitative Problems1.The following table lists foreign exchange rates between U.S. dollars and British pounds duringApril:DateU.S. Dollars per GBPDateU.S. Dollars per GBP4/11.95644/181.75044/41.92934/191.72554/51.9144/201.69144/61.93744/211.6724/71.9614/221.66844/81.89254/251.66744/111.88224/261.68574/121.85584/271.69254/131.7964/281.72014/141.79024/291.75124/151.7785Which day would have been the best day to convert $200 into British pounds?Which day would have been the worst day? What would be the difference in pounds?Solution:The best day is 4/25. At a rate of $1.6674/pound, you would have £119.95. The worstday is 4/7. At $1.961/pound, you would have £101.99, or a difference of £17.96.

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Chapter 2Overview of the Financial SystemFunction of Financial MarketsStructure of Financial MarketsDebt and Equity MarketsPrimary and Secondary MarketsExchanges and Over-the-Counter MarketsMoney and Capital MarketsInternationalization of Financial MarketsInternational Bond Market, Eurobonds, and EurocurrenciesGlobal Box: Are U.S. Capital Markets Losing Their Edge?World Stock MarketsFunction of Financial Intermediaries: Indirect FinanceTransaction CostsFollowing the Financial News: Foreign Stock Market IndexesGlobal Box: The Importance of Financial Intermediaries Relative to SecuritiesMarkets: An International ComparisonRisk SharingAsymmetric Information: Adverse Selection and Moral HazardEconomies of Scope and Conflicts of InterestTypes of Financial IntermediariesDepository InstitutionsContractual Savings InstitutionsInvestment IntermediariesRegulation of the Financial SystemIncreasing Information Available to InvestorsEnsuring the Soundness of Financial IntermediariesFinancial Regulation Abroad

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6Mishkin/Eakins•Financial Markets and Institutions,EighthEdition◼Overview and Teaching TipsChapter 2 is an introductory chapter that contains the background information on the structure and operationof financial markets that is needed in later chapters of the book. This chapter allows the instructor to branchout to various choices of later chapters, thus allowing different degrees of coverage of financial marketsand institutions.The most important point to transmit to the student is that financial markets and financial intermediariesare crucial to a well-functioning economy because they channel funds from those who do not have aproductive use for them to those who do. Some instructors will want to teach this chapter in detail, andthose who focus on international issues will want to spend some time on the section “Internationalizationof Financial Markets.” However, those who slant their course to public policy issues may want to give thischapter a more cursory treatment. No matter how much class time is devoted to this chapter,Wehavefound that it is a good reference chapter for students. You might want to tell them that if in later chaptersthey do not recall what particular financial intermediaries do and who regulates them, they can refer backto this chapter,especially to tables, such as Tables2.1 and2.3.◼Answers to End-of-Chapter Questions1.Examples of how financial markets allow consumers to better time their purchases include:•The purchase of a durable good, like a car or furniture.•Paying for tuition.•Paying the cost of repairing a flooded basement.In all three cases, consumers were able to pay for a good or service (education or the reparation of aflooded basement) without having to wait to save enough and only then being able to afford suchgoods and services.2.Yes, I should take out the loan, because I will be better off as a result of doing so. My interest paymentwill be $4,500 (90% of $5,000), but as a result, I will earn an additional $10,000, so I will be ahead ofthe game by $5,500. Since Larry’s loan-sharking business can make some people better off, as in thisexample, loan sharking may have social benefits. (One argument against legalizing loan sharking,however, is that it is frequently a violent activity.)3.Yes, because the absence of financial markets means that funds cannot be channeled to people whohave the most productive use for them. Entrepreneurs then cannot acquire funds to set up businessesthat would help the economy grow rapidly.4.The principal debt instruments used were foreign bonds which were sold in Britain and denominatedin pounds. The British gained because they were able to earn higher interest rates as a result oflending to Americans, while the Americans gained because they now had access to capital to start upprofitable businesses such as railroads.5.If the Yen denominated bond is sold in Tokyo, then it is not considered a Eurobond. If the bond issold in New York, then it is considered a Eurobond.6.You would rather hold bonds, because bondholders are paid off before equity holders, who are theresidual claimants.

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Chapter 2: Overview of the Financial System77.Because you know your family member better than a stranger, you know more about the borrower’shonesty, propensity for risk taking, and other traits. There is less asymmetric information than witha stranger and less likelihood of an adverse selection problem, with the result that you are more likelyto lend to the family member.8.Maria cannot participate in a hedge fund since this type of mutual fund requires minimumcontributions of $100.000 and sometimes more. This type of financial intermediary is targeted tospecific savers that have a less cautious perception of risks, using the collected funds to buy assetsthat are earn high returns, but are quite risky.9.Loan sharks can threaten their borrowers with bodily harm if borrowers take actions that mightjeopardize paying off the loan. Hence borrowers from a loan shark are less likely to engage inmoral hazard.10.They might not work hard enough while you are not looking or may steal or commit fraud.11.Yes, because eliminating moral hazard requires enforcement even if there is no informationasymmetry.Even if you know that a borrower is taking actions that might jeopardize paying off theloan, you must still stop the borrower from doing so. Because that may be costly, you may not spendthe time and effort to reduce moral hazard, and so moral hazard remains a problem.12.True. If there are no information or transaction costs, people could make loans to each other at nocost and would thus have no need for financial intermediaries.13.Because the costs of making the loan to your neighbor are high (legal fees, fees for a credit check,and so on), you will probably not be able to earn 5% on the loan after your expenses even though ithas a 10% interest rate. You are better off depositing your savings with a financial intermediary andearning 5% interest. In addition, you are likely to bear less risk by depositing your savings at the bankrather than lending them to your neighbor.14.Financial intermediaries benefit because theycan earn profits on the spreads between the returns theyearn on risky assets and they payments they make on the assets they have sold. Households and firmsbenefit because they can now own assets that have lower risk.15.This is a topic for which there is no clear answer. On one side, it would be beneficial to have financialregulations that are identical in all countries to avoid financial markets participants to migrate theirbusiness to countries with fewer regulations. On the other side, all countries are different anddesigning a common set of financial regulations seems to be a rather difficult task. Most countrieswould want to maintain at least part of their regulations, so consensus is difficult to reach.

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Part IIFundamentals of Financial Markets

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Chapter 3What Do Interest Rates MeanandWhat Is Their Role in Valuation?Measuring Interest RatesPresent ValueFour Types of Credit Market InstrumentsYield to MaturityThe Distinction Between Real and Nominal Interest RatesGlobal Box: NegativeInterestRates?Japan First, Then the United States, Then EuropeThe Distinction Between Interest Rates and ReturnsMini-Case Box: With TIPS, Real Interest Rates Have Become Observable in the United StatesMaturity and the Volatility of Bond Returns: Interest-Rate RiskReinvestment RiskSummaryMini-Case Box: Helping Investors to Select Desired Interest-Rate RiskThe Practicing Manager: Calculating Duration to Measure Interest-Rate RiskCalculating DurationDuration and Interest-Rate Risk◼Overview and Teaching TipsInouryears of teaching financial markets and institutions,wehave found that students have trouble withwhatweconsider to be easy material because they do not understand what an interest rate is—that it isnegatively associated with the price of a bond, that it differs from the return on a bond, and that there isan important distinction between real and nominal interest rates.This chapter spends more time on these issues than does any other competing textbook.Ourexperiencehas been that giving this material so much attention is well rewarded. After putting more emphasis on thismaterial in my financial markets and institutions course,wewitnessed a dramatic improvement instudents’ understanding of portfolio choice and asset and liability management in financial institutions.An innovative feature of the textbook is the set of over twenty special applications called, “The PracticingManager.” These applications introduce students to real-world problems that managers of financialinstitutions have to solve and make the course both more relevant and exciting to students. They are notmeant to fully prepare students for jobs in financial institutions—it is up to more specialized courses suchas bank or financial institutions management to do this—but these applications teach them some of thespecial analytical tools that they will need when they enter the business world.

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10Mishkin/Eakins•Financial Markets and Institutions,EighthEditionThis chapter contains the Practicing Manager application on “Calculating Duration to Measure Interest-Rate Risk.” The application shows how to quantify interest-rate risk using the duration concept and isa basic tool for managers of financial institutions. For those instructors who do not want a managerialemphasis in their financial markets and institutions course, this and other Practicing Manager applicationscan be skipped without loss of continuity.◼Answers to End-of-Chapter Questions1.When comparing amounts of money that are disbursed at different dates, one has to take intoconsideration theconcept of present value of money. To calculate the present value of the $5,500promised one year from today one needs to know the annual interest rate. In this case, for an interestrate larger than 10%, one would prefer to accept the $5,000 today (since one can deposit thatamountand receive more than $5,500 one year from today).2.You would rather be holding long-term bonds because their price would increase more than the priceof the short-term bonds, giving them a higher return.3.The rate of capital gain is the part of the rate of return formula that incorporates future changes in theprice of the bond. The other part of the formula, the current yield, is composed of the couponpayment (completely determined by the bond´s face value and coupon rate) and the price you paid forthe bond today. The rate of capital gain incorporates the future price of the bond and is therefore thepart of the formula that reflects the consequences of future price changes.4.People are more likely to buy houses because the real interest rate when purchasing a house has fallenfrom 3 percent (=5 percent–2 percent) to 1 percent (=10 percent-9 percent). The real cost of financingthe house is thus lower, even though mortgage rates have risen. (If the tax deductibility of interestpayments is allowed for, then it becomes even more likely that people will buy houses.)◼Quantitative Problems1.Calculate the present value of a $1,000 zero-coupon bond with 5 years to maturity if the requiredannual interest rate is 6%.Solution:PV=FV/(1 +i)nwhereFV=1000,i=0.06,n=5PV=747.252.A lottery claims its grand prize is $10 million, payable over 20 years at $500,000 per year. If the firstpayment is made immediately, what is this grand prize really worth? Use a discount rate of 6%.Solution:This is a simple present value problem. Using a financial calculator,N=20;PMT=500,000;FV=0;I=6%;Pmtsin BEGIN mode.ComputePV:PV=$6,079,058.253.Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table:Years to MaturityDiscount RateCurrent Price3537

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Chapter 3: What Do Interest Rates Mean and What Is Their Role in Valuation?11679799What relationship do you observe between yield to maturity and the current market value?Solution:Years to MaturityYield to MaturityCurrent Price35$1,054.4637$1,000.0067$1,000.0095$1,142.1699$880.10When yield to maturity is above the coupon rate, the band’s current price is below its facevalue. The opposite holds true when yield to maturity is below the coupon rate. For a givenmaturity, the bond’s current price falls as yield to maturity rises. For a given yield tomaturity, a bond’s value rises as its maturity increases. When yield to maturity equals thecoupon rate, a bond’s current price equals its face value regardless of years to maturity.4.Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is currentlyselling for $1,150 and has 8 years to maturity. What is the bond’s yield to maturity?Solution:To calculate the bond’s yield to maturity using a financial calculator,N=8;PMT=10000.10=100;FV=1000;PV=1150ComputeI:I=7.445.Suppose that a commercial bank wants to buy TreasuryBills. These instruments pay $5,000 in oneyear and are currently selling for $5,012. What is the yield to maturity of these bonds? Is this atypical situation? Why?Solution:The yield to maturity of these bonds solves the following equation:5,000/(1+i)=5,012.After some algebra, the yield to maturity happens to be around–0.24%. This is not a typicalsituation. In normal times banks will not choose to pay more than the face value of a discount bond,since that implies negative yields to maturity. This example illustrates situations as the ones describedin the Global Box in this chapter.6.What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of 2.5%? Ifthe yield to maturity doubles, what will happen to its price?Solution:The price would be $50/.025 = $2000. If the yield to maturity doubles to 5%, the pricewould fall to half its previous value, to $1000 = $50/.05.7.Property taxes in DeKalb County are roughly 2.66% of the purchase price every year. If you justbought a $100,000 home, what is thePVofallthe future property tax payments? Assume that thehouse remains worth $100,000 forever, property tax rates never change, and that a 9% discount rateis used for discounting.

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12Mishkin/Eakins•Financial Markets and Institutions,EighthEditionSolution:The taxes on a $100,000 home are roughly 100,0000.0266=2,660.ThePVof all future payments=2,660/0.09=$29,555.55 (a perpetuity).8.Suppose you want to take out a loan and that your local bank wants to charge you an annual realinterest rate equal to 3%. Assuming that the annualized expected rate of inflation over the life of theloanis 1%, determine the nominal interest rate that the bank will charge you. What happens if, overthe life ofthe loan,actual inflation is 0.5%?Solution:The bank will charge you a nominal interest rate equal to 1% + 3%=4%.However, ifactual inflation turns out to be lower than expected, then you will be worse off than originallyplanned, since the real cost of borrowing (measured by the real interest rate) turned out to be 4%–0.5%=3.5%.9.Lucia just bought two coupon bonds, one with a face value of $1,000 and the other with a face valueof $5,000. Both bonds have a coupon rate of 5% and sold at par today. Calculate both bonds´ currentyield and both bonds rate of return if Lucia is able to sell these bonds one year later for $100 more ofthe buying price. Can youestimate what happened to the interest rate over that year?Solution:Thecurrent yield (CY) is calculated as the coupon payment over the selling price of thebond. When a coupon bond sells at par, its current yield equals the coupon rate, since the numeratorof the CY is: Face Value x Coupon Rate (always) and the denominator is Face Value (in thisparticular situation only in which Price = FV). Both bonds have a CY = 5%. If Lucia is able to sellthe $1,000 FV coupon bond for $1,100, then the rate of return is: 5% + 10% (since the rate of capitalgain is 100/1,000 =10%). The same reasoning yields a RET = 5% + 2% (g = 100/5,000) for the otherbond. The interest rate must have fallen over that year for bond´s prices to increase. Note, however,that it is unlikely that both bond´s prices increased by the same amount. Other determinants of bond´sprices (see chapters 4 and 5) likely explained this effect.10.You have paid $980.30 for an 8% coupon bond with a face value of $1,000 that mature in five years.You plan on holding the bond for one year. If you want to earn a 9% rate of return on this investment,what price must you sell the bond for? Is this realistic?Solution:To find the price, solve:11180980.300.09for.988.53.980.30tttPPP++++−==Although this appears possible, the yield to maturity when you purchased the bond was8.5%. At that yield, you only expect the price to be $983.62 next year. In fact, the yieldwould have to drop to 8.35% for the price to be $988.53.11.Calculate the duration of a $1,000 6% coupon bond with three years to maturity. Assume that allmarket interest rates are 7%.Solution:Year123SumPayments60.0060.001060.00PVof Payments56.0752.41865.28973.76Time WeightedPVof Payments56.07104.812595.83Time WeightedPVof PaymentsDivided by Price0.060.112.672.83

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Chapter 3: What Do Interest Rates Mean and What Is Their Role in Valuation?13This bond has a duration of 2.83 years. Note that the current price of the bond is $973.76,which is the sum of the individual “PVof payments.”12.Consider the bond in the previous question. Calculate the expected price change if interest ratesdrop to 6.75% using the duration approximation. Calculate the actual price change using discountedcash flow.Solution:Using the duration approximation, the price change would be:0.0025DUR2.83973.766.44.11.07iPPi−= −= −=+The new price would be $980.20. Using a discounted cash flow approach, the price is980.23—only $.03 different.Year123SumPayments60.0060.001060.00PVof payments56.2152.65871.3980.2313.The duration of a $100 million portfolio is 10 years. $40 million dollars in new securities are added tothe portfolio, increasing the duration of the portfolio to 12.5 years. What is the duration of the$40 million in new securities?Solution:First, note that the portfolio now has $140 million in it. The duration of a portfolio is theweighted average duration of its individual securities. LetDequal the duration of the$40 million in new securities. Then, this implies:12.5(100/14010)(40/140D)12.57.1425 + 0.285718.75DD=+==The new securities have a duration of 18.75 years.14.A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 millionloan that requires a single payment of $37.8 million in 3 years, with no other payments until then.The second is for $40 million. It requires an annual interest payment of $3.6 million. The principal of$40 million is due in 3 years.a.What is the duration of the bank’s commercial loan portfolio?b.What will happen to the value of its portfolio if the general level of interest rates increased from8% to 8.5%?Solution:The duration of the first loan is 3 years since it is a zero-coupon loan. The duration of thesecond loan is as follows:Year123SumPayment3.603.6043.60PVof Payments3.333.0934.6141.03Time WeightedPVof Payments3.336.18103.83Time WeightedPVof PaymentsDivided by Price0.080.152.532.76

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14Mishkin/Eakins•Financial Markets and Institutions,EighthEditionThe duration of a portfolio is the weighted average duration of its individual securities.So, the portfolio’s duration=3/7(3)+4/7(2.76)=2.86If rates increased,0.005DUR2.8670,000,000926,852.11.08iPPi= −= −= −+15.Considera bond that promises the following cash flows. The required discount rate is12%.Year01234Promised Payments160170180230You plan to buy this bond, hold it for 2½ years, and then sell the bond.a.What total cash will you receive from the bond after the 2½ years? Assume that periodic cashflows are reinvested at 12%.b.If immediately after buying this bond, all market interest rates drop to 11% (including yourreinvestment rate), what will be the impact on your total cash flow after 2½ years? How doesthis compare to part (a)?c.Assuming all market interest rates are 12%, what is the duration of this bond?Solution:a.You will receive 160 reinvested for 1.5 years, and 170 reinvested for 0.5 years. Then you willsell the remaining cash flows, discounted at 12%. This gives you:1.50.50.51.5180230160(1.12)170(1.12)$733.69.1.121.12+++=b.This is the same as part (a), but the rate is now 11%.1.50.50.51.5180230160(1.11)170(1.11)$733.74.1.111.11+++=Notice that this is only $0.05 different from part (a).c.The duration is calculated as follows:Year1234SumPayments160.00170.00180.00230.00PVof Payments142.86135.52128.12146.17552.67Time WeightedPVof Payments142.86271.05384.36584.68Time WeightedPVof PaymentsDivided by Price0.260.490.701.062.50Since the durationand the holding period are the same, you are insulated from immediatechanges in interest rates! It doesn’t always work out this perfectly, but the idea is important.

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Chapter 4Why Do Interest Rates Change?Determinants of Asset DemandWealthExpected ReturnsRiskLiquidityTheory of Portfolio ChoiceSupply and Demand in the Bond MarketDemand CurveSupply CurveMarket EquilibriumSupply-and-Demand AnalysisChanges in Equilibrium Interest RatesShifts in the Demand for BondsShifts in the Supply of BondsCase: Changes in the Interest Rate Due to Expected Inflation: The Fisher EffectCase: Changes in the Interest Rate Due to a Business CycleExpansionCase: Explainingthe CurrentLow Interest Ratesin Europe, Japan and the United StatesThe Practicing Manager: Profiting from Interest-Rate ForecastsFollowing the Financial News: Forecasting Interest RatesAppendix 1: Models of AssetPricingAppendix 2: Applying the Asset Market Approach to a Commodity Market: The Case of GoldAppendix 3: Loanable Funds FrameworkAppendix 4: Supply and Demand in the Market for Money: The Liquidity Preference Framework◼Overview and Teaching TipsAs isclear in the Preface to the textbook,Webelieve that financial markets and institutions is taughteffectivelyby emphasizing a few analytic principles and then applying them over and over again to thesubject matter of this exciting field. Chapter 4 introduces one of these basic principles: the determinants ofasset demand. It indicates that there are four primary factors that influence people’s decisions to holdassets: wealth, expected returns, risk, and liquidity. The simple idea that these four factors explain thedemand for assets is, in fact, an extremely powerful one. It is used continually throughout the study offinancial markets and institutions and makes it much easier for the student to understand how interest rates

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16Mishkin/Eakins•Financial Markets and Institutions,EighthEditionare determined, how financial institutions manage their assets and liabilities, why financial innovationtakes place, how prices are determined in the stock market and the foreign exchange market.One teaching device thatwehave found helps students develop their intuition is the use of summarytables, such as Table 1, in class.Weuse the blackboard to write a list of changes in variables that affect thedemand for an asset and then ask students to fill in the table by reasoning how demand responds to eachchange. This exercise gives them good practice in developing their analytic abilities.Weuse this devicecontinually throughoutthecourse and in this book, as is evidenced from similar summary tables in laterchapters.Werecommend this approach highly.The rest of Chapter 4 lays out a partial equilibrium approach to the determination of interest rates using thesupply and demand in the bond market. An important feature of the analysis in this chapter is that supplyand demand is always done in terms of stocks of assets, not in terms of flows. Recent literature in theprofessional journals almost always analyzes the determination of prices in financial markets with anasset-market approach: that is, stocks of assets are emphasized rather than flows. The reason for this is thatkeeping track of stocks of assets is easier than dealing with flows. Correctly conducting analysis in termsof flows is very tricky, for example, when we encounter inflation. Thus there are two reasons for using astock approach rather than a flow approach: (1) it is easier, and (2) it is more consistent with moderntreatment of asset markets by financial economists.Another important feature of this chapter is that it lays out supply and demand analysis of the bond marketat a similar level to that found in principles of economics textbooks. The ceteris paribus derivations ofsupply and demand curves with numerical examples are presented, the concept of equilibrium is carefullydeveloped, the factors that shift the supply and demand curves are outlined, and the distinction betweenmovements along a demand or supply curve and shifts in the curve is clearly drawn.Ourfeeling is that thestep-by-step treatment in this chapter is worthwhile because supply and demand analysis is such a basictool throughout the study of financial markets and institutions.Wehave found that even those studentswho have had excellent training in earlier courses find that this chapter provides a valuable review ofsupply and demand analysis.The Practicing Manager application at the end of the chapter shows how interest rate forecasts can be usedby managers of financial institutions to increase profits. This application shows students how the analysisthey have learned is useful in the real world.This chapter has an extensive set of appendices on the web to enhance its material. Appendix 1 providesmodels of asset pricing in case an instructor wants to make use of the capital asset pricing model or thearbitrage pricing model in this course. Appendix 2 shows how the analysis developed in the chapter can beapplied to understanding how any asset’s price is determined. Students particularly like the application tothe gold market because this commodity piques almost everybody’sinterest. Appendix 3 providesanotherinterpretation of the supply and demand analysis for bonds using a different terminology involving thesupply and demand for loanable funds. Appendix 4 provides an alternative approach to interest ratedetermination developed by John Maynard Keynes, known as the liquidity preference framework.

Solution Manual for Financial Markets and Institutions, 9th Edition - Page 20 preview image

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Chapter 4: Why Do Interest Rates Change?17◼Answers to End-of-Chapter Questions1.a.Less, because your wealth has declinedb.More, because its relative expected return has risenc.Less, because it has become less liquid relative to bondsd.Less, because its expected return has fallen relativeto golde.More, because it has become less risky relative to bonds2.a.More, because your wealth has increasedb.More, because it has become more liquidc.Less, because its expected return has fallen relative to Polaroid stockd.More, because it has become less risky relative to stockse.Less, because its expected return has fallen3.Raphael is incorrect. If at the current level of interest rates there is an excess supply of bonds, thesupply and demand analysis tells us that interest rates will increase, creating a movement along boththe demand curve (in the southeast direction) and the supply curve (in the southwest direction) inorder to reach the equilibrium interest rate (and price). The bond’s price will therefore fall and theinterest rate will rise to the equilibrium level.4.Purchasing shares in the pharmaceutical company is more likely to reduce my overall risk becausethe correlation of returns on my investment in a football team with the returns on the pharmaceuticalcompany shares should be low. By contrast, the correlation of returns on an investment in a footballteam and an investment in a basketball team are probably pretty high, so in this case there would belittle risk reduction if I invested in both.5.Maria is choosing a bond with higher standard deviation, but also with higher expected return thanJennifer. In order to decide whether Maria or Jennifer is more risk averse, one will need to comparetwo bonds with the same expected return and different standard deviations of their expected returns.Since a high expected return is a desirable characteristic of a bond and a high volatility of its expectedreturn (high standard deviation) is a non-desirable characteristic, it is not uncommon that highlyvolatile bonds exhibit higher expected returns, as the bond preferred by Maria.6.When the Fed sells bonds to the public, it increases the supply of bonds, thus shifting the supplycurveBsto the right. The result is that the intersection of the supply and demand curvesBsandBdoccurs at a lower equilibrium bond price and thus a higher equilibrium interest rate, and the interestrate rises.7.When the economy booms, the demand for bonds increases: The public’s income and wealth riseswhile the supply of bonds also increases, because firms have more attractive investment opportunities.Both the supply and demand curves (BdandBs) shift to the right, but as is indicated in the text, thedemand curve probably shifts less than the supply curve so the equilibrium interest rate rises. Similarly,when the economy enters a recession, both the supply and demand curves shift to the left, but thedemand curve shifts less than the supply curve so that the bond price rises and the interest rate falls.The conclusion is that bond prices fall and interest rates rise during booms and fall during recessions,that is, interest rates are procyclical.

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18Mishkin/Eakins•Financial Markets and Institutions,EighthEdition8.If the government imposes a limit on the amount of daily transactions in the bond market, then bondswill become less liquid with respect to alternative assets. Such a regulation will mean that it will nowbe more difficult to find buyers and sellers in the bond market, thereby affecting the liquidity ofbonds and the demand curve (which will shift to the left), increasing the interest rate and loweringbond´s prices (for a given supply curve).9.Interest rates would rise. A sudden increase in people’s expectations of future real estate pricesraises the expected return on real estate relative to bonds, so the demand for bonds falls. Thedemand curveBdshifts to the left, and the equilibrium bond price falls, so the interest rate rises.10.If many big corporations decide not to issue bonds because of new financial markets regulations, thiswill affect the supply curve. The impact will translate into a shift to the left in the supply curve,increasing bond´s prices (lowering interest rates) and lowering the quantity of bonds bought and soldin the market.11.Yes. The increase in budget deficits increased the supply of bonds and shifts the supply curve BStothe right, which everything else equal would decrease bond prices and raise interest rates. However,the weak economy in the aftermath of the global financial crisis caused investment opportunities toshrink so dramatically that it shifted the supply curve BSto the left by more than the deficits shifted itto the right. The result was that the price of Treasury bonds rose and interest rates on these bondsfell.12.When news about accounting scandals in big corporations spread, people get worried about thequality of the bonds they are either holding or considering to buy. We can expect then that bonds arenot as desirable assets as they were before (maybe because the ability of corporations to honor theircommitments was overstated). This negatively affects demand for these bonds and shifts the demandcurve to the left, raising interest rates and lowering corporate bond´s prices (for a given supplycurve).13.Yes, interest rates will rise. The lower commission on stocks makes them more liquid than bonds,and the demand for bonds will fall. The demand curveBdwill therefore shift to the left, and theequilibrium bond price falls and the interest rate will rise.14.If a big commercial partner of the US enters into a recession, this will probably adversely affect thebusiness of many US companies that export goods and services to that country or region (theEurozone in this case). This will most likely result in job losses and a decrease in wealth, at the sametime that there will be a decrease in investment opportunities. The first effect will shift the demandfor bonds curve to the left, while the latter will shift the supply curve of bonds to the left. The result isthat the equilibrium quantity of bonds issued and bought will unambiguously decrease, while theeffect on bond´s prices and the interest rate will appear to be ambiguous. However, this might not bevery different from a domestic recession, so one can expect interest rates to decrease.15.The interest rate on the AT&T bonds will rise. Because people now expect interest rates to rise, theexpected return on long-term bonds such as the188sof 2022 will fall, and the demand for thesebonds will decline. The demand curveBdwill therefore shift to the left, and the equilibrium bondprice falls and the interest rate will rise.16.If people in France decide to permanently increase their savings rate, then more wealth will beaccumulated over the years. This increase in wealth determines that more bonds will be bought at anygiven interest rate (or bond´s price), creating a shift to the right in the demand curve for bonds inFrance. This European country can therefore expect permanent lower interest rates in the future.

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Chapter 4: Why Do Interest Rates Change?1917.If the government is planning to fund a major infrastructure plan, it will need to get funds, andthereby will probably issue more bonds. Since the government is a major player in the market forbonds, this will most likely result in a shift to the right in the supply curve, lowering the price ofbonds and increasing interest rates in the future. If you have the opportunity, it would be wise to lockin now a long term loan with current low interest rates.◼Quantitative Problems1.You own a $1,000-par zero-coupon bond thathas 5 years of remaining maturity. You plan on sellingthe bond in one year and believe that the required yield next year will have the following probabilitydistribution:ProbabilityRequired Yield0.16.60%0.26.75%0.47.00%0.27.20%0.17.45%a.What is your expected price when you sell the bond?b.What is the standard deviation?Solution:ProbabilityRequired YieldPriceProbPriceProb(Price−Exp. Price)20.16.60%$774.41$ 77.4412.847762410.26.75%$770.07$154.019.7756681310.47.00%$762.90$305.160.0130175120.27.20%$757.22$151.446.8626095410.17.45%$750.02$ 75.0216.5903224$763.0746.08937999The expected price is $763.07.The variance is $46.09, or a standard deviation of $6.79.2.Consider a $1,000-par junk bond paying a 12% annual coupon. The issuing company has 20% chanceof defaulting this year; in which case, the bond would not pay anything. If the company survives thefirst year, paying the annual coupon payment, it then has a 25% chance of defaulting in the secondyear. If the company defaults in the second year, neither the final coupon payment nor par value ofthe bond will be paid. What price must investors pay for this bond to expect a 10% yield to maturity?At that price, what is the expected holding period return? Standard deviation of returns? Assume thatperiodic cash flows are reinvested at 10%.Solution:The expected cash flow att1=0.20 (0)+0.80 (120)=96The expected cash flow att2=0.25 (0)+0.75 (1,120)=840The price today should be:0296840781.491.101.10P=+=

Solution Manual for Financial Markets and Institutions, 9th Edition - Page 23 preview image

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20Mishkin/Eakins•Financial Markets and Institutions,EighthEditionAt the end of two years, the following cash flows and probabilities exist:ProbabilityFinal CashFlowHoldingPeriodReturnProbHPRProb(HPR−Exp. HPR)20.2$0.00−100.00%−20.00%19.80%0.2$132.00−83.11%−16.62%13.65%0.6$1,252.0060.21%36.12%22.11%−0.50%55.56%The expected holding period return is almost zero (−0.5%). The standard deviation isroughly 74.5% (the square root of 55.56%).3.Last month, corporations supplied $250 billion in bonds to investors at an average market rate of11.8%.This month, an additional $25 billion in bonds became available, and market rates increased to 12.2%.Assuming a Loanable Funds Framework for interest rates, and that the demand curve remainedconstant, derive a linear equation for the demand for bonds, using prices instead of interest rates.Solution:First, translate the interest rates intoprices.100011.8%,or894.454PiPP−===100012.2%,or891.266PiPP−===We know two points on the demand curve:891.266,275894.454,250PQPQ====So, the slope=891.266894.4540.12755275250PQ−==−Using the point-slope form of the line,Price=0.12755Quantity+Constant. We cansubstitute in either point to determine the constant. Let’s use the first point:891.2660.12755275 + Constant,orConstant856.189==Finally, we have:: Price0.12755Quantity856.189dB=+4.An economist has estimated that, near the point of equilibrium, the demand curve and supply curvefor bonds can be estimated using the following equations:2: PriceQuantity9405: PriceQuantity500dsBB−=+=+a.What is the expected equilibrium price and quantity of bonds in this market?b.Given your answer to part (a), which is the expected interest rate in this market?Solution:

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Chapter 4: Why Do Interest Rates Change?21a.Solve the equations simultaneously:29405[500]70440,or314.28575PQPQQQ−=+−=+−=+=This implies thatP=814.2857.b.1000814.285722.8%814.2857i−==5.As in Question 6, the demand curve and supply curve for bonds are estimated using the followingequations:2: PriceQuantity9405: PriceQuantity + 500dsBB−=+=Following a dramatic increase in the value of the stock market, many retirees started moving moneyout of the stock market and into bonds. This resulted in a parallel shift in the demand for bonds, suchthat the price of bonds at all quantities increased $50. Assuming no change in the supply equation forbonds, what is the new equilibrium price and quantity? What is the new market interest rate?Solution:The new demand equation is as follows:2: PriceQuantity9905dB−=+Now, solve the equations simultaneously:29905[500]70490,or350.005PQPQQQ−=+−=+−=+=This implies thatP=850.00.1000850.0017.65%850.00i−==6.Following Question 5, the demand curve and supply curve for bonds are estimated using thefollowing equations:Bd:Price=2 Quantity9905−+Bs: Price=Quantity+500

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22Mishkin/Eakins•Financial Markets and Institutions,EighthEditionAs the stock market continued to rise, the Federal Reserve felt the need to increase the interest rates.As a result, the new market interest rate increased to 19.65%, but the equilibrium quantity remainedunchanged. What are the new demand and supply equations? Assume parallel shifts in the equations.Solution:Prior to the change in inflation, the equilibrium wasQ=350.00 andP=850.00. The newequilibrium price can be found as follows:100019.65%,or835.771PiPP−===This point (350, 835.771) will be common to both equations. Further since the shift was aparallel shift, the slope of the equations remainsunchanged. So, we use the equilibriumpoint and the slope to solve for the constant in each equation:Bd:835.771=2 350constant,orconstant975.7715−+=Bd: Price=2 Quantity975.7715−+andBs:835.771=350+constant,orconstant=485.771Bs: Price=Quantity+485.771

Solution Manual for Financial Markets and Institutions, 9th Edition - Page 26 preview image

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Chapter 5How Do Risk and Term StructureAffect Interest Rates?Risk Structure of Interest RatesDefault RiskLiquidityCase: TheGlobal Financial Crisisand the Baa-Treasury SpreadIncome Tax ConsiderationsSummaryCase: Effects of the Bush Tax Cutand the Obama Tax Increaseon Bond Interest RatesTerm Structure of Interest RatesFollowing the Financial News: Yield CurvesExpectations TheoryMarket Segmentation TheoryLiquidity Premium TheoryEvidence on the Term StructureSummaryMini-Case Box: The Yield Curve as a Forecasting Tool for Inflation and the Business CycleCase: Interpreting Yield Curves, 1980–2016The Practicing Manager: Using the Term Structure to Forecast Interest Rates◼Overview and Teaching TipsChapter 5applies the tools the student learned in Chapter 4 to understanding why and how various interestrates differ.In courses that emphasize financial markets, this chapter is important because students arecurious about the risk and term structure of interest rates. On the other hand, professors who focus on publicpolicy issues might want to skip this chapter.The book has been designed so that skipping this chapter willnot hinder the student’s understanding of later chapters.A particularly attractive feature of this chapter is that it gives students a feel for the interaction of data andtheory. As becomes clear in the discussion of the term structure, theories are modified because they cannotexplain the data. On the other hand, theories do help to explain the data, as the case on interpreting yieldcurves in the 1980–2016period demonstrates.This chapter also has two cases that will pique students’ interest because they are so current. First is theeffect of the Bush taxcut and the Obama tax increaseon bond interest rates. Since the topic of repeal ofthe Bush tax cutand the Obama tax increase aresuch a hot political issue, evaluating what impact the

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24Mishkin/Eakins•Financial Markets and Institutions,EighthEditionrepeal might have on interest rates is sure to be of interest to students. Also students are particularlyinterested right now in how the recent financial crisisaffected the economy, and this chapter hasacasethat looks at this topic. The case on theglobal financial crisis and the Baa-Treasury spreadapplies theanalysis in the chapter to show how the recent financial crisis led to a dramatic increase in the spreadbetween interest rates on Baa securities with credit risk relative to U.S. Treasury securities that do not.The Practicing Manager application at the end of the chapter shows how forecasts of interest rates from theterm structure using the theories outlined here can be used by financial institutions managers to set interestrates on their financial instruments.◼Answers to End-of-Chapter Questions1.The bond with a C rating should have a higher risk premium because it has a higher default risk,which reduces its demand and raises its interest rate relative to that of the Baa bond.2.U.S. government issued securities are usually considered to be default free. However, securitiesissued by other governments usually have a positive risk premium, depending in general on the fiscalimbalances that each country exhibits at a given point in time.3.During business cycle booms, fewer corporations go bankrupt and there is less default risk oncorporate bonds, which lowers their risk premium. Similarly, during recessions, default risk oncorporate bonds increases and their risk premium increases. The risk premium on corporate bonds isthus anticyclical, rising during recessions and falling during booms.4.True. When bonds of different maturities are close substitutes, a rise in interest rates for one bondcauses the interest rates for others to rise because the expected returns on bonds of differentmaturities cannot get too far out of line.5.Historically, mortgage backed securities were considered low risk assets, since homeowners had thehighest incentives to pay their mortgages (otherwise they might lose their home). However, afterstandards on lending practices decreased during the first years of the new century, many individualswere able to buy a house, but not to make their mortgage payments. This resulted in poor qualitymortgage backed securities that should never have had such good ratings. Both Standard and Poor´sand Moody´s were investigated for assigning such good ratings and therefore misleading investors inbuying these instruments. Sometimes credit rating agencies also make mistakes in assigning risks.6.The flat yield curve at shorter maturities suggests that short-term interest rates are expected to fallmoderately in the near future, while the steep upward slope of the yield curve at longer maturitiesindicates that interest rates further into the future are expected to rise. Because interest rates andexpected inflation move together, the yield curve suggests that the market expects inflation to fallmoderately in the near future but to rise later on.7.The steepupward-sloping yield curve at shorter maturities suggests that short-term interest rates areexpected to rise moderately in the near future because the initial, steep upward slope indicates thatthe average of expected short-term interest rates in the near future is above the current short-terminterest rate. The downward slope for longer maturities indicates that short-term interest rates areeventually expected to fall sharply. With a positive risk premium on long-term bonds, as in theliquidity premium theory, a downward slope of the yield curve occurs only if the average of expectedshort-term interest rates is declining, which occurs only if short-term interest rates far into the futureare falling. Since interest rates and expected inflation move together, the yield curve suggests that themarket expects inflation to rise moderately in the near future but fall later on.

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Chapter 5: How Do Risk and Term Structure Affect Interest Rates?258.If the trading volume of the corporate bonds market declines, then corporate bonds become lessliquid, as it will be more difficult to find buyers and sellers. This drop in liquidity makes thesesecurities less desirable assets, increasing their risk and “liquidity” premium.9.The government guarantee will reduce the default risk on corporate bonds, making them moredesirable relative to Treasury securities. The increased demand for corporate bonds and decreaseddemand for Treasury securities will lower interest rates on corporate bonds and raise them onTreasury bonds.10.If the federal government decides to guarantee payments on all municipal bonds, then these bondswill effectively be default free. This characteristic will make them very desirable assets, increasingtheir demand and thereby lowering their interest rates. If this were to happen, then municipal bondswill be even better than U.S. government bonds, since both are default free, but municipal bonds areincome tax exempted instruments. In this case, it will not make sense for municipal bonds to beexempted from paying taxes, since this exemption is made precisely to “help” local governments togain access to funds.11.Abolishing the tax-exempt feature of municipal bonds would make them less desirable relative toTreasury bonds. The resulting decline in the demand for municipal bonds and increase in demand forTreasury bonds would raise the interest rates on municipal bonds, while the interest rates on Treasurybonds would fall.◼Quantitative Problems1.Assuming that the expectations theory is the correct theory of the term structure, calculate the interestrates in the term structure for maturities of one to five years, and plot the resulting yield curves for thefollowing series of one-year interest rates over the next five years:a.5%, 7%, 7%, 7%, 7%b.5%, 4%, 4%, 4%, 4%How would your yield curves change if people preferred shorter-term bonds over longer-term bonds?Solution:a.The yield to maturity would be 5% for a one-year bond, 6% for a two-year bond, 6.33% for athree-year bond, 6.5% for a four-year bond, and 6.6% for a five-year bond.b.The yield to maturity would be 5% for a one-year bond, 4.5% for a two-year bond, 4.33% for athree-year bond, 4.25% for a four-year bond, and 4.2% for a five-year bond.The upward-sloping yield curve in (a) would be even steeper if people preferred short-term bondsover long-term bonds because long-term bonds would then have a positive risk premium. Thedownward-sloping yield curve in (b) would be less steep and might even have a slight positiveupward slope if the long-term bonds have a positive risk premium.2.Government economists have forecasted one-year T-bill rates for the following five years as follows:Year1-year rate14.25%25.15%35.50%46.25%57.10%

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26Mishkin/Eakins•Financial Markets and Institutions,EighthEditionYou have liquidity premium 0.25% for the next two years and 0.50% thereafter. Would you bewilling to purchase a 4-year T-bond at a 5.75% interest rate?Solution:Your required interest rate on a 4-year bond=Averageinterest on four 1-year bonds +Liquidity Premium= (4.25% +5.15%+5.50%+ 6.25%)/4 +0.5%=5.29%+ 0.50% =5.79%At a rate of 5.75%, the T-bond is just below your required rate.3.What is the yield on a $1,000,000 municipal bond with a coupon rate of 8%, paying interest annually,versus the yield of a $1,000,000 corporate bond with a coupon rate of 10% paying interest annually?Assume that you are in the 25% tax bracket.Solution:Municipal bond coupon payments equal $80,000 per year. No taxes are deducted;therefore, the yield would equal 8%.The coupon payments on a corporate bond equal $100,000 per year. But you onlykeep $75,000 because you are in the 25% tax bracket. Therefore your after-tax yieldis only 7.5%4.Consider the decision to purchase either a 5-year corporate bond or a 5-year municipal bond. Thecorporate bond is a 12% annual coupon bond with a par value of $1,000. It is currently yielding 11.5%.The municipal bond has an 8.5% annual coupon and a par value of $1,000. It is currently yielding 7%.Which of the two bonds would be more beneficial to you? Assume that your marginal tax rate is 35%.Solution:Municipal BondPurchase Price=$1,061.50After-tax Coupon Payment=$85Par Value=$1,000Calculated YTM=7%Corporate BondPurchase Price=$1,018.25After-tax Coupon Payment=$78Par Value=$1,000Calculated YTM=7.35%The corporate bond offers a higher yield and is the better buy.5.A municipal and a corporate bond of equal risk, liquidity and maturity yield 6% and 10%respectively. For which values of marginal tax rates would you prefer to buy the municipal bond?Solution:For marginal tax rates larger than 40%. These are the marginal tax rates thatsolve thefollowing inequality:0.06˃0.10 × (1 ‒t) → 0.06 ‒ 0.10 ˃ ‒0.1t→ ‒0.04 ˃ ‒0.1t0.040.40.1→=t6.1-year T-bill rates are expected to steadily increase by 150 basis points per year over the next 6 years.Determine the required interest rate on a 3-year T-bond and a 6-year T-bond if the current 1-yearinterest rate is 7.5%. Assume that the Pure Expectations Hypothesis for interest rates holds.

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Chapter 5: How Do Risk and Term Structure Affect Interest Rates?27Solution:3 year bond:Year 1 interest rate=7.5%Year 2 interest rate =9.0%Year 3 interest rate =10.5%Number of years=3(7.5% +9.0%+10.5%)/3=9.0%6 year bond:Year 1 interest rate =7.5%Year 2 interest rate =9.0%Year 3 interest rate =10.5%Year 4interest rate =12%Year 5 interest rate =13.5%Year 6 interest rate =15%(7.5% +9.0%+ 10.5% +12% + 13.5% + 15%)/6 =11.25%7.Short term (one year) interest rates over the next 6 years will be 0.5%, 0.6%, 0.7%, 0.76%, 0.80% and0.84%. Using the expectations theory, what will be the interest rates on a three, four and six-year bonds?Solution:Three-year bond = (0.5% + 0.6% + 0.7%) / 3=0.6%.Four-year bond = (0.5% + 0.6% + 0.7% + 0.76%) / 4=0.64%.Six-year bond = (0.5% + 0.6% + 0.7% + 0.76% + 0.80% + 0.84%) / 6=0.7%.8.Using the information from the previous question, now assume that the investor prefers holdingshort-term bonds. A liquidity premium of 10 basis points is required for each year of a bond’smaturity. What will be the interest rates on a 3-year bond, 6-year bond, and 9-year bond?Solution:To solve this problem, you will need to use the following equation:121eeettttnntntiiiiiln+++−+++    +=+3-year bond= (0.30) + [(3 +4.5+6)]/(3)=4.8%6-year bond = (0.60) + [(3 +4.5+6+7.5+9+ 10.5)]/(6) =7.35%9-year bond = (0.90) + [(3 +4.5+ 6 + 7.5 + 9 +10.5+13+14.5+16)]/(9)=10.233%9.Suppose that the expectations theory is true and that you can buy a three-year bond with an interestrate of 6% or three consecutive one-year bonds with interest rates of 4%, 5% and 6%. Which optionwould you choose to undertake?Solution:The three-year bond is a better option, since the three consecutive short term bonds yieldanaverage interest rate equal to (4% + 5% + 6%) / 3=5%.10.Little Monsters Inc. borrowed $1,000,000 for two years from NorthernBank Inc. at an 11.5% interestrate. The current risk-free rate is 2% and Little Monsters’s financial condition warrants a default riskpremium of 3% and a liquidity risk premium of 2%. The maturity risk premium for a two-year loan is1%, and inflation is expected to be 3% next year. What does this information imply about the rate ofinflation in the second year?Solution:If inflation were expected to remain constant at 3% over the life of the loan, the interestrate on the two-year loan would be 11%. Since the actual two-year interest rate is 11.5%,the one-year interest rate in year 2 must be 12%, since 11.5=(11+12)/2.The required rate of 12% =Rf+DRP+LP+MRP+Inflation Premium

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28Mishkin/Eakins•Financial Markets and Institutions,EighthEdition=2%+ 3% + 2% + 1% +Inflation PremiumSo, the Inflation Premium in year 2 is 4%. But this is an average premium over two years.Inflation Premium 4%=(Year 1 Inflation+Year 2 Inflation)/2= (3% +x)/2orx=5%11.One-year T-bill rates are 2% currently. If interest rates are expected to go up after 3 years by 2%every year, what should be the required interest rate on a 10-year bond issued today?Solution:272222(1.02)2(1.02)2(1.02)(10-year bond)1021.165 /102.1165%I+++++    +===12.Short term (one-year) interest rates over the next 3 years are expected to be 2%, 3% and 3.55%. Ifyou are ready to buy a three-year bond that yields 3%, which is your required liquidity premium forthis period?Solution:The minimum liquidity premium required for three years is 0.15%. The liquidity premiumsolves the following equation:330.020.030.03550.030.030.02850.15%3++=+→=−=ll13.At your favorite bond store, Bonds-R-Us, you see the following prices:a.1-year $100 zero selling for $90.19b.3-year 10% coupon $1000 par bond selling for $1000c.2-year 10% coupon $1000 par bond selling for $1000Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity ormaturity premium exists, and the bonds are equally risky. What is the implied 1-year rate two yearsfrom now?Solution:From (a), you know that the 1-year rate today is 10.877%.Using this information, (c) tells you that:1000 = 100/1.10877 + 1100/(1 +2-year rate)2So, the 2-year rate today is 9.95%.Using these two rates, (b) tells you that:1000 = 100/1.10877 +100/1.09952+ 1100/(1 +3-year rate)3So, the 3-year rate today is 9.97%1-year rate 2 years from now=(39.97%–29.95%) =10.01%14.You observe the following market interest rates, for both borrowing and lending:One-year rate=5%Two-year rate=6%One-year rate one year from now =7.25%How can you take advantage of these rates to earn a riskless profit? Assume that the Pure ExpectationTheory for interest rates holds.

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