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Solution Manual for Financial Markets and Institutions, 9th Edition

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    Online Instructor’s Manual For Financial Markets and Institutions Ninth Edition Frederic S. Mishkin Columbia University Stanley Eaki ns East Carolina University

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    Table of Contents I. Introduction ................................ ................................ ................................ ............................ 1 1. Why Study Fina ncial Markets and Institutions? ................................ ................................ ...... 2 2. Overview of the Financial System ................................ ................................ ........................... 5 II. Fundamentals of Financial Markets ................................ ................................ ...................... 8 3. What Do Interest Rates Mean and W hat Is Their Role in Valuation? ................................ ..... 9 4 . Why Do Interest Rates Change? ................................ ................................ ............................ 15 5. How Do Risk and Term S tructure Affect Interest Rates? ................................ ..................... 23 6. A re Financial Markets Efficient? ................................ ................................ .......................... 30 III. Fundame ntals of Financial Institutions ................................ ................................ .................. 3 3 7. Why D o Financial Institutions Exist? ................................ ................................ .................... 34 8. Why Do Financial Crises Occur and Why Are They So Damaging to the Economy? ................................ ................................ ................................ ........................ 40 IV. Central Banking and the Conduct of Monetary Policy ................................ ......................... 4 5 9. Central Banks and the Federal Reserve System ................................ ................................ .... 4 6 10. Conduct of Monetary Policy ................................ ................................ ................................ . 50 V. Financial Markets ................................ ................................ ................................ ..................... 57 11. The Money Markets ................................ ................................ ................................ ............ 58 12. The Bond Market ................................ ................................ ................................ .................. 64 13. The Stock Market ................................ ................................ ................................ ............... 70 14. The Mortgage Markets ................................ ................................ ................................ ....... 76 15. The Foreign Exchange Market ................................ ................................ ............................. 86 16. The International Financial System ................................ ................................ ...................... 92 VI. The F inancial Institutions Industry ................................ ................................ ........................ 9 7 17. Banking and the Manag ement of Financial Institutions ................................ ....................... 98 18. Financial Regulation ................................ ................................ ................................ ........... 106 19. Banking Indu stry: Structure and Competition ................................ ................................ .... 113 20. The Mutual Fund Industry ................................ ................................ ................................ .. 116 21. Insura nce Companies and Pension Funds ................................ ................................ .......... 123 22. Investment Banks, Security Brokers and Dea lers, and Venture Capital Firms .................. 128 VII. The Management of Financial Institutions ................................ ................................ .......... 13 2 23. Risk Manage ment in Financial Institutions ................................ ................................ ........ 13 3 24. Hedging with Financial Derivatives ................................ ................................ ................... 143 Chapters on the Web 25. Financial Cris es in Emerging Market Economies ................................ .............................. 153 26. Savings Associations and Credit Unions ................................ ................................ ............ 156 27. Finance Companies ................................ ................................ ................................ ............ 15 9

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    Part I Introduction

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    Chapter 1 Why Study Financial Markets and Institutions? Why Study Financial Markets? Debt Markets and Interest Rates The Stock Market The Foreign Exchange Market Why Study Financial Institutions? Structure of the Financial System Financial Crise s Central Banks and the Conduct of Monetary Policy The International Financial System Banks and Other Financial Institutions Financial Innovation Managing Risk in Financial Institutions Applied Managerial Perspective How We Will Study Financial M arkets and Institutions Exploring the Web Collecting and Graphing Data Web Exercise Concluding Remarks ◼ Overview and Teaching Tips Before embarking on a study of financial markets and institutions, the student must be convinced that this subject is wo rth studying. Chapter 1 pursues this goal by showing the student that financial markets and institutions is an exciting field because it focuses on phenomena that affect everyday life. An additional purpose of Chapter 1 is to provide an overview for the entire book, previewing the topics that will be covered in later chapters. The chapter also provides the students with a guide as to how they will be studying financial 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 have found that talking about the data presented in the figures helps achieve this goal by showing the students that the 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 that the course will have an applied managerial

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    Chapter 1: Why Study Financial Markets and Institutions? 3 perspective, which they will find useful latter in thei r careers. Going through the web exercise is also a way of encouraging the students to use the web to further their understanding of financial markets and institutions. ◼ Answers to End - of - Chapter Questions 1. Well performing financial markets tend to allo cate funds to its more efficient use, thereby allowing the best investment opportunities to be undertaken. The improvement in the allocation of funds results in a more efficient economy, which stimulates economic growth (and thereby poverty reduction). 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 their purchase is higher. 3. A change in interest rates affects the cost of acquiring funds for financial institution as well as changes the income on assets such as loans, both of which affect profits. In addition, changes in interest rates affect the price of assets such as stock and bonds that the financial institution owns which 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 a corporate bond or the interest rate charged to a homeowner, it is also true that all of these interest rates tend to move together. Evidence shows that movements in different interest rates over time are in large part explained by the same events, and thereby allow economists to refer to “the” interest rate when 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 investment in 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 that stockholders are residual claimants (i.e. the corporation has to pay all bondholders before paying stockholders). 7. It makes foreign goods more expensive and so British consumers will buy less foreign goods and more domestic goods. 8. It makes British goods more expensive relative to American goods. American businesses will find it easier 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 thus lead to gains and losses on these assets. Also changes in foreign exchange rates affect the profits made 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, making travel abroad relatively more expensive; that would have been a good time to vacation in the United States and see the Grand Canyon. As the dollar’s value rose in the early 1980s, travel abroad became relatively cheaper, making it a good time to visit the Tower of London.

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    4 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition 11. In general people do not lend large amounts of mo ney to one another because of several information problems. In particular, people do not know about the capacity of other people of repaying their debts, or the effort they will provide to repay their debts. Financial intermediaries, in particular commercial banks, tend to solve these problems by acquiring information about potential borrowers and writing and enforcing contracts that encourage lenders to repay their debt and/or maintain the value of the collateral. 12. Savings and loan associations, mutual savings banks, credit unions, insurance companies, mutual funds, pension funds, and finance companies. 13. The latest financial crisis in the US and Europe occurred in 2007 – 2009. At the beginning it hit mostly the US financial system, but it then quickly moved to Europe, since financial markets are highly interconnected. One specific way in which these markets were related, is that some financial intermediaries in Europe held securities backed by mortgages originated in the US, and when these securities lost their a considerable part of their value, the balance sheet of European financial intermediaries were adversely affected. 14. The profitability of financial institutions is affected by changes in interest rates, stock prices, and foreign 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 have an important impact on the profitability of financial institutions. ◼ Quantitative Problems 1. The following table lists foreign exchange rates between U.S. dollars and British pounds during April: Date U.S. Dollars per GBP Date U.S. Dollars per GBP 4/1 1.9564 4/18 1.7504 4/4 1.9293 4/19 1.7255 4/5 1.914 4/20 1.6914 4/6 1.9374 4/21 1.672 4/7 1.961 4/22 1.6684 4/8 1.8925 4/25 1.6674 4/11 1.8822 4/26 1.6857 4/12 1.8558 4/27 1.6925 4/13 1.796 4/28 1.7201 4/14 1.7902 4/29 1.7512 4/15 1.7785 Which 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 worst day is 4/7. At $1.961/pound, you would have £101.99, or a difference of £17.96.

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    Chapter 2 Overview of the Financial System Function of Financial Markets Structure of Financial Markets Debt and Equity Markets Primary and Secondary Markets Exchanges and Over - the - Counter Markets Money and Capital Markets I nternationalization of F inancial Markets International Bond Market, Eurobonds, and Eurocurrencies Global Box: Are U.S. Capital Markets Losing Their Edge? World Stock Markets Function of Financial Intermediaries: Indirect Finance Transaction Costs Following the Financial Ne ws : Foreign Stock Market Indexes Global Box: The Importance of Financial Intermediaries Relative to Securities Markets: An International Comparison Risk Sharing Asymmetric Information: Adverse Selection and Moral Hazard Economies of Scope and Confli cts of Interest Types of Financial Intermediaries Depository Institutions Contractual Savings Institutions Investment Intermediaries Regulation of the Financial System Increasing Information Available to Investors Ensuring the Soundness of Financ ial Intermediaries Financial Regulation Abroad

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    6 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition ◼ Overview and Teaching Tips Chapter 2 is an introductory chapter that contains the background information on the structure and operation of financial markets that is needed in later chapters of the book. Th is chapter allows the instructor to branch out to various choices of later chapters, thus allowing different degrees of coverage of financial markets and institutions. The most important point to transmit to the student is that financial markets and financial intermediaries are crucial to a well - functioning economy because they channel funds from those who do not have a productive use for them to those who do. Some instructors will want to teach this chapter in detail, and those who focus on international issues will want to spend some time on the section “Internationalization of Financial Markets.” However, those who slant their course to public policy issues may want to give this chapter a more cursory treatment. No matter how much class time is devoted to this chapter, We have found that it is a good reference chapter for students. You might want to tell them that if in later chapters they do not recall what particular financial intermediaries do and who regulates them, they can refer back to this chapter, especially to tables, such as Tables 2. 1 and 2. 3. ◼ Answers to End - of - Chapter Questions 1. 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 tuit ion. • 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 a flooded basement) without having to wait to save enough and only then being able to afford such goods and services. 2. Y es, I should take out the loan, because I will be better off as a result of doing so. My interest payme nt will be $4,500 (90% of $5,000), but as a result, I will earn an additional $10,000, so I will be ahead of the game by $5,500. Since Larry’s loan - sharking business can make some people better off, as in this example, 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 who have the most productive use for them. Entrepreneurs then cannot acquire funds to set up businesses that would help the economy grow rapidly. 4. The principal debt instruments used were foreign bonds which were sold in Britain and denominated in pounds. The British gained because they were able to earn higher interest rates as a result of lending to Americans, while the Americans gained because they now had access to capital to start up profitable businesses such as railroads. 5. If the Yen denominated bond is sold in Tokyo, then it is not considered a Eurobond. If the bond is sold 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 the residual claimants.

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    Chapter 2: Overview of the Financial System 7 7. Because you know your family member better than a stranger, you know more about the borrower’s honesty, propensity for risk taking, and other traits. There is less asymmetric information than with a stranger and less likelihood of an adverse selection problem, with the result that you are more likely to lend to the family member. 8. Maria cannot participate in a hedge fund since this type of mutual fund requires minimum contributions of $100.000 and sometimes more. This type of financial intermediary is targeted to specific savers that have a less cautious perception of risks, using the collected funds to buy assets that are earn high returns, but are quite risky. 9. Loan sharks can threaten their borrowers with bodily harm if borrowers take actions that might jeopardize paying off the loan. Hence borrowers from a loan shark are less likely to engage in moral 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 information asymmetry. Even if you know that a borrower is taking actions that might jeopardize paying off the loan, you must still stop the borrower from doing so. Because that may be costly, you may not spend the 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 no cost 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 it has a 10% interest rate. You are better off depositing your savings with a financial intermediary and earning 5% interest. In addition, you are likely to bear l ess risk by depositing your savings at the bank rather than lending them to your neighbor. 14. Financial intermediaries benefit because they can earn profits on the spreads between the returns they earn on risky assets and they payments they make on the assets they have sold. Households and firms benefit 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 financial regulations that are identical in all countries to avoid financial markets participants to migrate their business to countries with fewer regulations. On the other side, all countries are different and designing a common set of financial regulations seems to be a rather difficult task. Most countries would want to maintain at least part of their regulations, so consensus is difficult to reach.

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    Part II Fundamentals of Financial Markets

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    Chapter 3 W hat Do Interest Rates Mean and What Is Their Role in Valuation? Measuring Interest Rates Present Value Four Types of Credit Market Instruments Yield to Maturity The Distinction Between Real and Nominal Interest Rates Global Box: Negat ive Interest Rates? Japan First, Then the United States, Then Europe The Distinction Between Interest Rates and Returns Mini - Case Box: With TIPS, Real Interest Rates Have Become Observable in the United States Maturity and the Volatility of Bond Retu rns: Interest - Rate Risk Reinvestment Risk Summary Mini - Case Box: Helping Investors to Select Desired Interest - Rate Risk The Practicing Manager: Calculating Duration to Measure Interest - Rate Risk Calculating Duration Duration and Interest - Rate R isk ◼ Overview and Teaching Tips In our years of teaching financial markets and institutions, we have found that students have trouble with what we consider to be easy material because they do not understand what an interest rate is — that it is negatively a ssociated with the price of a bond, that it differs from the return on a bond, and that there is an important distinction between real and nominal interest rates. This chapter spends more time on these issues than does any other competing textbook. Our experience has been that giving this material so much attention is well rewarded. After putting more emphasis on this material in my financial markets and institutions course, we witnessed a dramatic improvement in students’ 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 Practicing Manager.” These applications introduce students to real - world problems that managers of financial institutions have to solve and make the course both more relevant and exciting to students. They are not meant to fully prepare students for jobs in financial institutions — it is up to more specialized courses such as bank or financial institutions management to do this — but these applications teach them some of the special analytical tools that they will need when they enter the business world.

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    10 Mishkin/Eakins • Financial Markets and Instit utions, Eighth Edition This 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 is a basic tool for managers of financial institutions. For those instructors who do not want a managerial emphasis in their financial markets and instit utions course, this and other Practicing Manager applications can be skipped without loss of continuity. ◼ Answers to End - of - Chapter Questions 1. When comparing amounts of money that are disbursed at different dates, one has to take into consideration the concept of present value of money. To calculate the present value of the $5 , 500 promised one year from today one needs to know the annual interest rate. In this case, for an interest rate larger than 10%, on e would prefer to accept the $5, 000 today (since one can deposit that amount and 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 price of 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 the price of the bond. The other part of the formula, the current yield, is composed of the coupon payment (completely determined by the bond´s face value and coupon rate) and the price you paid for the bond today. The rate of capital gain incorporates the future price of the bond and is therefore the part 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 fallen from 3 percent ( = 5 percent – 2 percent) to 1 percent ( = 10 percent - 9 percent). The real cost of financing the house is thus lower, even though mortgage rates have risen. (If the tax deductibility of interest payments is allowed for, then it becomes even more likely that people will buy houses.) ◼ Quantitative Problems 1. Calculate the present value of a $1,000 zero - coupon bond with 5 years to maturity if the required annual interest rate is 6%. Solution: PV = FV /(1 + i ) n where FV = 1000, i = 0.06, n = 5 PV = 747.25 2. A lottery claims its gra nd prize is $10 million, payable over 20 years at $500,000 per year. If the first payment 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%; Pmts in BEGIN mode. Compute PV : PV = $6,079,058.25 3. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table: Years to Maturity Discount Rate Current Price 3 5 3 7

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    Chapter 3: What Do Interest Rates Mean and What Is Their Role in Valuation? 11 6 7 9 7 9 9 What relationship do you observe between yield to maturity and the current market value? Solution: Years to Maturity Yield to Maturity Current Price 3 5 $1,054.46 3 7 $1,000.00 6 7 $1,000.00 9 5 $1,142.16 9 9 $ 880.10 When yield to maturity is above the coupon rate, the band’s current price is below its face value. The opposite holds true when yield to maturity is below the coupon rate. For a given maturity, the bond’s current price falls as yield to maturity rises. For a given yield to maturity, a bond’s value rises as its maturity increases. When yield to maturity equals the coupon 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 currently selling 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 = 1150 Compute I : I = 7.44 5. Suppose that a commercial bank wants to buy Treasury Bills. These instruments pay $5, 000 in one year and are currently selling for $5 , 012. What is the yield to maturity of these bonds? Is this a typical 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 typical situation. 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 described in 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%? If the 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 price would 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 just bought a $100,000 home, what is the PV of all the future property tax payments? Assume that the house remains worth $100,000 forever, property tax rates never change, and that a 9% discount rate is used for discounting.

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    12 Mishkin/Eakins • Financial Markets and Instit utions, Eighth Edition Solution: The taxes on a $100,000 home are roughly 100,000  0.0266 = 2,660. The PV of 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 real interest rate equal to 3%. Assuming that the annualized expected rate of inf lation over the life of the loan is 1%, determine the nominal interest rate that the bank will charge you. What happens if , over the life of the loan , actual inflation is 0.5%? Solution: The bank will charge you a nominal interest rate equal to 1% + 3% = 4%. However, if actual inflation turns out to be lower than expected, then you will be worse off than originally planned, 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 value of $5,000. Both bonds have a coupon rate of 5% and sold at par today. Calculate both bonds´ current yield and both bonds rate of return if Lucia is able to sell these bonds one year later for $100 more of the buying price. Can you estimate what happened to the in terest rate over that year? Solution: The current yield (CY) is calculated as the coupon payment over the selling price of the bond. When a coupon bond sells at par, its current yield equals the coupon rate, since the numerator of the CY is: Face Value x Coupon Rate (always) and the denominator is Face Value (in this particular situation only in which Price = FV). Both bonds have a CY = 5%. If Lucia is able to sell the $1,000 FV coupon bond for $1,100, then the rate of return is: 5% + 10% (since the rate of capital gain is 100/1,000 =10%). The same reasoning yields a RET = 5% + 2% (g = 100/5,000) for the other bond. 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´s prices (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: 1 1 1 80 980.30 0.09 for . 988.53. 980.30 t t t P P P + + + + − = = Although this appears possible, the yield to maturity when you purchased the bond was 8.5%. At that yield, you only expect the price to be $983.62 next year. In fact, the yield would 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 all market interest rates are 7%. Solution: Year 1 2 3 Sum Payments 60.00 60.00 1060.00 PV of Payments 56.07 52.41 865.28 973.76 Time Weighted PV of Payments 56.07 104.81 2595.83 Time Weighted PV of Payments Divided by Price 0.06 0.11 2.67 2.83

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    Chapter 3: What Do Interest Rates Mean and What Is Their Role in Valuation? 13 This bond has a duration of 2.83 ye ars. Note that the current price of the bond is $973.76, which is the sum of the individual “ PV of payments.” 12. Consider the bond in the previous question. Calculate the expected price change if interest rates drop to 6.75% using the duration approximation. Calculate the actual price change using discounted cash flow. Solution: Using the duration approximation, the price change would be: 0.0025 DUR 2.83 973.76 6.44. 1 1.07 i P P i  −  = −   = −   = + The new price would be $980.20. Using a discounted cash flow approach, the price is 980.23 — only $.03 different. Year 1 2 3 Sum Payments 60.00 60.00 1060.00 PV of payments 56.21 52.65 871.3 980.23 13. The duration of a $100 million portfolio is 10 years. $40 million dollars in new securities are added to the 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 the weighted average duration of its individual securities. Let D equal the duration of the $40 million in new securities. Then, this implies: 12.5 (100/140 10) (40/140 D) 12.5 7.1425 + 0.2857 18.75 D D =  +  = = 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 million loan 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 from 8% to 8.5%? Solution: The duration of the first loan is 3 years since it is a zero - coupon loan. The duration of the second loan is as follows: Year 1 2 3 Sum Payment 3.60 3.60 43.60 PV of Payments 3.33 3.09 34.61 41.03 Time Weighted PV of Payments 3.33 6.18 103.83 Time Weighted PV of Payments Divided by Price 0.08 0.15 2.53 2.76

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    14 Mishkin/Eakins • Financial Markets and Instit utions, Eighth Edition The 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) = 2.86 If rates increased, 0.005 DUR 2.86 70,000,000 926,852. 1 1.08 i P P i   = −   = −   = − + 15. Consider a bond that promises the following cash flows. The required discount rate is 12%. Year 0 1 2 3 4 Promised Payments 160 170 180 230 You 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 cash flows are reinvested at 12%. b. If immediately after buying this bond, all market interest rates drop to 11% (including your reinvestment rate), what will be the impact on your total cash flow after 2½ years? How does this 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 will sell the remaining cash flows, discounted at 12%. This gives you: 1.5 0.5 0.5 1.5 180 230 160 (1.12) 170 (1.12) $733.69. 1.12 1.12  +  + + = b. This is the same as part (a), but the rate is now 11%. 1.5 0.5 0.5 1.5 180 230 160 (1.11) 170 (1.11) $733.74. 1.11 1.11  +  + + = Notice that this is only $0.05 different from part (a). c. The duration is calculated as follows: Year 1 2 3 4 Sum Payments 160.00 170.00 180.00 230.00 PV of Payments 142.86 135.52 128.12 146.17 552.67 Time Weighted PV of Payments 142.86 271.05 384.36 584.68 Time Weighted PV of Payments Divided by Price 0.26 0.49 0.70 1.06 2.50 Since the duration and the holding period are the same, you are insulated from immediate changes in interest rates! It doesn’t always work out this perfectly, but the idea is important.

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    Chapter 4 Why Do Interest Rates Change? Determinants of Asset Demand Wealth Expected Returns Risk Liquidity Theory of Portfolio Choice Supply and Demand in the Bond Market Demand Curve Supply Curve Market Equilibrium Supply - and - Demand Ana lysis Changes in Equilibrium Interest Rates Shifts in the Demand for Bonds Shifts in the Supply of Bonds Case : Changes in the Interest Rate Due to Expected Inflation: The Fisher Effect Case : Changes in the Interest Rate Due to a Business Cycle Expansion Case : Explaining the Current Low Interest Rates in Europe, Japan and the United States The Practicing Manager: P rofiting from Interest - Rate Forecasts Following the Financial News : Forecasting Interest Rates Appendix 1: Models of Asset Pricing Appendix 2: Applying the Asset Market Approach to a Commodity Market: The Case of Gold Appendix 3: Loanable Funds Framework Appendix 4: Supply and Demand in the Market for Money: The Liquidity Preference Framework ◼ Overview and Teaching Tips As is clear in the Preface to the textbook, We believe that financial markets and institutions is taught effectively by emphasizing a few analytic principles and then applying them over and over again to the subject matter of this exciting field. Chapter 4 introduces one of these basic principles: the determinants of asset demand. It indicates that there are four primary factors that influence people’s decisions to hold assets: wealth, expected returns, risk, and liquidity. The simple idea that these four factor s explain the demand for assets is, in fact, an extremely powerful one. It is used continually throughout the study of financial markets and institutions and makes it much easier for the student to understand how interest rates

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    16 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition are determined, how financial institutions manage their assets and liabilities, why financial innovation takes place, how prices are determined in the stock market and the foreign exchange market. One teaching device that we have found helps students develop their intuition is the use of summary tables, such as Table 1, in class. We use the blackboard to write a list of changes in variables that affect the demand for an asset and then ask students to fill in the table by reasoning how demand responds to each change. This exercise gives them good practice in developing their analytic abilities. We use this device continually throughout the course and in this book, as is evidenced from similar summary tables in later chapters. We recommend this approach highly. The rest of Chapter 4 lays out a partial equilibrium approach to the determination of interest rates using the supply and demand in the bond market. An important feature of the analysis in this chapter is that supply and demand is always done in terms of stocks of assets, not in terms of flows. Recent literature in the professional journals almost always analyzes the determination of prices in financial markets with an asset - market approach: that is, stocks of assets are emphasized rather than flows. The reason for this is that keeping track of stocks of assets is easier than dealing with flows. Correctly conducting analysis in terms of flows is very tricky, for example, when we encounter inflation. Thus there are two reasons for using a stock approach rather than a flow approach: (1) it is easier, and (2) it is more consistent with modern treatment of asset markets by financial economists. Another important feature of this chapter is that it lays out supply and demand analysis of the bond market at a similar level to that found in principles of economics textbooks. The ceteris paribus derivations of supply and demand curves with numerical examples are presented, the concept of equilibrium is carefully developed, the factors that shift the supply and demand curves are outlined, and the distinction between movements along a demand or supply curve and shifts in the curve is clearly drawn. Our feeling is that the step - by - step treatment in this chapter is worthwhile because supply and demand analysis is such a basic tool throughout the study of financial markets and institutions. We have found that even those students who have had excellent training in earlier courses find that this chapter provides a valuable review of supply and demand analysis. The Practicing Manager application at the end of the chapter shows how interest rate forecasts can be used by managers of financial institutions to increase profits. This application shows students how the analysis they 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 provides models of asset pricing in case an instructor wants to make use of the capital asset pricing model or the arbitrage pricing model in this course. Appendix 2 shows how the analysis developed in the chapter can be applied to understanding how any asset’s price is determined. Students particularly like the application to the gold market because this commodity piques almost everybody’s interest. Appendix 3 provides another interpretation of the supply and demand analysis for bonds using a different terminology involving the supply and demand for loanable funds. Appendix 4 provides an alternative approach to interest rate determination developed by John Maynard Keynes, known as the liquidity preference framework.

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    Chapter 4: Why Do Interest Rates Change? 17 ◼ Answers to End - of - Chapter Questions 1. a. Less, because your wealth has declined b. More, because its relative expected return has risen c. Less, because it has become less liquid relative to bonds d. Less, because its expected return has fallen relative to gold e. More, because it has become less risky relative to bonds 2. a. More, because your wealth has increased b. More, because it has become more liquid c. Less, because its expected return has fallen relative to Polaroid stock d. More, because it has become less risky relative to stocks e. Less, because its expected return has fallen 3. Raphael is incorrect. If at the current level of interest rates there is an excess supply of bonds, the supply and demand analysis tells us that interest rates will increase, creating a movement along both the demand curve (in the southeast direction) and the supply curve (in the southwest direction) in order to reach the equilibrium interest rate (and price). The bond’s price will therefore fall and the interest rate will rise to the equilibrium level. 4. Purchasing shares in the pharmaceutical company is more likely to reduce my overall risk because the correlation of returns on my investment in a football team with the returns on the pharmaceutical company shares should be low. By contrast, the correlation of returns on an investment in a football team and an investment in a basketball team are probably pretty high, so in this case there would be little risk reduction if I invested in both. 5. Maria is choosing a bond with higher standard deviation, but also with higher expected return than Jennifer. In order to decide whether Maria or Jennifer is more risk averse, one will need to compare two 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 expected return (high standard deviation) is a non - desirable characteristic, it is not uncommon that highly volatile 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 supply curve B s to the right. The result is that the intersection of the supply and demand curves B s and B d occurs at a lower equilibrium bond price and thus a higher equilibrium interest rate, and the interest rate rises. 7. When the economy booms, the demand for bonds increases: The public’s income and wealth rises while the supply of bonds also increases, because firms have more attractive investment opportunities. Both the supply and demand curves ( B d and B s ) shift to the right, but as is indicated in the text, the demand 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 the demand 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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    18 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition 8. If the government imposes a limit on the amount of daily transactions in the bond market, then bonds will become less liquid with respect to alternative assets. Such a regulation will mean that it will now be more difficult to find buyers and sellers in the bond market, thereby affecting the liquidity of bonds and the demand curve (which will shift to the left), increasing the interest rate and lowering bond´s prices (for a given supply curve). 9. Interest rates would rise. A sudden increase in people’s expectations of future real estate prices raises the expected return on real estate relative to bonds, so the demand for bonds falls. The demand curve B d shifts 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, this will 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 sold in the market. 11. Yes. The increase in budget deficits increased the supply of bonds and shifts the supply curve B S to the 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 to shrink so dramatically that it shifted the supply curve B S to the left by more than the deficits shifted it to the right. The result was that the price of Treasury bonds rose and interest rates on these bonds fell. 12. When news about accounting scandals in big corporations spread, people get worried about the quality of the bonds they are either holding or considering to buy. We can expect then that bonds are not as desirable assets as they were before (maybe because the ability of corporations to honor their commitments was overstated). This negatively affects demand for these bonds and shifts the demand curve to the left, raising interest rates and lowering corporate bond´s prices (for a given supply curve). 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 curve B d will therefore shift to the left, and the equilibrium 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 the business of many US companies that export goods and services to that country or region (the Eurozone in this case). This will most likely result in job losses and a decrease in wealth, at the same time that there will be a decrease in investment opportunities. The first effect will shift the demand for bonds curve to the left, while the latter will shift the supply curve of bonds to the left. The result is that the equilibrium quantity of bonds issued and bought will unambiguously decrease, while the effect on bond´s prices and the interest rate will appear to be ambiguous. However, this might not be very 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, the expected return on long - term bonds such as the 1 8 8 s of 2022 will fall, and the demand for these bonds will decline. The demand curve B d will therefore shift to the left, and the equilibrium bond price falls and the interest rate will rise. 16. If people in France decide to permanently increase their savings rate, then more wealth will be accumulated over the years. This increase in wealth determines that more bonds will be bought at any given interest rate (or bond´s price), creating a shift to the right in the demand curve for bonds in France. This European country can therefore expect permanent lower interest rates in the future.

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    Chapter 4: Why Do Interest Rates Change? 19 17. If the government is planning to fund a major infrastructure plan, it will need to get funds, and thereby will probably issue more bonds. Since the government is a major player in the market for bonds, this will most likely result in a shift to the right in the supply curve , lowering the price of bonds and increasing interest rates in the future. If you have the opportunity, it would be wise to lock in now a long term loan with current low interest rates. ◼ Quantitative Problems 1. You own a $1,000 - par zero - coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year and believe that the required yield next year will have the following probability distribution: Probability Required Yield 0.1 6.60% 0.2 6.75% 0.4 7.00% 0.2 7.20% 0.1 7.45% a. What is your expected price when you sell the bond? b. What is the standard deviation? Solution: Probability Required Yield Price Prob  Price Prob  (Price − Exp. Price) 2 0.1 6.60% $774.41 $ 77.44 12.84776241 0.2 6.75% $770.07 $154.01 9.775668131 0.4 7.00% $762.90 $305.16 0.013017512 0.2 7.20% $757.22 $151.44 6.862609541 0.1 7.45% $750.02 $ 75.02 16.5903224 $763.07 46.08937999 The expect ed 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% chance of defaulting this year; in which case, the bond would not pay anything. If the company survives the first year, paying the annual coupon payment, it then has a 25% chance of defaulting in the second year. If the company defaults in the second year, neither the final coupon payment nor par value of the 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 that periodic cash flows are reinvested at 10%. Solution: The expected cash flow at t 1 = 0.20 (0) + 0.80 (120) = 96 The expected cash flow at t 2 = 0.25 (0) + 0.75 (1,120) = 840 The price today should be: 0 2 96 840 781.49 1.10 1.10 P = + =

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    20 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition At the end of two years, the following cash flows and probabilities exist: Probability Final Cash Flow Holding Period Return Prob  HPR Prob  (HPR − Exp. HPR) 2 0.2 $ 0.00 − 100.00% − 20.00% 19.80% 0.2 $ 132.00 − 83.11% − 16.62% 13.65% 0.6 $1,252.00 60.21% 36.12% 22.11% − 0.50% 55.56% The expected holding period return is almost zero ( − 0.5%). The stand ard deviation is roughly 74.5% (the square root of 55.56%). 3. Last month, corporations supplied $250 billion in bonds to investors at an average market rate of 11.8%. 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 remained constant, derive a linear equation for the demand for bonds, using prices instead of interest rates. Solution: First, translate the interest rates into prices. 1000 11.8% , or 894.454 P i P P − = = = 1000 12.2% , or 891.266 P i P P − = = = We know two points on the demand curve: 891.266, 275 894.454, 250 P Q P Q = = = = So, the slope = 891.266 894.454 0.12755 275 250 P Q  − = =  − Using the point - slope form of the line, Price = 0.12755  Quantity + Constan t . We can substitute in either point to determine the constant. Let’s use the first point: 891.266 0.12755 275 + Constant, or Constant 856.189 =  = Finally, we have: : Price 0.12755 Quantity 856.189 d B =  + 4. An economist has estimated that, near the point of equilibrium, the demand curve and supply curve for bonds can be estimated using the following equations: 2 : Price Quantity 940 5 : Price Quantity 500 d s B B − = + = + 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? 21 a. Solve the equations simultaneously: 2 940 5 [ 500] 7 0 440, or 314.2857 5 P Q P Q Q Q − = + − = + − = + = This implies that P = 814.2857. b. 1000 814.2857 22.8% 814.2857 i − = = 5. As in Question 6, the demand curve and supply curve for bonds ar e estimated using the following equations: 2 : Price Quantity 940 5 : Price Quantity + 500 d s B B − = + = Following a dramatic increase in the value of the stock market, many retirees started moving money out of the stock market and into bonds. This resulted in a parallel shift in the demand for bonds, such that the price of bonds at all quantities increased $50. Assuming no change in the supply equation for bonds, what is the new equilibrium price and quantity? What is the new market interest rate? Solution: The new demand equation is as follows: 2 : Price Quantity 990 5 d B − = + Now, solve the equations simultaneously: 2 990 5 [ 500] 7 0 490, or 350.00 5 P Q P Q Q Q − = + − = + − = + = This implies that P = 850.00. 1000 850.00 17.65% 850.00 i − = = 6. Following Question 5, the de mand curve and supply curve for bonds are estimated using the following equations: B d : Price = 2 Quantity 990 5 − + B s : Price = Quantity + 500

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    22 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition As 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 remained unchanged. What are the new demand and supply equations? Assume parallel shifts in the equations. Solution: Prior to the change in inflation, the equilibrium was Q = 350.00 and P = 850.00. The new equilibrium price can be found as follows: 1000 19.65% , or 835.771 P i P P − = = = This point (350, 835.771) will be common to both equations. Further since the shift was a parallel shift, the slope of the equations remains unchanged. So, we use the equilibrium point and the slope to solve for the constant in each equation: B d : 835.771 = 2 350 constant, or constant 975.771 5 − + = B d : Price = 2 Quantity 975.771 5 − + and B s : 835.771 = 350 + constant, or constant = 485.771 B s : Price = Quantity + 485.771

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    Chapter 5 How Do Risk and Term Structure Affect Interest Rates? Risk Structure of Interest Rates Default Risk Liquidity Case : The Global Financial Crisis and the Baa - Treasury Spread Income Tax Considerations Summary Case : Effects of the Bush Ta x Cut and the Obama Tax Increase on Bond Interest Rates Term Structure of Interest Rates Following the Financial News : Yield Curves Expectations Theory Market Segmentation Theory Liquidity Premium Theory Evidence on the Term Structure Summary Mini - Case Box: The Yield Curve as a Forecasting Tool for Inflation and the Business Cycle Case : Interpreting Yield Curves, 1980 – 201 6 The Practicing Manager: Using the Term Structure to Forecast Interest Rates ◼ Overview and Teaching Tips Chapter 5 applies the tools the student learned in Chapter 4 to understanding why and how various interest rates differ. In courses that emphasize financial markets, this chapter is important because students are curious about the risk and term structure of interest rates. On the other hand, professors who focus on public policy issues might want to skip this chapter. The book has been designed so that skipping this chapter will not 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 and theory. As becomes clear in the discussion of the term structure, theories are modified because they cannot explain the data. On the other hand, theories do help to explain the data, as the case on interpreting yield curves in the 1980 – 201 6 period demonstrates. This chapter also has two cases that will pique students’ interest because they are so current. First is the effect of the Bush tax cut and the Obama tax increase on bond interest rates. Since the topic of repeal of the Bush tax cut and the Obama tax increase are such a hot political issue, evaluating what impact the

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    24 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition repeal might have on interest rates is sure to be of interest to students. Also students are particularly interested right now in how the recent financial crisis affected the economy, and this chapter has a case that looks at this topic. The case on the global financial crisis and the Baa - Treasury spread applies the analysis in the chapter to show how the recent financial crisis led to a dramatic increase in the spread between 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 the term structure using the theories outlined here can be used by financial institutions managers to set interest rates on their financial instruments. ◼ Answers to End - of - Chapter Questions 1. 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 se curities are usually considered to be default free. However, securities issued by other governments usually have a positive risk premium, depending in general on the fiscal imbalances 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 on corporate bonds, which lowers their risk premium. Similarly, during recessions, default risk on corporate bonds increases and their risk premium increases. The risk premium on corporate bonds is thus 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 bond causes the interest rates for others to rise because the expected returns on bonds of different maturities cannot get too far out of line. 5. Historically, mortgage backed securities were considered low risk assets, since homeowners had the highest incentives to pay their mortgages (otherwise they might lose their home). However, after standards on lending practices decreased during the first years of the new century, many individuals were able to buy a house, but not to make their mortgage payments. This resulted in poor quality mortgage backed securities that should never have had such good ratings. Both Standard and Poor´s and Moody´s were investigated for assigning such good ratings and therefore misleading investors in buying 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 fall moderately in the near future, while the steep upward slope of the yield curve at longer maturities indicates that interest rates further into the future are expected to rise. Because interest rates and expected inflation move together, the yield curve suggests that the market expects inflation to fall moderately in the near future but to rise later on. 7. The steep upward - sloping yield curve at shorter maturities suggests that short - term interest rates are expected to rise moderately in the near future because the initial, steep upward slope indicates that the average of expected short - term interest rates in the near future is above the current short - term interest rate. The downward slope for longer maturities indicates that short - term interest rates are eventually expected to fall sharply. With a positive risk premium on long - term bonds, as in the liquidity premium theory, a downward slope of the yield curve occurs only if the average of expected short - term interest rates is declining, which occurs only if short - term interest rates far into the future are falling. Since interest rates and expected inflation move together, the yield curve suggests that the market 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? 25 8. If the trading volume of the corporate bonds market declines, then corporate bonds become less liquid, as it will be more difficult to find buyers and sellers. This drop in liquidity makes these securities less desirable assets, increasing their risk and “liquidity” premium. 9. The government guarantee will reduce the default risk on corporate bonds, making them more desirable relative to Treasury securities. The increased demand for corporate bonds and decreased demand for Treasury securities will lower interest rates on corporate bonds and raise them on Treasury bonds. 10. If the federal government decides to guarantee payments on all municipal bonds, then these bonds will effectively be default free. This characteristic will make them very desirable assets, increasing their demand and thereby lowering their interest rates. If this were to happen, then municipal bonds will be even better than U.S. government bonds, since both are default free, but municipal bonds are income tax exempted instruments. In this case, it will not make sense for municipal bonds to be exempted from paying taxes, since this exemption is made precisely to “help” local governments to gain access to funds. 11 . Abolishing the tax - exempt feature of municipal bonds would make them less desirable relative to Treasury bonds. The resulting decline in the demand for municipal bonds and increase in demand for Treasury bonds would raise the interest rates on municipal bonds, while the interest rates on Treasury bonds would fall. ◼ Quantitative Problems 1. Assuming that the expectations theory is the correct theory of the term st ructure, calculate the interest rates in the term structure for maturities of one to five years, and plot the resulting yield curves for the following seri es 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 a three - 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 a three - 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 bonds over long - term bonds because long - term bonds would then have a positive risk premium. The downward - sloping yield curve in (b) would be less steep and might even have a slight positive upward 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: Year 1 - year rate 1 4.25% 2 5.15% 3 5.50% 4 6.25% 5 7.10%

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    26 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition You have liquidity premium 0.25% for the next two years and 0.50% thereafter. Would you be willing to purchase a 4 - year T - bond at a 5.75% interest rate? Solution: Your required interest rate on a 4 - year bond = Average interest 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 only keep $75,000 because you are in the 25% tax bracket. Therefore your after - tax yield is only 7.5% 4. Consider the decision to purchase either a 5 - year corporate bond or a 5 - year municipal bond. The corporate 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 Bond Purchase Price = $1,061.50 After - tax Coupon Payment = $85 Par Value = $1,000 Calculated YTM = 7% Corporate Bond Purchase Price = $1,018.25 After - tax Coupon Payment = $78 Par Value = $1,000 Calculated 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 a nd maturity yield 6% and 10% re spectively. 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 that solve the following inequality: 0.06 ˃ 0.10 × (1 ‒ t ) → 0.06 ‒ 0.10 ˃ ‒0.1 t → ‒0.04 ˃ ‒0.1 t 0.04 0.4 0.1 →  = t 6. 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 - year interest 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? 27 Solution: 3 year bond: Y ear 1 interest rate = 7.5% Y ear 2 interest rate = 9.0% Ye ar 3 interest rate = 10.5% N umber of y ears = 3 (7.5% + 9.0% + 10.5%)/3 = 9.0% 6 year bond: Y ear 1 interest rate = 7.5% Y ear 2 interest rate = 9.0% Ye ar 3 interest rate = 10.5% Y ear 4 interest rate = 12% Y ear 5 interest rate = 13.5% Y ear 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% and 0 .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 holding short - term bonds. A liquidity premium of 10 basis points is required for each year of a bond’s maturity. 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: 1 2 1 e e e t t t t n nt nt i i i i i l n + + + − + + +    + = + 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 interest rate of 6% or three consecutive one - year bonds with interest rates of 4%, 5% and 6%. Which option would you choose to undertake? Solution: The three - year bond is a better option, since the three consecutive short term bonds yield an average 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% interest rate. The current risk - free rate is 2% and Little Monsters’s financial condition warrants a default risk premium of 3% and a liquidity risk premium of 2%. The maturity risk premium for a two - year loan is 1%, and inflation is expected to be 3% next year. What does this information imply about the rate of inflation in the second year? Solution: If inflation were expected to remain constant at 3% over the life of the loan, the interest rate 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% = R f + DRP + LP + MRP + Inflation Premium

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    28 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition = 2% + 3% + 2% + 1% + Inflation Premium So, 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 )/2 or x = 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: 2 7 2 2 2 2(1.02) 2(1.02) 2(1.02) (10-year bond) 10 21.165 /10 2.1165% I + + + + +    + = = = 12. Short term (o ne - year) interest rates over the next 3 years are expected to be 2%, 3% and 3.55%. If you are ready to buy a three - year bond that yields 3%, which is your r equired li quidity premium for this period? Solution: The minimum liquidity premium required for three years is 0.15%. The liquidity premium solves the following equation: 3 3 0.02 0.03 0.0355 0.03 0.03 0.0285 0.15% 3 + + = + → = − = l l 13. At your favorite bond store, Bonds - R - Us, you see the following prices: a. 1 - year $100 zero selling for $90.19 b. 3 - year 10% coupon $1000 par bond selling for $1000 c. 2 - year 10% coupon $1000 par bond selling for $1000 Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity or maturity premium exists, and the bonds are equally risky. What is the implied 1 - year rate two years from 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) 2 So, the 2 - year rate today is 9.95%. Using these two rates, (b) tells you that: 1000 = 100/1.10877 + 100/1.0995 2 + 1100/(1 + 3 - year rate) 3 So, 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: O ne - year rate = 5% T wo - year rate = 6% O ne - 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 Expectation Theory for interest rates holds.

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