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Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 18 Conduct of Monetary Policy Goals and Targets 1 Goals of Monetary Policy Three Principal Goals of Monetary Policy Challenges for the Fed 2 Targets for Monetary Policy Money Supply Targets Interest Rate Targets The Effects of Shifts in the Demand for Money Targeting in Practice Now that we ve considered the choice between the various tools of monetary policyithat is the various ways in which the Fed can manage the money supplyiwe can move on and ask about the principles that guide the Fed s monetary policy decisions in the rst place That is we can consider the goals of monetary policy In practice the Fed appears to have at least three goals that it tries to achieve in conducting monetary policy But the Fed faces two challenges in trying to achieve those goals The rst challenge is the most serious namely it may not be possible for the Fed to simultaneously achieve all of its goals And so at times the best the Fed can do is to choose between two or more con icting goals But a second challenge is easier to solve That problem arises because the Fed doesn t directly control the variables that it cares about the most So to achieve its goals it adopts a strategy through which it sets targets for variables that it can directly control in an effort to in uence the variables that it cannot directly control 1 Thus after identifying the principal goals of monetary policy we ll go on to consider two types of targets for monetary policy money supply targets and interest rate targets We ll see how the choice between money supply and interest rate targets is affected by shifts in the demand for money And we ll conclude by identifying the reasons why in practice the Fed has chosen to target interest rates instead of the money supply 1 Goals of Monetary Policy 11 Three Principal Goals of Monetary Policy The Employment Act of 1946 and the Full Employment and Balanced Growth Act of 1978 instruct the Federal Reserve to promote 1 High employment and economic growth 2 Stable prices or low in ation And in addition to trying to achieve these two goals the Federal Reserve also tries to promote 3 Stable nancial markets and interest rates 12 Two Challenges for the Fed ln trying to achieve its three goals the Fed faces at least two challenges 1 The three goals might not always be consistent Example Mishkin s Chapter 5 Figure 8 p102 shows that interest rates tend to rise during business cycle expansions Thus a higher rate of economic growth might not be possible without rising interest rates ln this case the goal of high employment and economic growth con icts with the goal of stable nancial markets and interest rates 2 Although the Fed can in uence employment economic growth and in ation it does not control these variables directly lt may not be possible for the Fed to solve the rst problem sometimes it simply must choose between con icting goals But the second problem can be solved through a process of setting targets for monetary policy that is setting targets for variables that the Fed can directly control in order to achieve its goals for variables that it cannot directly control 2 Targets for Monetary Policy Since the Fed cannot control employment economic growth and in ation directly it must choose settings or targets for variables that it can control in order to best achieve its goals In practice the Fed has a choice between two types of targets Money supply targets Interest rate targets Mishkin s Figure 1 p416 illustrates the role of target variables within the Fed s overall monetary policy strategy 21 Money Supply Targets Our model of the money supply process implies that MmXMB where 10 7717 rec Thus the Fed can decide what level of the money supply M is consistent with achieving its goals for employment growth in ation and nancial market and interest rate stability and set M as its target It can then use open market operations to control MB and thereby hit its money supply target M 22 Interest Rate Targets To see how the Fed can set targets for interest rates we will need to consider money demand as well as money supply Mishkin Figure 1 p416 used to control Tools for Monetary Policy 39 Targets for Monetary Policy Open Market Operations Money Supply Discount Loans Interest Rates Changes in Reserve Requirements i set to achieve Goals for Monetary Policy FEDERAL RESERVE High Employment and Growth STRATEGY Price Stability or Low Inflation Financial Market and Interest Rate Stability In our model of the money supply process the money supply M corresponds most closely to the Federal Reserve s M1 monetary aggregate M1 currency traveler s checks demand deposits other checkable deposits Currency traveler s checks and demand deposits do not pay interest Other checkable deposits NOW accounts pay interest but at a lower rate than other assets such as government or corporate bonds since they offer check writing privileges Thus when interest rates on bonds rise individuals and non bank corporations transfer funds out of M1 into other assets And when interest rates on bonds fall individuals and non bank corporations transfer funds into M1 and out of other assets We can illustrate this graphically with a downward sloping money demand curve The money demand curve slopes downward since money demand falls when interest rates rise Now suppose that the Fed wants to set a target 1 for the interest rate It can hit this target by choosing the appropriate value M for the money supply The money supply curve is vertical because the Fed xes the money supply at M Equilibrium occurs where the demand and supply curves intersect the equilibrium interest rate is 1 Hence the Fed can decide what level of the interest rate f is consistent with achieving its goals for employment growth in ation and nancial market and interest rate stability and set i as its target It can then use open market operations to control MB and thereby supply the amount of money M that makes the equilibriuln interest rate equal to its target 1 23 The Effects of Shifts in the Demand for Money So far it appears that targeting the money supply is not much different from targeting the interest rate Either the Fed chooses a target M for the money supply or it chooses a target f for the interest rate and then nds the value M of the money supply that makes the equilibrium interest rate equal to f Interest Rate i Money Demand Md Quantity of Money M Interest Rate i Ms lt Money Supply By fixing the money supply at 39 M the Fed hits its interest rate target i Md Quantity of Money M But if the demand curve for money shifts over time then the Fed must choose between a target for the money supply and a target for the interest rate To see why consider two examples Example 1 Money Supply Targeting Suppose that the Fed chooses a money supply target M The target M implies that the equilibrium interest rate is 1 But when the money demand curve shifts the interest rate rises from f to i This example shows that if the Fed chooses a money supply target and the money demand curve shifts the interest rate will change The Fed cannot target both the money supply and the interest rate Example 2 Interest Rate Targeting Suppose instead that the Fed chooses an interest rate target 1 Initially the target f requires the money supply to equal M But when the money demand curve shifts the money supply must increase to M H to prevent the interest rate from rising This example shows that if the Fed chooses an interest rate target and the money demand curve shifts the Fed must act to change the money supply Again the Fed cannot target both the money supply and the interest rate 24 Targeting in Practice At various times in the past the Fed has announced targets for the money supply In practice however the Fed has rarely taken those targets seriously Instead the Fed has been much more concerned with targeting interest rates And today monetary policy decisions are made in order to target interest rates Thus Federal Reserve policy decisions are always described based on their effects on interest rates Why has the Fed chosen interest rate targeting over money supply targeting Example 1 Interest Rate i Ms The Fed targets the money supply i and the money demand curve shifts i The interest rate rises M1d M0d Mat Quantity of Money M Example 2 Interest Rate i M05 M15 The Fed targets the interest rate gtlt and the money demand curve shifts M1d M0d M M gt The Fed must increase the money supply to keep the Interest rate from rising Quantity of Money M 1 Federal Reserve o icials believe that the link between interest rates and employ ment economic growth and in ation is stronger than the link between the money supply and those same variables Thus Fed o icials believe that they can best achieve their goals for employment economic growth and in ation by setting targets for interest rates 2 Federal Reserve o icials also believe that the demand for money is highly unstable and hence that money supply targeting would lead to large swings in interest rates Thus Fed o icials believe that they can best achieve their goal of promoting nancial market and interest rate stability by setting targets for interest rates But even though the Federal Reserve has chosen to target interest rates it is important to remember that the Fed hits its target for the interest rate f by rst determining the level of the money supply M that is consistent with its interest rate target and then conducting open market operations to adjust the monetary base so that the money supply equals M And so open market operations and the Fed s control over the monetary base underlie the Fed s policy actions even when those actions are taken to target the interest rate Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 4 Understanding Interest Rates 1 Types of Credit Market Instruments Simple Loan Fixed Payment Loan Coupon Bond Discount Bond 2 Present Value 3 Yield to Maturity Simple Loan Fixed Payment Loan Coupon Bond Discount Bond 4 Other Measures of Interest Rates Current Yield Yield on a Discount Basis 5 Interest Rates versus Returns This chapter begins the second part of the course which focuses on the behavior of interest rates The analysis starts on familiar ground by reviewing some of the types of credit market instruments that we discussed earlier in our overview of the nancial system particular it usefully classi es those credit market instruments into four types simple loans xed payment loans coupon bonds and discount bonds Next it deals with the question how can we come up with a uni ed way of measuring interest rates on all of these different types of credit market instruments It turns out that the concept of present value gives us the key to answering this question So the chapter introduces us to this concept Then the chapter shows us how we can use the concept of present value to de ne the yield of maturity which is the most widely applicable and most accurate measure of interest rates on credit market instruments The chapter shows us how we can calculate the yield to maturity on each of the four main types of credit market instruments Although the yield to maturity is the most accurate measure of interest rates there are two other measures of interest rates that are also widely used and therefore of some im portance Hence this chapter also includes a discussion of these alternative measures the current yield and the yield on a discount basis Finally the chapter concludes by highlighting an important distinction for investors in bonds the distinction between the interest rate and the rate of return on a bond Perhaps the most important lesson that we learn from this chapter is that bond prices and interest rates are negatively related That is when interest rates rise bond prices fall and when interest rates fall bond prices rise At rst this negative relationship between bond prices and interest rates might seem coun terintuitive But once we see how the various measures of interest rates are de ned the negative relationship actually becomes quite easy to see 1 Types of Credit Market Instruments In our overview of the nancial system we learned about a wide variety of credit market instruments For the purposes of thinking about interest rates it is useful to classify those credit market instruments into four types Credit market instruments 2 debt instruments Debt instrument 2 a contractual agreement by the issuer of the instrument the borrower to pay the holder of the instrument the lender xed dollar amounts interest and principal payments at regular intervals until a speci ed date maturity date when a nal payment is made 1 1 Simple Loan Provides the borrower with an amount of funds principal that must be repaid to the lender at maturity along with an additional amount interest Example Borrow 100 today repay 100 principal plus 10 interest in one year Many commercial loans are of this type 12 Fixed Payment Loan Sometimes called a fully amortized loan Provides the borrower with an amount of funds that is to be repaid with interest by making xed regular payments until maturity Example Borrow 1000 today repay 126 per year for 25 years as we ll see below this loan has a 12 interest rate Auto loans and mortgages are of this type 13 Coupon Bond Pays the owner a xed interest payment coupon payment each year until maturity when a speci ed amount face value or par value is repaid The name coupon bond comes from the fact that years ago before the time of computer record keeping such bonds came with coupons attached which the holder would mail to the issue to request payment Example Coupon bond with face value 1000 100 coupon payment and ten year matu rity pays 100 per year for ten years and 1000 at the end of ten years Coupon rate Coupon payment as a percentage of face value Example Coupon Payment 7 100 coupon Rate Face Value 7 1000 010 10 Many corporate bonds and US Treasury notes and bonds are of this type 14 Discount Bond Also called a zero coupon bond Bought at a price below face value bought at a discount makes no interest payments but returns face value at maturity Example Discount bond with 1000 face value and one year maturity sells for 900 today and returns 1000 in one year The 100 difference between the purchase price and face value represents the interest payment US Treasury bills are of this type 2 Present Value The various types of credit market instruments all require payments at different times simple loans and discount bonds make payments only at maturity while xed payment loans and coupon bonds make regular payments until maturity How can we nd a uni ed approach to measuring interest rates on these various types of instruments The key to answering this question lies with the concept of present value Present value captures the idea that a dollar received in the future is less valuable than a dollar received today To see how the concept of present value works let s consider a series of examples Example 1 A simple loan of 100 requires the borrower to repay 100 principal plus 10 interest one year from now For this simple loan the interest payment expressed as a percentage of the principal is a sensible way of measuring the interest rate 1n fact when we measure the interest rate in this way we are computing the simple interest rate 1nterest 10 839 llt th 39 01010 imp e n eres a e 1 Principal 100 Example 2 1f you make a simple loan of 100 at the simple interest rate i 010 for one year you get 100 100 x i 100 x 11 100 x 110 110 at the end of the year 1f you lend this 110 out again for another year at the same simple interest rate 1 010 you get 110 110 X 139 110 X 1 1 110 X 110 121 at the end of the second year Equivalently we can write 100 x 11 x 11 100 x 1 12 100 x 1102 121 1f you lend the 121 out for a third year at the simple interest rate 1 010 you get 121 x 11 100 x 1 13 100 x 1103 13310 at the end of the third year Example 3 Starting with 100 if the simple interest rate on one year loans is i and if you make these loans for 71 consecutive years you get 100 X 1 at the end of those 71 years Example 4 Working backwards if the simple interest rate is i 010 then 110 100 X 1 received next year is worth 100 1101 1 today 121 100 X 1 i2 received two years from now is worth 100 1211 i2 today 13310 100 X 113 received three years from now is with 100 133101Jri3 today This process of working backwards is called discounting the future Example 5 1f the simple interest rate is i then the present value of 1 received 71 years from now is de ned as 1 1 1quot Present value of 1 received 71 years from now lt 1 Thus the idea of present value captures the face that 1 received in the future is worth less than 1 received today More generally Present value of X received 71 years from now 1 1quot39 3 Yield to Maturity Yield to Maturity the simple interest rate that equates the present value of payments received from a debt instrument to the price or value of that debt instrument today Also sometimes called the internal rate of return This is the most accurate and Widely applicable measure of interest rates 1n fact we can use this de nition to compute the yield to maturity on each of our four types of credit market instruments 31 Simple Loan Consider a simple loan of 100 that repays 100 principal plus 10 interest for a total of 110 in one year The yield to maturity i must satisfy 110 Value today 100 Present value of future payments 1 1 Let s solve for i 110 1i 100 x 11 110 100100 xi 110 100 x i 110 7 100 1107 100 10 Wm01010 Thus for simple loans the yield to maturity equals the simple interest rate 100 32 Fixed Payment Loan Consider a xed payment loan of 1000 that requires payments of 126 per year for 25 years The yield to maturity i must satisfy Value today 1000 Present value of future payments 126 126 126 126 1i 11 103 quot39 1 2539 A nancial calculator or a computer W111 generally be needed to solve for i 1n this example the yield to maturity turns out to be i 01183 or approximately 12 More generally for any xed payment loan if LV loan value amount today F P xed annual payment 71 years to maturity i yield to maturity then FF 1 iquot39 LV FPnL FP FP 71i 11 1i3 33 Coupon Bond Consider a coupon bond With 1000 face value 100 coupon payment 10 coupon rate and ten year maturity that sells at price P today The yield to maturity i must satisfy 7100 100 100 1000 71i 112 1i10 1i1039 Note that since both the nal 100 coupon payment and the 1000 payment of face value are received at the end of the tenth year both must be included in the present value calculation on the right hand side Once again a nancial calculator or a computer is needed to solve for i A range of results depending on the purchase price P are displayed in Mishkin s Table 1 p66 Price of Bond P Yield to Maturity 139 1200 713 1110 848 1000 1000 900 1175 800 1381 From this table we can ascertain three important facts about the yield to maturity on a coupon bond 1 When the bond price P equals the face value of 1000 the yield to maturity i equals the coupon rate 2 The bond price P and the yield to maturity i are negatively related When the bond price falls the yield to maturity rises and When the bond price rises the yield to maturity falls 3 The yield to maturity is below the coupon rate When the bond price is above face value and the yield to maturity is above the coupon rate When the bond price is below face value More generally for any coupon bond if P today s bond price C annual coupon payment F face value n years to maturity i yield to maturity then 11 112 1zquot 1zquot Once again because the last coupon payment C and face value F are both received at the end of the nth year both must be included in the present value calculation on the right hand side Notice that in this general formula we can see the inverse relationship between the bond price P and the yield to maturity i 1f i rises then each term on the right hand side gets smaller Hence P must fall 1f i falls then each term on the right hand side gets bigger Hence P must rise 34 Discount Bond Consider a US Treasury bill With one year maturity and face value 1000 that sells for 900 today The yield to maturity i must satisfy 1000 900 z 1 900 X 11 1000 900 900 X i 1000 900 X i 1000 7 900 1000 7 900 100 39 0111111 900 900 More generally for any discount bond if P today s bond price F face value n years to maturity i yield to maturity then i F 1 1quot From this general formula we can see that for a discount bond too the bond price and the yield to maturity are negatively related when the yield to maturity falls the bond price rises and when the yield to maturity rises the bond price falls 1n the special case where n 1 13 11 PX1iF PPXiF PXiF7P iiFiP P Suppose we rewrite this last formula as 1 i FiP P i FiP P P F 71 P Once again the bond price and the yield to maturity are negatively related when P falls i rises and when P rises i falls 4 Other Measures of Interest Rates Although the yield to maturity is the most accurate and Widely applicable measure of interest rates it is often dif cult to calculate For this reason a couple of other measures of interest rates are frequently used the current yield and the yield on a discount basis 41 Current Yield Applies only to coupon bonds Recall that the yield to maturity on a coupon bond usually cannot be found Without the help of a computer As a result the yield to maturity on a coupon bond is often approximated by the current yield To calculate the current yield let P today s bond price C annual coupon payment ic current yield then the current yield ic is de ned as Four facts about the current yield 1 ic better approximates i When today s bond price P is closer to the face value F and When the maturity of the bond is longer 21nfact lfPFtheniCi lfPgtFtheniCgti lfPlt F theniclti 3 ic and i always move in the same direction ic rises When i rises and ic falls When i falls 4 The bond price P and the current yield ic are negatively related When P rises ic falls and When P falls ic rises 42 Yield on a Discount Basis Applies only to discount bonds Although it is fairly easy to calculate the yield to maturity on a oneyear discount bond it is more dif cult to calculate the yield to maturity on a discount bond With maturity less than or greater than one year For this reason interest rates on discount bonds including US Treasury bills are often quoted in terms on the yield on a discount basis To calculate the yield on the discount basis for a discount bond let P today s bond price F face value id yield on a discount basis then the yield on a discount basis id is de ned as F i P 360 z x db F days to maturity Recall that for a discount bond With one year maturity F i P yield to maturity z P Thus the yield on a discount basis calculation has two peculiarities l lt uses the percentage gain on face value P 7 FF rather than the percentage gain on the purchase price F 7 PP 2 lt considers the year to be 360 days long instead of 365 As a result of both of these peculiarities the yield on a discount basis always understates the yield to maturity Example Discount bond With 1000 face value and oneyear maturity sells for 900 today P 900 F 1000 n 1 ll and hence FiP 360 w X360009999 39 gtlt 7 1d F days to maturity 1000 365 F 7 P 1000 7 900 7 P 900 Nevertheless it is still true that the bond price and its yield on a discount basis are nega tively related 0111 111 To see this return to the de nition F i P X 360 z db F days to maturity Since the P on the right hand side has a minus side out in front of it id falls when P rises and id rises when P falls 1n addition the yield on a discount basis and the yield to maturity always move in the same direction id rises when i rises and id falls when i falls 5 Interest Rates and Returns For investors the distinction between interest rates and returns on bonds can be quite important The rate of return on a bond takes into account not only any interest payments made by the bond but also any changes in the price of the bond itself Example Consider a coupon bond with 1000 face value and 100 coupon payment 10 coupon rate that is bought today for 1000 1f interest rates fall over the next year the bond price will rise Suppose to continue the example that the investor is able to sell the bond one year from now at the price of 1200 Then the investors total earnings from holding the bond include the 100 coupon payment plus the capital gain of 1200 1000 200 Expressing these earnings as a percentage of the original purchase price gives us a total return on the investment of 100 200 7 300 7 30 1000 1000 12 Of course this process can work in the opposite direction as well Suppose instead that interest rates rise over the next year so that the bond price falls to 800 If the investor sells the bond after one year the 100 coupon payment is completely offset by a capital loss of 1000 800 200 In this case the total return would be 100 7 200 100 7 710 1000 1000 These examples reveal that although bonds are often considered to be very conservative investments they can in fact be quite risky for those who do not plan to hold them until maturity 6 Conclusion This chapter has shown us that for any type of credit market instrument the yield to maturity serves as the most accurate measure of the interest rate The yield to maturity is de ned as the simple interest rate that equates the present value of payments received from a debt instrument to the price or value of that debt instrument today Two other measures of the interest rate the current yield and the yield on a discount basis are less accurate but are often easier to calculate Nevertheless for any type of bond and any measure of the interest rate bond prices and interest rates are negatively related bond prices fall when interest rates rise and bond prices rise when interest rates fall Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 6 The Risk and Term Structure of Interest Rates 1 Risk Structure of Interest Rates Three Facts About the Risk Structure Default Risk Liquidity Income Tax Considerations 2 Term Structure of Interest Rates Three Facts About the Term Structure Expectations Hypothesis Segmented Markets Theory Liquidity Premium and Preferred Habitat Theories In developing the loanable funds framework in Chapter 5 we kept things simple by assuming that there is just one type of bond and hence just one interest rate for the economy as a whole Our overview of the nancial system however showed us that there in fact many different types of credit market instruments with potentially different interest rates For instance bonds of the same maturity may still differ in terms of their riskiness The relationship between interest rates on bonds with the same term to maturity is called the risk structure of interest rates Bonds can also differ in terms of their term to maturity The relationship between interest rates on bonds of different maturities is called the term structure of interest rates This chapter focuses on the risk and term structure of interest rates The chapter begins by identifying three facts about the risk structure of interest rates At the heart of the analysis of the risk structure of interest rates is a concept called default risk which refers to the chance that the issue of the bond the borrower will be unable to make interest payments on the bond or to pay off the face value of the bond when it matures But in addition to default risk there are two other factors that contribute to the risk structure of interest rates liquidity and income tax considerations Thus this chapter shows how these three factorsidefault risk liquidity and income tax considerationsican jointly explain our three facts about the risk structure The chapter then goes on to consider the term structure of interest rates 1t begins again by identifying three facts about the term structure 1t then goes on to consider three theories of the term structurthe expectations hypothesis segmented markets theory and liquidity premium or preferred habitat theoryiand evaluates each theory in terms of its ability to explain our three facts 1 Risk Structure of Interest Rates 11 Three Facts About the Risk Structure Risk structure 2 the relationship between interest rates on bonds with the same term to maturity Mishkin s Figure 1 p121 plots the interest rates on various types of long term bonds 1919 2002 By examining this graph we can identify three important facts about the risk structure of interest rates 4 Corporate bonds tend to have higher interest rates than US government bonds E0 The spread between the interest rates on corporate bonds and US government bonds varies over time 1n particular the spread tends to widen during periods of recession or depression 03 Since 1940 the interest rate on municipal bonds has been lower than the interest rate on US government bonds We can explain these three facts by appealing to three factors 1 Default risk 2 Liquidity 3 lncome tax considerations 12 Default Risk Default risk 2 the chance that the issuer of the bond borrower will default that is be unable to make interest payments when they are due or pay off the face value of the bond when it matures The loanable funds framework implies that when the riskiness of a bond increases the interest rate rises Hence the loanable funds framework also implies that bonds with higher default risk will have higher interest rates US Treasury securities are default free or almost default free since there is very little chance that the US government will go bankrupt But corporations sometimes do default on their bonds Hence default risk can explain fact 1 why corporate bonds tend to have higher interest rates than US government bonds The spread between interest rates on bonds with default risk and interest rates on default free bonds is called the risk premium During recessions and depressions more corporations go bankrupt Since default risk on corporate bonds increases during these times the risk premium also rises Hence default risk can also explain fact 2 why the spread between interest rates on cor porate and US government bonds varies over time and tends to widen during recessions and depressions Two major rms Moody s and Standard and Poor s are in the business of rating bonds according to their default risk The categories are shown in Mishkin s Table l p123 Moody s Rating SampP s Rating Description Examples 2003 Aaa AAA Highest Quality General Electric Aa AA High Quality Wal Mart A A Upper Medium Grade Hewlett Packard Baa BBB Medium Grade Motorola Ba BB Lower Medium Grade Levi Strauss B B Speculative Rite Aid Caa CCC CC Poor United Airlines Ca C Highly Speculative Polaroid C D Lowest Grade Enron Bonds with ratings of Baa BBB or above are referred to as investment grade bonds Bonds with ratings of BaBB or below are called speculative grade high yield or junk bonds 13 Liquidity Liquidity the ease and speed with which an asset can be bought and sold that is converted to a medium of exchange US Treasury bonds are more widely and actively traded than corporate bonds Hence US government bonds are more liquid than corporate bonds The loanable funds framework implies that when the liquidity of a bond increases the interest rate falls Hence the loanable funds framework also implies that more liquid bonds will have lower interest rates Hence liquidity can also help explain fact 1 why corporate bonds tend to have higher interest rates than US government bonds 14 Income Tax Considerations Municipal bonds 2 bonds issued by state and local governments Unlike the US government state and local governments sometimes do go bankrupt For example Orange County California defaulted on its debt in 1994 Thus municipal bonds are not default free 1n addition municipal bonds are not as widely traded and hence not as liquid as US government bonds Thus based on risk and liquidity considerations alone municipal bonds should have higher interest rates than US government bonds So how can we explain fact 3 that interest rates on municipal bonds are actually lower than interest rates on US government bonds The answer is that interest payments on municipal bonds are exempt from federal income taxes This tax advantage increases the demand for municipal bonds and thereby makes their interest rate lower Hence income tax considerations can explain fact 3 why since 1940 interest rates on municipal bonds have been lower than interest rates on US government bonds Before 1940 federal income tax rates were quite low hence the tax advantages of municipal bonds were not as important Hence risk and liquidity considerations can explain why before 1940 interest rates on municipal bonds were higher than interest rates on US government bonds 2 Term Structure of Interest Rates 21 Three Facts About the Term Structure Term Structure 2 the relationship between interest rates on bonds with different terms to maturity Yield curve 2 a plot of interest rates yields on bonds with different maturities Each day the yield curve for Treasury bills notes and bonds is printed in the Wall Street Journal For an example see Mishkin page 128 By examining how the yield curve behaves over time we can identify three important facts about the term structure of interest rates 1 1nterest rates on bonds of different maturities tend to move together over time 2 The yield curve can slope up or down 1t tends to slope up when short term interest rates are low and tends to slope down when short term interest rates are high 3 Most of the time the yield curve is upward sloping 5 Note the atypical case where the yield curve slopes down is often referred to as the case of an inverted yield curve Three main theories of the term structure have been proposed 1 The Expectations Hypothesis 7 explains facts 1 and 2 Segmented Markets Theory 7 explains fact 3 Liquidity Premium or Preferred Habitat Theory 7 a combination of the rst two theories 7 explains all three facts 22 Expectations Hypothesis Expectations hypothesis 2 the interest rate on a long term bond will equal an average of the short term interest rates that people expect to prevail over the life of the long term bond Key assumption 2 investors regard bonds of different maturities to be perfect substitutes To see how this assumption leads to the expectations hypothesis consider two investment strategies Strategy 1 Buy a oneyear bond and when it matures in one year buy another one year bond Strategy 2 Buy a two year bond and hold it until maturity 1f bonds of different maturities really are perfect substitutes then these two strategies must provide the same expected return Example 1f the interest rate on a one year bond is 9 today and is expected to be 11 one year from now then the annualized interest rate on a two year bond today must be 10 To make this argument more formal let it today s time t interest rate on a one year bond if expected interest rate on a oneyear bond next year time t 1 igt today s time t annualized interest rate on a two year bond Then the expected return on strategy 1 can be calculated as Expected Return on Strategy 1 1 13 X 1 i 1 1itif1it X 144 m 1iti 1 And the expected return on strategy 2 can be calculated as Expected Return on Strategy 2 l X l 1i22i22i t l 272 Hence if these strategies have the same expected return it must be that 11 1211 1212t it 114 21392 2125 it 1 r it 131 121 T7 that is the annualized interest rate on the two year bond is an average of the one year rates that are expected to prevail over the next two years Extending this argument would tells that if int today s annualized interest rate on an n year bo then 5 5 5 it 1 7 t2 JV JV 7 tn71 in V Example Suppose that it 5 141 6 if2 7 it 8 if 9 Then the expectations hypothesis predicts that am i 56 11 55 2 WT 2 iti 1i 2if3i 4 56789 35 15 5 7 5 7739 Note that in this example the one year rate is expected to rise Hence the yield curve slopes up Suppose on the other hand that it 9 if1 8 12 7 it 6 if 5 Then the expectations hypothesis predicts that 21 98 17 85 12 2 2 2 and fiti 1if2if3if4i98765735770 15quot 5 5 0 Now the one year rate is expected to fall and so the yield curve slopes down or is inverted The expectations hypothesis can explain fact Since interest rates at all maturities depend on today s short term rate it then they Will tend to move together rising When it rises and falling When it falls The expectations hypothesis can also explain fact As our examples show the yield curve can slope up or down Moreover it tends to slope up When short term interest rates are low and therefore expected to rise and to slope up When short term interest rates are high and therefore expected to fall But the expectations hypothesis cannot explain fact Since short term interest rates are as likely to rise as they are to fall the expectations hypothesis predicts that the yield curve is as likely to slope upward as it is to slope down It cannot explain Why most of the time the yield curve slopes up 23 Segmented Markets Theory Recall that the key assumption underlying the expectations hypothesis is that investors regard bonds of different maturities as perfect substitutes Segmented markets theory starts with exactly the opposite assumption that investors regard markets for bonds of different maturities as completely separate or segmented That is bonds of different maturities are not substitutes at all Example lnvestors saving for a short period of time buy only short term bonds lnvestors saving for a long period of time buy only long term bonds Such behavior makes sense if we recall from our previous analysis that an investor who sells a bond before it matures may incur large capital losses if interest rates rise between the time the bond is bought and sold lf bonds of different maturities are not substitutes at all then the interest rate for each maturity is determined solely by the supply of and demand for bonds of that maturity with no effects from interest rates on bonds of other maturities Segmented markets theory can explain fact lf most investors prefer short term bonds the demand for short term bonds will be greater than the demand for long term bonds Hence the interest rate on short term bonds will be lower than the interest rate on long term bonds That is the yield curve will typically slope upward Why might most investors prefer short term bonds They may wish to avoid the risk of incurring capital losses if they need to sell long term bonds before maturity They may also wish to take advantage of the greater liquidity of short term bonds But segmented markets theory cannot explain fact lf bonds of different maturities are really traded in completely separated markets and are not substitutes at all then their interest rates should show no tendency to move together Likewise segmented markets theory cannot explain fact 2 without assuming that investors preferences for bonds of different maturities shift drastically over time so that they sometimes prefer short term bonds and sometimes prefer long term bonds It does not seem likely that preferences would shift in this way 24 Liquidity Premium and Preferred Habitat Theories We have seen that the expectations hypothesis can explain two of our three facts while segmented markets theory can explain the third We ve also seen that both the expectations hypothesis and segmented markets theory make assumptions that are somewhat extreme Expectations hypothesis 2 bonds of different maturities are perfect substitutes Segmented markets theory 2 bonds of different maturities are not substitutes at all These observations suggest that if we combine the two theories in a way that makes less extreme assumptions we ll have an explanation for all three facts This is exactly when liquidity premium or preferred habitat theory does The key assumption of liquidity premium or preferred habitat theory is that investors regard bonds of different maturities as substitutes but not perfect substitutes To see how this theory works recall that according to the expectations hypothesis 5 5 5 1t 11 1H2 JV JV 1244771 7 Tl int so that the interest rate on a 71 year bond is the average of the oneyear interest rates that are expected to prevail over the next n years Liquidity premium theory modi es this equation to iti81i82ie 1m H H tn 1 W n where m liquidity term premium for the 71 year bond at time t The rst part of this equation comes from the expectations hypothesis It implies that investors still care about the interest rates on bonds of different maturities so they will not let the expected returns on different investment strategies to get too far out of line But the second part of this equation comes from segmented markets theory It tells us that investors do have preferences for some maturities over others lf in particular investors prefer short term bondsithat is if their preferred habitat is in short term bondsithen the demand for short term bonds will be greater than the demand for long term bonds Thus the interest rate on long term bonds will be higher than the interest rate on short term bonds In other words if investors prefer short term bonds then the liquidity or term premium M will be positive and will tend to rise as n increases 10 The term premium makes investors Willing to hold long term bonds even though they would otherwise prefer short term bonds Again Why might most investors prefer short term bonds They may Wish to avoid the risk of incurring capital losses if they need to sell long term bonds before maturity They may also Wish to take advantage of the greater liquidity of short term bonds Example Suppose that investors preferred habitat is in short term bonds so that 2 liquidity premium on 2 year bonds 2 025 5 liquidity premium on 5 year bonds 1 Case 1 Short term interest rates are expected to rise it 5 1Z1 6 1Z2 7 1Z3 8 if 9 Then igt 2 w 025 112 025 575 and 5 5 3 5 5 6 7 8 9 13amt 1H2zt3zt41 213 1 18 Hence When short term interest rates are expected to rise the yield curve slopes up I 7 5t 735 7 5 Case 2 Short term interest rates are expected to fall slightly it 9 if 875 if 850 if3 825 if 8 11 Then i i5 9 875 i2 12 w 025 9125 and 5 5 3 5 i5t xi 1H1 1H2 1H3 1H4 at 9 875 850 825 8 1 1 95 5 5 Hence When short term rates are expected to fall only slightly the yield curve still slopes up Case 3 Short term interest rates are expected to fall sharply it 9 if 8 if 7 if3 6 554 5 Then iti 1 98 12 T 12 T 025 875 and i i5 i5 i3 i5 9 8 7 6 5 i5t t t1 t2 t3 t4 15t 18 5 Hence only When short term rates are expected to fall sharply does the yield curve slope down This example shows that liquidity premium or preferred habitat theory can explain all three facts 1 Since interest rates at all maturities depend on today s short term rate it then they Will tend to move together rising When it rises and falling When it falls 2 The yield curve Will slope up if investors expect short term interest rates to rise or fall slightly the yield curve Will slope down if investors expect short term interest rates to fall sharply Hence in general the yield curve can slope up or down Moreover the yield curve Will tend to slope up When short term interest rates are lowiand therefore expected to riseiwhile the yield curve Will tend to slope down When short term interest rates are highiand therefore expected to fall 3 Since the yield curve slopes down only When short term interest rates are expected to fall sharply most of the time the yield curve Will slope up 12 3 Conclusion The rst part of this chapter introduces us to three facts about the risk structure of interest rates 1 Corporate bonds tend to have higher interest rates than US government bonds 2 The spread between the interest rates on corporate bonds and US government bonds varies over time 1n particular the spread tends to widen during periods of recession or depression 3 Since 1940 the interest rate on municipal bonds has been lower than the interest rate on US government bonds The rst part of this chapter also shows us how these three facts can be explained by a combination of three factors 1 Default risk 2 Liquidity 3 1ncome tax considerations The second part of this chapter introduces us to three facts about the term structure of interest rates 1 1nterest rates on bonds of different maturities tend to move together over time 2 The yield curve can slope up or down 1t tends to slope up when short term interest rates are low and tends to slope down when short term interest rates are high 3 Most of the time the yield curve is upward sloping The second part of this chapter also shows us how some or all of these facts can be explained by three theories of the term structure 1 The Expectations Hypothesis 7 explains facts 1 and 2 Segmented Markets Theory 7 explains fact 3 Liquidity Premium or Preferred Habitat Theory 7 a combination of the rst two theories 7 explains all three facts Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 2 An Overview of the Financial System 1 Function of Financial Markets and Financial Intermediaries 2 Structure of Financial Markets Debt and Equity Markets Primary and Secondary Markets Exchanges and Over theCounter Markets Money and Capital Markets 3 Financial Instruments Money Market Instruments Capital Market Instruments 4 Role of Financial Intermediaries Transaction Costs and Economies of Scale Risk Sharing and Diversi cation Adverse Selection and Moral Hazard 5 Types of Financial Intermediaries Depository Institutions Banks Contractual Savings Institutions Investment Intermediaries This chapter provides an overview of the nancial system in the US economy by describing the various types of nancial markets nancial instruments and nancial institutions or intermediaries that exist The chapter begins with a general statement that clari es what function nancial markets and nancial intermediaries have in the economy as a whole lt then deals more speci cally with The structure of nancial markets and the ways in which different types of nancial markets can be distinguished Here it discusses debt versus equity markets primary versus secondary markets exchanges versus over the counter markets and money versus capital markets The various types of nancial instruments including both money market instruments and capital market instruments The special role played by nancial intermediaries in the economy Here it describes how nancial intermediaries take advantage of economies of scale to reduce trans action costs how nancial institutions assist in the process of risk sharing and diversi cation and how nancial institutions overcome the problems of adverse selection and more hazard The major types of nancial intermediaries including depository institutions banks contractual savings institutions and investment intermediaries Repeatedly throughout this course we ll be coming across references to the numerous types of nancial markets nancial instruments and nancial institutions As we go along we can always refer back to this overview to recall how a particular type of nancial instrument works or what a particular type of nancial intermediary does 1 Function of Financial Markets and Financial Inter mediaries Financial markets and nancial intermediaries perform the function of channeling funds from agents who have saved funds and want to lend to agents who need funds and want to borrow This function is illustrated quite nicely in Mishkin s gure 1 p24 which also serves conveniently to introduce us to a number of other concepts and terms 2 Structure of Financial Markets 21 Debt and Equity Markets Debt instrument 2 a contractual agreement by the issuer of the instrument the borrower to pay the holder of the instrument the lender xed dollar amounts interest and 2 Mishkin Chapter 2 Figure 1 p24 Financial Intermediaries I d39 tF39 n lrec lnance Financial Institutions Financial Intermediaries Funds Funds Lenders Borrowers 1 Households Funds 1 Businesses 2 Businesses 2 Governments 3 Governments 3 Households 4 Foreigners 4 Foreigners Funds Funds Buy Securities Assets Issue Securities Liabilities Financial Markets Direct Finance Securities Financial Instruments Claims on Income or Assets principal payments at regular intervals until a speci ed date maturity date When a nal payment is made Examples Government and corporate bonds Maturity number of years or months until the expiration date Short term maturity of less than one year Long term maturity of more than ten years lntermediateterm maturity between one and ten years Equity 2 a contractual agreement representing claims to a share in the income and assets of a business Example Corporate stock May pay regular dividends Have no maturity date hence are considered long term securities Since equity holders own the rm they are entitled to elect members of the rm s board of directors and vote on major issues concerning how the rm is managed A key feature distinguishing equity from debt is that the equity holders are the residual claimants the rm must make payments to its debt holders before making payments to its equity holders We can refer to this feature in identifying the major advantages and disadvantages of holding debt versus equity Advantage to holders of debt instruments Receive xed payments regardless of Whether the borrower s income and assets become more or less valuable over time Disadvantage to holders of debt instruments Do not bene t from an increase in the value of the borrower s income or assets Advantage to holders of equities Receive larger payments When the business becomes more pro table or the value of its assets rises Disadvantage to holders of equities Receive smaller payments When the business becomes less pro table or the value of its assets falls Although more attention is given to the equity stock markets the debt markets are actually much larger Value of all equities US end of 2002 11 trillion Value of all debt instruments US end of 2002 20 trillion 22 Primary and Secondary Markets Primary market 2 market in which newly issued securities are sold to initial buyers by the corporation or government borrowing the funds Example US Treasury issues a new US Government bond and sells it to JP Morgan Investment banks play an important role in many primary market transactions by underwriting securities they guarantee a price for a corporation s securities and then sell those securities to the public Secondary market 2 market in which previously issued securities are traded Example JP Morgan sells the existing US government bond to Merrill Lynch Brokers and dealers play an important role in secondary markets Brokers 2 facilitate secondary market transactions by matching buyers with sell ers Dealers 2 facilitate secondary market transactions by standing ready to buy and sell securities Note that the originally issuer or borrower receives funds only when its securities are rst sold in the primary market the issuer does not receive funds when its securities are traded in the secondary market Nevertheless secondary markets perform two essential functions They allow the original buyers of securities to sell them before the maturity date if necessary That is they make the securities more liquid They allow participants in the primary markets to make judgements about the value of newly issued securities by looking at the prices of similar existing securities that are traded in the secondary markets 23 Exchanges and Overthe Counter Markets Exchange 2 buyers and sellers meet in a central location Example New York Stock Exchange Over theCounter OTC Market 2 dealers at different locations trade via computer and telephone networks Examples NASDAQ National Association of Securities Dealers Automated Quota tion System US Government bond market 24 Money and Capital Markets Money market 2 only short term debt instruments are traded Capital market 2 intermediateterm debt long term debt and equities traded 3 Financial Instruments 31 Money Market Instruments The principal money market instruments are US Treasury Bills Negotiable Bank Certi cates of Deposit Commercial Paper Banker s Acceptances Repurchase Agreements Federal Funds Eurodollars All of these money market instruments are by de nition short term debt instruments With maturities less than one year US Treasury Bills lssued by the US Government Currently issued With maturities of l 3 and 6 months Pay a xed amount at maturity Make no regular interest payments but sell at a discount Example A Treasury bill that pays off 1000 at maturity 6 months from now sells for 950 today The 50 difference between the purchase price and the amount paid at maturity is the interest on the loan Trade on a very active secondary market Are the safest of all money market instruments since it is very unlikely that the US Government Will go bankrupt Negotiable Certi cates of Deposit CDs Issued by banks Make regular interest payments until maturity At maturity return the original purchase price Large CDs With value over 100000 trade on a secondary market Negotiable means that the CD trades on a secondary market Commercial Paper Short term debt issued by corporations Make no interest payments but sell at a discount Trade on a secondary market Banker s Acceptances Bank draft like a check issued by a rm and payable at some future date Stamped accepted by the rm s bank Which then guarantees that it Will be paid Often arise in the process of international trade Make no interest payments but sell at a discount Trade on a secondary market Repurchase Agreements Very short term loans often overnight With Treasury bills as collateral between a non bank corporation as the lender and a bank as the borrower Non bank corporation buys the Treasury bill from the bank 6 Simultaneously the bank agrees to repurchase the easury bill later at a slightly higher price The difference between the original price and the repurchase price is the interest Federal Funds Overnight loans between banks of deposits at the Federal Reserve Interest rate on these loans is called the federal funds rate Eurodollars US dollar deposits at foreign banks 32 Capital Market Instruments The principal capital market instruments are Corporate Stocks Residential Commercial and Farm Mortgages Corporate Bonds US Government Securities Intermediate and Long Term State and Local Government Municipal Bonds US Government Agency Bonds Bank Commercial and Consumer Loans All of these capital market instruments are by de nition intermediateterm debt instruments long term debt instruments or equities Corporate Stocks Equity claims to the income and assets of corporations Mortgages Residential Commercial and Farm Loans to individuals and rms used to purchase land houses and other structures The land or structure then serves as collateral The mortgage market is the biggest debt market in the US Secondary markets for mortgages rst developed in the 1970s and 1980s and are now quite large and active Corporate Bonds Intermediate and long term debt issued by corporations Usually make regular interest payments twice per year Return a xed amount face value at maturity US Government Securities Treasury Notes 2 Currently issued with maturities of 2 5 and 10 years hence intermediate term debt Treasury Bonds 2 Before October 2001 issued with maturity of 30 years hence long term debt In October 2001 the US Treasury stopped issuing 30 year bonds making the 10 year US Treasury note the US Government security with the longest maturity Make regular interest payments twice per year and return a xed amount at maturity State and Local Government Municipal Bonds Intermediate and long term debt issued by state and local governments lnterest payments are exempt from federal income taxes making municipal bonds especially attractive to some investors US Government Agency Bonds Somewhat like a combination between US Treasury bonds and notes and corporate bonds but issued by US Government agencies government sponsored corpora tions Examples Federal National Mortgage Association FNMA Fannie Mae and Fed eral Home Loan Mortgage Corporation FHLMC Freddie Mac sell bonds and use the proceeds to buy mortgages Student Loan Marketing Association SLMA Sallie Mae sells bonds and uses the proceeds to buy student loans Commercial and Consumer Loans Loans originally made by banks to businesses and households Secondary markets for these loans are only now just developing 4 Role of Financial Intermediaries We have now considered a wide variety of nancial instruments that arise through the process of direct nance in which the lender sells securities directly to the borrower Why does some borrowing and lending take place instead through indirect nancthat is with the help of a nancial intermediary Financial intermediaries play a number of special roles and help solve a number of special problems in the process of indirect nance 41 Transaction Costs and Economies of Scale Transaction costs 2 the time and money spent in carrying out nancial transactions Financial intermediaries help reduce transaction costs by taking advantage of economies of scale Example a bank can use the same loan contract again and again thereby reducing the costs of making each individual loan 42 Risk Sharing and Diversi cation Risk 2 uncertainty about the returns investors will receive on any particular asset By purchasing a large number of different assets issued by a wide range of borrowers nancial intermediaries use diversi cation to help with risk sharing Example by lending to a large number of different businesses a bank might see a few of its loans go bad but most of the loans will be repaid making the overall return less risky Here again the bank is taking advantage of economies of scale since it would be di icult for a smaller investor to make a large number of loans 43 Adverse Selection and Moral Hazard Financial intermediaries also use their expertise to screen out bad credit risks and monitor borrowers They thereby help solve two problems related to imperfect information in nancial markets Adverse Selection 2 refers to the problem that arises before a loan is made because bor rowers who are bad credit risks tend to be those who most actively seek out loans Financial intermediaries can help solve this problem by gathering information about potential borrowers and screening out bad credit risks Moral Hazard 2 refers to the problem that arises after a loan is made because borrowers may use their funds irresponsibly Financial intermediaries can help solve this problem by monitoring borrowers activ ities 5 Types of Financial Intermediaries The main types of nancial intermediaries are listed in Mishkin s Table l p35 Depository lnstitutions Banks Commercial Banks Savings and Loan Associations Mutual Savings Banks Credit Unions Contractual Savings lnstitutions Life lnsurance Companies Fire and Casualty lnsurance Companies Pension Funds lnvestment lntermediaries Finance Companies Mutual Funds Money Market Mutual Funds 51 Depository Institutions Banks Depository institutions as a group Accept issue deposits which then become their liabilities Make loans which then become their assets Commercial Banks Sources of funds liabilities issue deposits 10 Checking deposits 2 provide check writing privileges Savings deposits 2 do not provide check writing privileges but allow funds to be withdrawn at any time Time deposits 2 require that funds be deposited for a xed period of time with penalty for early withdrawal Uses of funds assets make commercial consumer and mortgage loans buy US Government and municipal bonds Savings and Loan Associations SampLs Sources of funds issue deposits Uses of funds make loans mainly mortgage loans Mutual Savings Banks Like SampLs but structured as mutuals meaning that the depositors own the bank Sources of funds issue deposits Uses of funds make loans mainly mortgage loans Credit Unions Set up to serve small groups union members employees of a particular rm etc Sources of funds issue deposits Uses of funds make loans mainly consumer loans Collectively savings and loan associations mutual savings banks and credit unions are called thrift institutions The distinctions between commercial banks and thrift institutions are mainly historical and have blurred over the years Example before 1980 thrift institutions were not permitted to issue checking deposits SampLs and mutual savings banks were not allowed to make consumer loans and credit unions were not allowed to make mortgage loans 511 Contractual Savings Institutions Contractual savings institutions as a group Acquire funds at periodic or regular intervals on a contractual basis Life insurance Companies Sources of funds collect premiums from policies Uses of funds buy corporate bonds and mortgages some stocks Fire and Casualty insurance Companies Sources of funds collect premiums from policies Uses of funds buy US Government and municipal bonds corporate stocks and bonds Pension Funds Sources of funds collect contributions from employers and employees Uses of funds buy corporate stocks and bonds 52 Investment Companies Finance Companies Sources of funds sell commercial paper stocks bonds Uses of funds make consumer and business loans Example Ford Motor Credit sells commercial paper and bonds and uses the proceeds to make loans to people Who buy Ford cars and trucks Mutual Funds Mutual funds allow individual investors to pool their resources and thereby hold a more diversi ed portfolio of assets With lower transaction costs Sources of funds sells shares to individuals Uses of funds buy stocks and bonds Money Market Mutual Funds Sources of funds sell shares to individuals Uses of funds buy money market instruments 12 Shareholders can often write checks against the value of their shareholdings Mishkin s Table 2 p36 provides information on the growth and size of these various nancial intermediaries Type of Intermediary Value of Assets 1970 2002 Depository Institutions Commercial Banks 517 billion dollars 7161 SampLs and Mutual Savings Banks 250 1338 Credit Unions 18 553 Contractual Savings Institutions Life 1nsurance Companies 201 3269 Fire and Casualty 1nsurance Companies 50 894 Private Pension Funds 112 3531 State and Local Gov t Pension Funds 60 1895 Investment Intermediaries Finance Companies 64 1165 Mutual Funds 47 3419 Money Market Mutual Funds 0 2106 Observations Commercial banks are the largest type of depository institution Thrift institutions have declined in importance but still remain signi cant Mutual funds and money market mutual funds have grown spectacularly 6 Conclusion Throughout this course we ll be considering various aspects of the role that these various nancial instruments and nancial intermediaries play in the economy as a whole With all of these de nitions in hand and collected in one place we ll always be able to refer back to this overview if we need to remember how a particular type of nancial instrument works or what a particular type of nancial intermediary does Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 7 A Model of Stock Prices 1 The Dividend Valuation Model 2 Key Assumptions and Questions 3 The Gordon Growth Model 4 Example Valuing the Dow Jones Industrial Average Mishkin s Chapter 7 presents a model of stock prices called the dividend valuation model These notes show how this model can be derived by comparing the stream of future divi dends paid by a stock to the stream of cash ows paid by a portfolio or combination of discount bonds Deriving the dividend valuation model in detail this way allows us to see more clearly the key assumptions that are built into the model and to identify the key questions we need to answer in order to apply the model in practice When combined with an additional set of assumptions the dividend valuation model can be used to obtain a version of the Gordon growth model a famous and still widely used model of stock prices After deriving the Gordon growth model we can use it to ask whether stocks pricesias measured by the Dow Jones Industrial Averageiwere too high or too low at the end of 2002 1 The Dividend Valuation Model Equity 2 a contractual agreement representing claims to a share in the income and assets of a business Common stock is the principal form of equity Owners of common stock receive a bundle of rights which include The right to vote on issues that are most important to the corporation The right to be the corporation s residual claimant stockholders receive whatever funds remain after holders of debt are paid Stockholders receive these funds in the form of dividend payments which are autho rized by the rm s board of directors and typically paid quarterly Consider a share of stock that sells for price Pt today at time t Recall that equities have no maturity date Consistent with this fact suppose that each share of stock pays dividends Di DHZ Dt3 starting next period time 15 1 and continuing out into the in nite future How does the price P of the stock today depend on this stream of future dividends or cash ows The dividend valuation model shows us how to answer this question Step one in deriving the dividend valuation model is to recognize the following fact Fact The stream of dividends Dt1 DHZ Dt3 paid by the stock can be replicated by a portfolio or combination of discount or zero coupon bonds having different maturities To see why this fact must be true consider the following investment strategy today at time t Buy a oneperiod discount bond with face value Di Buy a two period discount bond with face value DHZ Buy a three period discount bond with face value Dt3 And so on out into the in nite future This portfolio of discount bonds pays off DZH when the one period bond matures at time t l DHZ when the two period bond matures at time t 2 Dt3 when the threeperiod bond matures at time t 3 And so on out into the in nite future The portfolio of discount bonds therefore replicates the stream of dividends paid by the stock Next let s ask what are today s time t prices of all of these discount bonds To answer this question let in yield to maturity on the oneperiod discount bond igt annualized yield to maturity on the two period discount bond 13 annualized yield to maturity on the threeperiod discount bond and so on out into the in nite future Then oneperiod discount bond has price Dt1 Qt1 7 1 1 at time t The two period discount bond has price Dt2 Qt T 1 12 The three period discount bond has price Dt3 Qt3 7 1 130 And so on out into the in nite future Finally note that the price of the stock must be equal to the total cost of this portfolio of discount bonds so that P Qt1 Qt2 Qt3 1 To see why this must be the case suppose instead that the stock price is greater than the cost of the portfolio of bonds so that P gt Qt1 Qt2 Qt3 Since the stock and the portfolio of bonds both pay off the same stream of future cash ows Di Di Dt3 in this case it would make sense for investors to sell the stock and buy the portfolio of bonds The stock price would then fall and the bond prices would then rise until Pt Qt1 Qt2 Qt3 1 as required Suppose on the other hand that the stock price is less than the cost of the portfolio of bonds so that P lt Qt1 Qt2 Qt3 Since the stock and the portfolio of bonds both pay off the same stream of future cash flows Di DHZ Dt3 in this case it would make sense for investors to buy the stock and sell the portfolio of bonds The stock price would then rise and the bond prices would then fall until Pt Qt1 Qt2 Qt3 1 as required Now let s rewrite equation 1 using the expressions for the bond prices that we derived earlier Pt Qt1 Qt2 Qt3 1 is equivalent to D D D B t1 th 2 tf3 3 1112 1122 1132 or more compactly DO Dtj mg01quot 13 Equation 2 summarizes the dividend valuation model Note that the expression on the right hand side of equation 2 measures the present value of all future dividends paid by the stock Hence in words the dividend valuation model says that the price of a share of stock should equal the present value of all future dividends paid by that share of stock 2 Key Assumptions and Questions The dividend valuation model tells us that the price of a share of stock should equal the present value of all future dividends paid by that share of stock that is DO Dtj P 2 t 1 ljt One key assumption that underlies the derivation of equation 2 is that a portfolio of discount bonds exists that exactly replicates the stream of dividends or cash ows Di DHZ Dt3 paid by the stock ln practice these future dividends are not known with certainty that is the stock is a risky asset Hence the discount bonds used in our derivation of 2 should probably not be default free According to the loanable funds framework when the riskiness of bonds increases the price of bonds decreases and hence the interest rate increases Hence the interest rates used in 2 should be higher than the interest rates on US govern ment bonds But how do we know exactly what interest rates in igt 1393 to use in applying the dividend valuation model And how do we forecast the future dividends Dt1 Di Dt3 Security analysts and other nancial market participants work hard to nd answers to these questions But the answers are seldom if ever clear cut 3 The Gordon Growth Model The Gordon growth model named after its inventor Myron Gordon makes the dividend valuation model easier to use by combining it with three additional assumptions 1 Dividends are growing at the constant rate 9 so that Dt1 19Dt7 Dz2 1 9Dz1 1 g1 9Dt 1 g2Dt Dt3 1 9Dz2 1 g1 g2Dz 1 g3Dt or more generally Dtj 1 31th for all 012 2 The interest rates in igt 1393 are constant so that 1 13 1 k where k required return on equity Remember that since the stock is a risky asset the required return If should generally be greater than the interest rate on US Government bonds 3 The required return on equity exceeds the dividend growth rate so that k gt g This assumption is needed for technical reasons as we ll see below To derive the Gordon growth model combine these assumptions with equation 2 from before 8 D B J 2 1 My x H B CO 09th 2 mm 11 1 Equation 3 is still rather complicated but it can be simpli ed using the following fact j1 Fact If k gt g Proving this fact requires some algebra To see why is must be true start with yg F1 1k keg and multiply both sides by l Err l to obtain 19 19 jg 19 19 1 1kgt 1kgt 7 1 1k k9 11 01 DO DO 2 1 1 1m 1k 1k 1k 1k k9 11 11 01 19 19 2 19 3 1kgt1k 11 19 2 19 3 19 4 1k 1k 1k B 1g 1k k9 OI 1k71K all of which implies that the two sides of the original equation 4 must be equal Since 4 only holds true if k gt 9 we need Gordon s third assumption to make the theory work Using equation 4 equation 3 becomes Equation 5 allows us to determine today s time t stock price Pt based on 1 Today s time t dividend Di which is presumably known 2 The constant dividend growth rate 9 which must be estimated or assumed 3 The required return on equity k which must also be estimated or assumed Before moving on let s ask if equation 5 makes sense It implies that today s stock price P will be higher if 1 Today s dividend D is larger 2 The growth rate of future dividends g is larger 7 3 The required return of equity is k is smaller The rst two of these implications seem sensible of course if the dividend is larger or growing at a faster rate the stock price should be higher But what about the third implication that P is higher when k is smaller Recall that k the required return on equity is assumed to be equal to the constant yield to maturity on a portfolio of discount bonds with the same risk characteris tics as the stock The loanable funds framework implies that if the bonds become less risky the interest rate will fall Hence a smaller value of k corresponds to a lower level of risk So this third implication makes sense too if the stock is less risky the stock price should be higher 4 Example Valuing the Dow Jones Industrial Average The Dow Jones Industrial Average DJIA is an index or average of stock prices for 30 of the largest US corporations Alcoa Altria American Express ATampT Boeing Cater pillar CitiGroup Coca Cola Disney DuPont Eastman Kodak Exxon Mobil General Electric General Motors Hewlett Packard Home Depot Honeywell IBM Intel 1n ternational Paper JP Morgan Johnson amp Johnson McDonalds Merck Microsoft Proctor amp Gamble SBC Communications 3M United Technologies and Wal Mart Hence the DJIA can also be regarded as the price of a portfolio that contains these 30 stocks There are other widely cited stock indices for example the Standard and Poor s SampP 500 But the DJIA is probably the most famous Let s apply the Gordon growth model to value the DJIA at the end of 2002 To start note that the dividends paid by the stocks in the DJIA during 2002 equaled 18970 This fact dictates a setting of Di 18970 Next let s make an assumption about 9 the growth rate of future dividends by taking a look at the growth rate of dividends in the past Dividends paid by the stocks in the DJlA during 1992 equaled 10070 Hence over the ten years from 1992 through 2002 dividends grew at the average annual rate of 654 Dividends paid by the stocks in the DJlA during 1982 equaled 5410 Hence over the twenty years from 1982 through 2002 dividends grew at the average annual rate of 647 Based on these gures it seems reasonable to expect that dividends will continue to grow at an annual rate of about 65 This assumption dictates a choice of g 0065 Finally let s make an assumption about If the required return on equity We ve noted before that k should be higher than the interest rate on US government bonds At the end of 2002 the yield to maturity on the 10 year US Treasury note was 383 So If should de nitely be bigger than 383 At the end of 2002 the yield on corporate bonds with Moody s highest rating of Aaa was 609 But equityholders are residual claimants meaning that bondholders get paid rst And besides not all of the companies in the DJlA have Aaa bond ratings So the stocks in the DJlA are probably more risky than Aaa bonds Hence k should probably be bigger than 609 as well Based on these observations let s choose a value of k equal to 85 or k 0085 Now let plug our choices of D 1897 g 0065 and k 0085 into equation 5 1 0065 B 1897 0085 7 0065 1065 B 1897 1010153 002 Hence under our assumptions the Gordon growth model implies that the DJlA should have been traded at 1010153 at the end of 2002 1n fact the DJlA stood at 834163 at the end of 2002 9 Under our assumptions the Gordon growth model implies that stocks were undervalued by over 20 But suppose on the other hand that stocks are more risky than we ve initially assumed so that a higher value of k is called for In particular let s redo our calculations assuming that k equals 9 or k 009 instead of 85 19 P D 5 t by t 1 0065 Pt 1897 009070065 Pt 1897808122 0025 Now under our new assumption about risk the model implies that stocks were slightly overvalued instead This example illustrates that Gordon s model can be useful in translating assumptions about future dividend growth and risk into implications for stock prices But the model s implications are only as reliable as the assumptions that we feed into it Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 1710 Federal Reserve Operating Procedures 1 A Model of Reserves and the Federal Funds Rate Demand for Reserves Supply of Reserves Market Equilibrium 2 Changes in the Federal Funds Rate Target 3 Operation of the Discount Window Our previous analysis showed how in practice the Federal Reserve sets interest rate targets for monetary policy that help it achieve its goals for employment economic growth in ation and nancial market and interest rate stability Now we will extend that analysis to provide a more detailed and realistic view of how the Federal Reserve s operating procedures actually work Here in particular we ll note that the Federal Reserve s interest rate target is a target for the federal funds ratthe rate charged on loans between banks of deposits at the Fedithat is on loans of reserves Hence we ll begin by constructing a model of reserves and the federal funds rate rst by considering banks demand for reserves and then by considering the Fed s supply of reserves As usual the intersection of the demand and supply curves will determine the equilibrium in the market for federal funds Then we ll use our model to see how the Fed brings about changes in its federal funds rate target and to see what those target changes imply for the overall stance of monetary policy Finally we ll use our model to see how the Fed operates the discount window in its role as a lender of last resort 1 A Model of Reserves and the Federal Funds Rate In practice the Federal Reserve s interest rate target is a target for the federal funds rat the rate charged on interbank loans of reserves To see how the Fed s targeting procedures work we need to begin by constructing a model of the market for reserves We ll do this in the usual way rst by considering the demand for reserves and then by considering the supply of reserves Our demand and supply analysis will allow us to see how the Fed hits its target for the federal funds rate as well as what happens when it changes that federal funds rate target 11 Demand for Reserves Recall from our previous analysis that total reserves consist of required reserves plus excess reserves R RR ER where R total reserves RR required reserves ER excess reserves Recall also that by law banks must hold a fraction of their checkable deposits as required reserves RR 7 gtlt D7 where 7 required reserve ratio 10 D checkable deposits Checkable deposits pay interest but at a lower rate than other assets since they offer check writing privileges Hence when interest rates rise individuals and non bank corporations transfer funds out of deposits and into other assets Hence when interest rates rise required reserves fall Likewise from a bank s perspective excess reserves pay no interest 2 Hence when the interest rates rise banks hold fewer excess reserves Recall that we saw evidence of this negative relationship between interest rates and excess reserves in Mshkin s Chapter 16 Figure l p381 In particular when the federal funds rate rises a bank holding excess reserves will want to lend some of those reserves out to other banks and earn the higher federal funds rate Since both required reserves RR and excess reserves ER fall when interest rates rise total reserves R fall when interest rates rise Thus we can trace out a downward sloping demand curve for reserves 12 Supply of Reserves To analyze the demand for reserves we decomposed total reserves B into required reserves RR and excess reserves ER To analyze the way that the Federal Reserve supplies reserves to the banking system it is useful to decompose the total amount of reserves R in a different way DL discount loans reserves borrowed from the Fed Ba nonborrowed reserves R 7 DL In practice the Fed 1 Sets a target for the federal funds rate 2 Determines the amount of nonborrowed reserves B it must supply to make the equilibrium federal funds equal to f 3 Sets the discount rate id above its target for the federal funds rate 4 Stands willing to make discount loans to banks at the discount rate id These operating procedures give the supply curve for reserves an unusual shape When the federal funds rate if is below the discount rate id it is cheaper for a bank to borrow reserves from another bank than it is for a bank to obtain a discount loan Hence when if is below id banks will not use the discount window and the supply of reserves is xed at Bi Below id therefore the supply curve for reserves is vertical Federal Funds Rate if Demand for Reserves 4 Rd Quantity of Reserves R Federal Funds Rate if Rs id Discount rate lt Supply of Reserves f Federal funds rate target Rd Quantity of Reserves R When the federal funds rate rises to id however banks will become willing to use the discount window Since the Fed stands willing to make as many discount loans as banks want at the discount rate id the supply curve for reserves then becomes horizontal 13 Market Equilibrium As usual equilibrium occurs at the point where the demand and supply curves intersect Under normal conditions 1 The equilibrium federal funds rate equals the Fed s target 2 The discount rate id is above the equilibrium federal funds rate 3 The equilibrium level of reserves equals 4 The Fed does not make any discount loans 2 Changes in the Federal Funds Rate Target What happens when the Federal Reserve raises its federal funds rate target Suppose that initially the federal funds rate target is and that the Federal Reserve hits this target by supplying R in nonborrowed reserves To raise the target to if the Fed must decrease the supply of nonborrowed reserves to R This shifts the supply curve for reserves while leaving the demand curve unchanged The equilibrium federal funds rate equals the new target To decrease the supply of nonborrowed reserves the Fed conducts an open market sale This open market sale also works to decrease the monetary base and the money supply as a whole Hence the increase in the federal funds rate target is associated with a smaller money supplyithat is a tighter monetary policy Similarly to lower its federal funds rate target the Fed must increase the supply of non borrowed reserves by conducting an open market purchase This open market purchase also works to increase the monetary base and the money supply as a whole Federal Funds Rate if R1s To increase its federal funds rate target the Fed must use open market operations to decrease the supply of nonborrowed reserves Rd Quantity of Reserves R Hence a decrease in the federal funds rate target is associated with a larger money supplyi that is a looser monetary policy 3 Operation of the Discount Window As illustrated above the Fed sets the discount rate above its federal funds rate target Hence most of the time discount lending is zero During a nancial panic however the demand for reserves may unexpectedly increase by a large amount Under such circumstances banks want to hold more reserves at any given interest rate the demand curve for reserves shifts out Since the Fed stands ready to make discount loans at the discount rate id the equilibrium federal funds rate will never rise above id Thus the Fed s operating procedures allow it to act as a lender of last resort during a panic and prevent the equilibrium federal funds rate from rising too far above its target 4 Conclusion Current Federal Reserve operating procedures focus on targeting the federal funds rate When the Fed increases its federal funds rate target it conducts open market sales that contract the money supply And when the Fed decreases its federal funds rate target it conducts open market purchases that expand the money supply Current operating procedures also allow the Fed to act as a lender of last resort By setting the discount rate above its federal funds rate target and by standing ready to make discount loans at that discount rate the Fed limits the extent to which the federal funds rate can rise during a nancial panic Federal Funds Rate if Rs The demand for reserves may increase sharply during a financial panic R1d R0d Rn But the Fed s operating procedures Quantlty Of Reserves R won t let the federal funds rate rise above the discount rate Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 17a The Tools of Monetary Policy 1 Open Market Operations 2 Discount Loans 3 Changes in Reserve Requirements Before working through Mishkin s Chapter 17 on the Tools of Monetary Policy it is helpful to state a de nition that clari es what is meant by the term monetary policy in the rst place We can nd such a de nition in Chapter 1 of Mishkin s book on page 12 Monetary policy 2 the management of money and interest rates Next it is useful to recall from our analysis of the money supply process that M m gtlt M B where M is the money supply MB is the monetary base and m the money multiplier is determined as l c m 7 rec These equations reveal that the Fed can manage the money supplyithat is conduct mon etary policy in three ways By changing the monetary base through open market operations By changing the monetary base through discount lending By changing the money multiplier by changing the required reserve ratio Thus the Fed has three tools of monetary policy Open market operations Discount loans Changes in reserve requirements Which of these tools is most effective Mishkin s Chapter 17 helps us answer this question 1 Open Market Operations We have already distinguished between two types of open market operations Open market purchases 2 Fed buys US government securities to increase the monetary base Open market sales 2 Fed sells US government securities to decrease the monetary base Thus the Fed conducts open market operations by buying and selling US government securitiesgespecially US Treasury bills Since the market for US Treasury bills is so active the Fed can make large purchases and sales quickly and easily without disrupting the market Although the FOMC makes decisions on how open market operations are to be conducted the trades themselves are executed at the Open Market Desk at the Federal Reserve Bank of New York Open market purchases and sales have permanent affects on the monetary base but some times the Fed will want to change the monetary base only temporarily At these times it engages in two other types of transactions Repurchase Agreement repo The Fed purchases US government securities will an agreement that the seller will buy them back repurchase them at a speci ed price on a speci ed date usually within two weeks A repo is therefore like a temporary open market purchase temporarily increasing the monetary base Matched Sale Purchase Transaction reverse repo The Fed sells US government securities with an agreement that the buyer will sell them back at a speci ed price on a speci ed date again usually within two weeks A reverse repo is therefore like a temporary open market sale temporarily decreasing the monetary base Hence in conducting monetary policy open market operations have a number of advan tages They are under the direct and complete control of the Fed They can be large or small They can be easily reversed They can be implemented quickly 2 Discount Loans When a bank receives a discount loan from the Fed it is said to have received a loan at the discount window The Fed can affect the volume of discount loans by setting the discount rate A higher discount rate makes discount borrowing less attractive to banks and will therefore reduce the volume of discount loans A lower discount rate makes discount borrowing more attractive to banks and will therefore increase the volume of discount loans Discount lending is most important during nancial panics When depositors lose con dence in the nancial system they will rush to withdraw their money This large deposit out ow puts the banking system in great need of reserves The Fed stands ready to supply these reserves by making discount loans In such situations the Fed acts as a lender of last resort Hence in October 1987 and again in September 2001 the Fed made it clear that it would supply additional reserves to the nancial system as necessary through the discount window Advantage of discount loans They allow the Fed to act as a lender of last resort during a nancial panic Disadvantages of using discount loans as a tool for monetary policy during normal times The volume of discount loans can be in uenced by the Fed but not completely con trolled The Fed cannot be sure how many banks will request discount loans at any given interest rate Changes in the discount rate must be proposed by the Federal Reserve Banks before being approved by the Board of Governors Hence they are neither quickly made nor easily reversed 3 Changes in Reserve Requirements By affecting the money multiplier changes in the required reserve ratio can lead to changes in the money supply Disadvantages to using changes in reserve requirements as a tool for monetary policy Large changes in reserves must be approved by Congress Hence large changes cannot be made quickly and easily Also if a bank holds only a small amount of excess reserves and the required reserve ratio is increased the bank Will have to quickly acquire reserves by borrowing selling securities or reducing its loans Each of these three options is costly and disruptive Hence changes in reserve requirements can cause problems for banks by making liquidity management more di icult 4 Conclusion Open market operations are by far the most effective tool With Which the Fed can conduct monetary policy on a day to day basis Thus in practice the Fed relies most heavily on open market operations in conducting monetary policy Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 150 The Fed s Control of the Monetary Base 1 Control of the Monetary Base Open Market Operations Discount Loans Shifts from Deposits into Currency 2 Overview of the Fed s Control of the Monetary Base Recall that in our simple model of multiple deposit creation showed how the Federal Reserve can give rise to an expansion or contraction of deposits by supplying more or less reserves to the banking system More speci cally our simple model indicates that if the Fed wants to bring about a change in deposits it can perform an open market operation or make a discount loan to change the level of reserves and then rely on the formula ADleR 7 But recall also that in deriving our simple model we made two unrealistic assumptions Banks never hold excess reserves Individuals and non bank corporations never hold currency Accordingly our next major goal will be to consider how the money supply works in a more general and realistic setting where banks decisions about excess reserve holdings and depositors decisions about currency holdings are explicitly taken into account But to set the stage for this more general and realistic analysis it will help to begin by working through another set of examples that show how the Fed can exercise much more precise control over the monetary base than it can over reserves alone These examples will trace out what happens to both reserves and the monetary base when 1 The Fed conducts and open market operation The Fed makes a new discount loan Individuals and non bank corporations shift funds out of deposits and into currency These examples will allow us to conclude our analysis of Mshkin s Chapter 15 with an overview of the Fed s control of the monetary base 1 Control of the Monetary Base Recall from our introductory discussion of the Federal Reserve s balance sheet that if MB monetary base high powered money C currency in circulation outside of banks R reserves then by de nition MB C R We ve already seen how the Fed can in uence the level of reserves by conducting open market operations and by making discount loans And the de nition MB C R suggests that by changing the level of reserves R the Fed can also change the level of the monetary base MB And this is true In turns out however that the Fed can actually exercise more precise control over the monetary base as a whole than it can over reserves alone To see why let s consider a set of examples 11 Open Market Operations One way that the Fed can change reserves and hence the monetary base as well is through open market operations At this point as we seek to make our analysis more general it is useful to distinguish between two types of open market operations Open market purchase 2 purchase of US government securities by the Fed Open market sale 2 purchase of US government securities by the Fed Let s take a look at three examples of open market purchases Example 1 Open Market Purchase from a Bank When the Fed decides to make an open market purchase the open market desk at the Federal Reserve Bank submits a buy order to the over the counter OTC market for US government securities just like any other investor And just like any other investor the Fed can t be sure at the time it places its buy order Who the seller Will be But suppose that it turns out that Fleet Bankor some other bankihas placed a sell order at the same time that the Fed places its buy order The Fed s buy order is matched With Fleet s sell order in the OTC market and the Fed buys 100 in US easury bills from Fleet Fleet receives a 100 check from the Fed Which it deposits in its account at the Fed FLEET Assets I Liabilities Reserves 100 Securities 100 FEDERAL RESERVE Assets Liabilities Securities 100 Reserves 100 1n this case reserves increase by 100 and since currency in circulation does not change the monetary base also increase by 100 Example 2 Open Market Purchase from the Non Bank Public 1 Suppose once again that the Fed decides to make an open market purchase But suppose that this time the Fed s buy order is matched With a sell order placed not by a bank but instead by an individual or a non bank corporation So in this example the Fed buys 100 in US easury bills from the non bank public The seller of the easury bills receives a 100 check from the Fed Which he or she Will deposit in his or her checking account at Fleet Bank NONBANK PUBLIC Assets Liabilities Checkable Deposits 100 Securities 100 Fleet Bank Will then deposit the check in its account at the Fed FLEET Assets I Liabilities Reserves 100 Checkable Deposits 100 FEDERAL RESERVE Assets Liabilities Securities 100 Reserves 100 1n this case the effect of the open market purchase on the Fed s balance sheet is the same as if the Fed had purchased the Treasury bill directly from a bank reserves increase by 100 and since currency in circulation does not change the monetary base also increases by 100 Example 3 Open Market Purchase from the Non Bank Public 11 Suppose that the Fed purchases 100 in US Treasury bills from an individual or a non bank corporation as just described above But now suppose that instead of depositing the Fed s check in his or her checking account the seller cashes the Fed s check at Fleet Bank NONBANK PUBLIC Assets Liabilities Currency 100 Securities 100 Fleet Bank pays out 100 in vault cash and deposits the Fed s check in its account at the Fed FLEET Assets Liabilities Vault Cash 100 Deposits at the Fed 100 Reserves are unchanged but currency in circulation has increased by 100 FEDERAL RESERVE Assets Liabilities Securities 100 Currency in Circulation 100 1n this case the open market purchase has no effect on reserves But since currency in circulation increases by 100 the monetary base also increases by 100 Comparing examples 2 and 3 shows that the effect of an open market purchase on reserves depends on whether the seller of securities keeps the proceeds from the sale as currency or as deposits But the effect of the open market purchase on the monetary base is always the same the monetary base rises regardless of whether then seller keeps the proceeds as currency or as deposits Conclusion Since the Fed does not know whether sellers of securities will hold the proceeds as currency or as deposits the effects of an open market purchase on the monetary base are much more certain than the effects of an open market purchase on reserves 1n this sense the Fed can control the monetary base much more precisely that it can control reserves What about open market sales 1f the Fed sells 100 in US easury bills and the buyer pays with a check then Reserves fall by 100 Currency in circulation remains unchanged The monetary base falls by 100 1f the Fed sells 100 in US easury bills and the buyer pays with currency then Reserves remain unchanged Currency in circulation falls by 100 The monetary base falls by 100 Once again the Fed controls the monetary base much more precisely than it controls reserves 12 Discount Loans All of our examples so far have looked at the effects of open market operations But we also know from before than the Fed can increase reserves by making discount loans to banks How do discount loans affect the monetary base Suppose that Fleet Bank borrows 100 as a discount loan from the Fed When it makes this loan the Fed credits Fleet s account at the Fed with an additional 100 FLEET Assets Liabilities Reserves 100 Borrowings 1 00 FEDERAL RESERVE Assets Liabilities Discount Loans 100 l Reserves 100 When the Fed makes a 100 discount loan reserves increase by 100 and since currency in circulation does not change the monetary base also increases by 100 13 Shifts from Deposits into Currency As a nal example let s consider what happens when a depositor withdraws 100 from his or her checking account at Fleet Bank NONBANK PUBLIC Assets Liabilities Currency 1 00 Checkable Deposits 100 We know from our analysis of bank management that when Fleet loses 100 in deposits it loses an equal amount of reserves FLEET Assets Liabilities Reserves 100 Checkable Deposits 100 Reserves have decreased by 100 but currency in circulation has increased by 100 FEDERAL RESERVE Assets Liabilities Currency in Circulation 100 Reserves 100 The monetary base remains unchanged Conclusion Shifts from deposits into currency increase currency in circulation but decrease reserves by an equal amount leaving the monetary base unchanged Since the Fed cannot predict exactly When these shifts Will occur it controls the monetary base more precisely than it controls reserves Note that the same conclusion applies When one of Fleet s depositors decides to deposit 100 in currency into his or her checking account 1n this case currency in circulation decreases by 100 And since Fleet gains 100 in vault cash reserves increase by an equal amount Hence reserves increase by 100 but the monetary base remains unchanged Once again the Fed controls the monetary base more precisely than it controls reserves 2 Overview of the Fed s Control of the Monetary Base The Fed can control the monetary base by conducting open market operations A 100 open market purchase increases the monetary base by 100 but may or may not increase reserves A 100 open market sale decreases the monetary base by 100 but may or may not decrease reserves The Fed can also control the monetary base by making discount loans A 100 discount loan increases the monetary base by 100 and also increases reserves Random shifts from deposits into currency and from currency into deposits do not affect the monetary base but do change reserves Conclusion The Fed controls the monetary base much more precisely than it controls reserves Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 3 What Is Money 1 Meaning of Money 2 Functions of Money Medium of Exchange Unit of Account Store of Value 3 Measuring Money Theoretical Measures Empirical Measures Federal Reserve s Monetary Aggregates This chapter begins by de ning money in basic terms It then discusses the various functions of money in the economy as a Whole Finally it considers how economists and the Federal Reserve measure money in the US economy 1 Meaning of Money Money 2 anything that is generally accepted in payment for goods and services or in the repayment of debts Objects that qualify as money under this de nition Currency dollar bills and coins Checking account deposits Perhaps even savings deposits This concept of money must be distinguished from two other terms Wealth value of all property or assets including currency and bank deposits but also including stocks real estate etc Income 2 ow of earnings per unit of time 2 Functions of Money Three principal functions of money Medium of Exchange Unit of Account Store of Value 21 Medium of Exchange Money serves as a medium of exchange it is used to pay for goods and services By serving as a medium of exchange money promotes economic e iciency be reducing transaction costs the time and effort spent in exchange Without money trade must take place through barter But barter can be quite costly it can take time for you to nd someone who both Has the good that you want Wants the good that you have This is the problem of nding a double coincidence of wants Money can solve this problem since everyone will accept it 22 Unit of Account Money serves as a unit of account values of goods and services can be measured in terms of money As serving as a unit of account money reduces transaction costs by allowing all prices to be stated in common terms With barter you must keep track of each good s price in terms of every other good But with money you only need to keep track of each good s price in terms of one good money 23 Store of Value Money serves as a store of value it serves as a way of storing wealth Other assets also serve as a store of value stocks bonds real estate etc But money is unique in terms of its liquidity Liquidity the ease and speed with which an asset can be converted into a medium of exchange By de nition money is the most liquid store of value On the other hand money s usefulness as a store of value is eroded by in ation a general rise in the prices of all goods If through in ation all prices double then the value of money has been cut in half Under conditions of hyperin ation where the in ation rate exceeds 50 per month con sumers have sometimes abandoned the use of money altogether and resorted to barter 3 Measuring Money 31 Theoretical Measures Some economists prefer to measure money on theoretical grounds including only those assets that clearly serve as a medium of exchange currency checking account deposits traveler s checks The problem with this way of measuring money is that it is not clear cut There are some assets like money market mutual fund shares that provide limited check writing privileges should these be including in the measure of money 32 Empirical Measures Given the ambiguities associated with the theoretical approach other economists take an empirical or data based approach to measuring money These economists suggest that the correct measure of money is one that is most closely linked to the behavior of in ation and output The problem with this de nition is that historically measures of money that work well in predicting in ation and output in one period do not work as well during other periods 33 Federal Reserve s Monetary Aggregates Given the problems associated with both theoretical and empirical measures of money the Federal Reserve provides data on several measures of money called monetary aggregates M1 assets that are clearly used as a medium of exchange Currency Traveler s checks Demand deposits 2 checking accounts that pay no interest Other checkable deposits 2 checking accounts that pay interest including negotiable order of withdrawal NOW accounts M2 M1 other assets that provide limited check writing privileges or are extremely liquid Small denomination under 100000 time deposits CDs and repurchase agreements RPs Savings deposits Money market deposit accounts MMDAs high yielding bank deposits that offer limited check writing privileges Like money market mutual fund shares but Are issued by banks Are insured by the Federal Deposit Insurance Corporation FDIC Retail or noninstitutional money market mutual fund shares owned by individuals M3 M2 other liquid assets Large denomination over 100000 time deposits CDs lnstitutional money market mutual fund shares owned by businesses Large denomination over 100000 repurchase agreements RPs Eurodollar deposits Mishkin s Table 1 shows the value of M1 M2 and M3 and their various components as of December 2002 M1 2 Currency 6265 billion Traveler s checks 77 Demand deposits 2907 Other checkable deposits 2812 Total M1 12061 billion M2 M1 Small time deposits and RPs 13323 billion Savings deposits and MMDAs 23404 Noninstitutional MMMF shares 9237 Total M2 58025 billion M3 M2 Large time deposits 11052 billion 1nstitutional MMMF shares 7677 Large repurchase agreements 5117 Eurodollar deposits 3411 Total M3 85282 billion Observations M3 is always bigger than M2 and M2 is always bigger than M1 These relationships must always hold of course because M3 includes everything in M2 and M2 includes everything in M1 1n December 2002 the total US population ages 16 and over was about 220 million Take 6265 billion 626500 million in currency and divide by 220 million people to calculate Currency per capita 6267 500 million in total currency 2 84773 220 million people 7 A large fraction of this currency must be held by foreigners as a store of value and by people engaged in criminal activitiesl Mishkin s Figure 1 p54 plots the growth rates of M1 M2 and M3 from 1960 through 2 2 The monetary aggregates show some tendency to move together but often grow at different rates This fact highlights the di iculty of using the monetary aggregates to forecast in ation and output The gure on the next page plots 10 year averages of Core Consumer Price In ation and M2 growth in the US 1969 2003 M2 growth and in ation share similar long run trends throughout most of the period Both rise during the 1970s and fall during the 1980s and early to mid 1990s Beginning in the late 1990s however the two series diverge M2 growth begins to rise but in ation continues to fall Either M2 growth is no longer useful in explaining long run movements in in ation or in ation is due to rise Again these observations highlight the di icult in nding relationships between in ation output and measures of money 4 Conclusion This chapter has shown that it is fairly easy To provide a basic de nition of money To identify the functions performed by money in the economy as a whole But this chapter has also shown that it is more di icult in practice to decide exactly which assets qualify as money and which do not For this reason the Federal Reserve provides several measures of money or monetary aggregates Often these measures of money move together but sometimes they do not Often these measures of money help predict movements in in ation and output but sometimes they do not Hence Federal Reserve economists and nancial market participants spend a lot of time and effort trying to determine what is going on with the money supply and what it means for the economy as a whole M2 Growth and Core CPI Inflation 10Year Averages 19692003 Inflation M2 Growth Lecture Notes on MONEY BANKING AND FINANCIAL MARKETS Peter N Ireland Department of Economics Boston College irelandpbcedu httpWWW2bceduirelandpec261html Chapter 9 Banking and the Management of Financial Institutions 1 The Bank Balance Sheet Liabilities Sources of Funds Assets Uses of Funds 2 Basic Operation of a Bank T accounts 3 General Principles of Bank Management Liquidity Management Asset Management Liability Management Capital Adequacy Management In our overview of the nancial system we brie y considered the role that banks play in channelling funds from agents Who have saved funds and want to lend to agents Who need funds and want to borrow We also identi ed the main sources and uses of funds that banks have Mishkin s Chapter 9 begins by taking a much closer look at the typical bank s balance sheet rst listing its sources of funds or liabilities and then listing its uses of funds or assets Then the chapter illustrates in more detail how banks operate how they obtain their funds from agents Who want to lend and channel those funds to agents Who want to borrow In the process of doing this the chapter introduces us to a valuable analytic device called a T account T accounts Will prove useful not only in this part of the course on banking but also in the next part of the course that looks at the money supply process Finally the chapter helps us identify and understand four basic principles of bank man agement liquidity management asset management liability management and capital adequacy management 1 The Bank Balance Sheet A bank s balance sheet lists Source of funds or liabilities Uses of funds or assets Bank Capital in de ned as Capital 2 Assets Liabilities which implies that capital serves as a measure of net worth Since we can rearrange this de nition to read Assets 2 Liabilities Capital it also implies that if we put assets on one side of the bank s balance sheet and liabilities plus capital on the other then the two sides of the balance sheet will always balance Looking at the bank s balance sheet shows us that banks make pro ts by charging an interest rate on their assets that exceeds the interest rate that they pay on their liabilities Mishkin s Table 1 p202 shows the combined balance sheet of all commercial banks as of January 2003 with all items listed as a percentage of total assets or liabilities Liabilities Sources of Funds Checkable Deposits 9 Nontransaction Deposits Small denomination Time Deposits and Savings Deposits 42 Largedenomination Time Deposits 14 Borrowings 28 Bank Capital 7 Total 100 Assets Uses of Funds Reserves Cash Items in the Process of Collection and Deposits at Other Banks Securities US Government and Agency State and Local Government Loans Commercial and Industrial Real Estate Consumer Interbank Other Physical Assets Total 11 Liabilities Sources of Funds Checkable Deposits 5 15 10 14 29 9 4 8 6 100 Checkable deposits are deposits in bank accounts that allow their owners to write checks Checkable deposits include Demand deposits 2 checking accounts that pay no interest Negotiable Order of Withdrawal NOW accounts 2 checking accounts that pay interest Money Market Deposit Accounts MMDAS high yielding deposit accounts that allow limited check writing privileges Unlike demand deposits and NOW accounts WDAS are not included in MI and are not subject to reserve requirements Checkable deposits are payable on demand if the depositor requests a withdrawal or writes a check the bank must pay immediately Checkable deposits are a bank s lowest cost source of funds since depositors are willing to accept a lower interest rate in exchange for the convenience of being able to write checks But checkable deposits are also costly to maintain the bank must process the checks prepare monthly statements maintain bank branches etc Nontransaction Deposits Owners cannot write checks on nontransaction deposits But they pay higher interest rates than checkable deposits Nontransaction deposits include Savings deposits 2 funds can be withdrawn without penalty at any time Small under 100000 time deposits certi cates of deposit or CDs 2 have a xed maturity with penalty for early withdrawal Large over 100000 time deposits CDs 2 also have a xed maturity date but they are negotiable meaning that they can be resold in a secondary market Borrowings Borrowings include Borrowings from the Federal Reserve 2 discount loans Borrowings from other banks 2 federal funds Borrowings from non bank corporations 2 repurchase agreements Bank Capital As noted above Capital 2 Assets Liabilities 2 Net Worth And as we ll see below bank capital is a cushion against a drop in the value of the bank s assets since the bank becomes insolvent bankrupt if the value of its assets falls below the value of its liabilities ie it owes more than it can repay 12 Assets Uses of Funds Reserves Reserves include The bank s deposits at the Federal Reserve Vault cash 2 currency that is physically held by the bank Reserves do not pay interest Required reserves By law the bank must hold a certain fraction 10 of every dollar of checkable deposits more precisely demand deposits and NOW accounts it receives as reserves 10 required reserve ratio Excess reserves 2 additional reserves held by the bank to meet its customers requests for withdrawals Cash Items in the Process of Collection A check that had been deposited at the bank but not yet collected from the check writer s bank is a cash item in the process of collection Deposits at Other Banks Many small banks hold deposits at larger banks In return the large banks provide services such as check collection and help with securities purchases This relationship between large and small banks is called correspondent banking and is less important today than in was years ago when check collection and securities transactions were considerably more di icult Securities Securities include US government and US government agency securities State and local government municipal securities By law banks can only hold debt instruments they cannot own equities Because they are default free and highly liquid a bank s holdings of short term US government securities Treasury bills are sometimes call its secondary reserves Lo ans Loans include Commercial and industrial loans Real estate loans mortgages Consumer loans Interbank loans Other Assets Physical assets owned by banks buildings and land computers and of ce equipment etc 2 Basic Operation of a Bank T accounts By looking at their balance sheets we can see that banks sell liabilities with one set of char acteristics and use the proceeds to acquire assets with a different set of characteristics For example a bank will accept a savings deposit from one customer and use the proceeds to make a mortgage loan to another customer This process is called asset transformation By engaging in asset transformation the bank hopes to pro t by charging a higher interest rate on its assets than it must pay on its liabilities Bank operations can be illustrated with the help of a diagram called a T account A T account is set up in the same format as a balance sheet with assets on one side and liabilities on the other But the T account is simpli ed since it only shows the changes on each side that occur as a result of speci c bank operations To see how banks engage in asset transformation let s consider three examples 21 Example 1 Suppose a customer deposits a 100 bill into his or her checking account at Fleet Bank The bank puts the 100 bill in its vault and adds 100 to the customer s checking account balance The 100 deposit shows up as a new liability on Fleet s balance sheet while the extra 100 in vault cash adds to Fleet s reserves and therefore shows up as a new asset Hence the T account looks like this FLEET Assets I Liabilities Reserves 100 Checkable Deposits 100 6 Thus When a bank receives additional deposits it gains an equal amount of reserves 22 Example 2 Now suppose that instead of depositing a 100 bill Fleet s customer deposits a check for 100 written on an account at Citibank The initial effect of this transaction can be shown in a T account for Fleet FLEET Assets I Liabilities Cash ltems in the Process of Collection 100 Checkable Deposits 100 Fleet then deposits the check in its account at the Fed The Fed transfers 100 from Citibank s account to Fleet s account Now we can draW T accounts for both Fleet and Citibank FLEET Assets I Liabilities Reserves 100 l Checkable Deposits 100 CITIBANK Assets Liabilities Reserves 100 Checkable Deposits 100 Thus When a bank receives additional deposits it gains an equal amount of reserves And When a bank loses deposits it loses an equal amount of reserves 23 Example 3 Consider Fleet Bank s situation after it receives 100 in checkable deposits and hence 100 in additional reserves By laW Fleet must hold 10 or 10 as required reserves The remaining 90 is excess reserves FLEET Assets Liabilities Required Reserves 10 Checkable Deposits 100 Excess Reserves 90 Since reserves pay no interest and since Fleet is not required to hold excess reserves it may decide to use the 90 to make a new loan to one of its other customers FLEET Assets Liabilities Required Reserves 10 Checkable Deposits 100 Loans 90 lf Fleet charges a 10 interest rate on this loan its revenues increase by 90X10 or 9 lf Fleet pays only 5 on its checking account balances its costs increase by 100X5 or Hence Fleet makes a pro t from this process of asset transformation Strictly speaking however a fraction of the salaries paid to the bank s tellers who received the deposit and loan o icers who made the loan as well as a fraction of the costs of running the bank s branches must be subtracted from this pro t 3 General Principles of Bank Management A bank manager has four basic concerns Liquidity management 2 making sure that the bank has enough cash to cover depos itors requests for withdrawals deposit out ows Asset management 2 acquiring assets with the highest return and the lowest risk Liability management 2 acquiring funds at the lowest cost Capital adequacy management 2 maintaining su icient capital while still providing decent returns to shareholders 3 1 Liquidity Management To illustrate the basic principles of liquidity management let s consider two examples of how a bank can cope with deposit out ows 311 Example 1 Suppose that the required reserve ratio is 10 but that Fleet Bank holds some excess reserves as well Fleet s balance sheet is FLEET Assets Liabilities Reserves 20 Checkable Deposits 100 Securities 10 Capital 10 Loans 80 Required reserves are 100X10 or 10 So Fleet has 10 in excess reserves Now suppose that Fleet experiences a deposit out ow either because one of its customers withdraws 10 or because one of its customers writes a check for 10 on his or her account We know from our previous analysis that as a result of this transaction Fleet loses 10 in deposits and 10 in reserves Fleet s balance sheet is now FLEET Assets Liabilities Reserves 10 Checkable Deposits 90 Securities 10 Capital 10 Loans 80 Required reserves are 90X10 or 9 So Fleet is still meeting its reserve requirement and in fact still has 1 in excess reserves This example shows that by holding excess reserves a bank can cope with a deposit out ow without changing any other part of its balance sheet 312 Example 2 Now suppose that the required reserve ratio is 10 but Fleet holds no excess reserves This time Fleet s balance sheet is FLEET Assets Liabilities Reserves 1 0 Checkable Deposits 1 00 Securities 10 Capital 10 Loans 90 Required reserves are 100X10 or 10 Hence excess reserves are 0 1f Fleet experiences a 10 deposit out ow it loses 10 in deposits and 10 in reserves Now it s balance sheet is FLEET Assets Liabilities Reserves 0 Checkable Deposits 90 Securities 10 Capital 10 Loans 90 By laW Fleet must hold 90X10 or 9 in required reserves But right now it has no reserves at all Hence Fleet s manager must take action to obtain 9 in reserves Fleet has three options Option 1 Borrow reserves as a discount loan from the Federal Reserve borrow from another bank in the federal funds market or borrow from a non bank corporation by entering into a repurchase agreement In this case Fleet s balance sheet becomes FLEET Assets Liabilities Reserves 9 Checkable Deposits 90 Securities 10 Borrowings 9 Loans 90 Capital 10 The cost of choosing this option is the interest rate on the borrowing Option 2 Sell securities 1n this case Fleet s balance sheet becomes FLEET Assets I Liabilities Reserves 9 Checkable Deposits 90 Securities 1 Capital Loans 90 The cost of choosing this option is the brokerage cost of selling securities Also the bank no longer gets the interest paid by the securities it sold Option 3 Reduce its loans 1n this case Fleet s balance sheet becomes FLEET Assets Liabilities Reserves 9 Checkable Deposits 90 Securities 10 Capital 10 Loans 81 This third option may be the most costly of all since it might antagonize the bank s customers who want to borrow Also the bank no longer gets the interest that would have been paid by the borrower Comparing examples 1 and 2 illustrates why a bank might hold some excess reserves even though reserves do not pay interest 1f the bank does not hold excess reserves it must meet deposit out ows by borrowing selling securities or reducing its loans All of these options are costly excess reserves provide insurance against these costs 32 Asset Management The bank must hold a mix of assets that provides the highest return with the lowest risk Thus asset management involves four basic principles 4 Finding borrowers who will pay high interest rates but who are unlikely to default Finding securities with high returns and low risk 93M Diversifying the bank s asset holdings to minimize risk holding many types of securities and making many types of loans offers protection when there are losses in one type of security or one type of loan t Holding some liquid assets including excess reserves and US Treasury bills sec ondary reserves to protect against deposit out ows even though the interest rate on these assets may be lower 33 Liability Management Checkable deposits are a bank s lowest cost source of funds But checkable deposits are unlikely to provide a bank with all of the funds that it needs Thus the bank may obtain additional funds at higher costs by issuing CDs or by borrowing from other banks federal funds or non bank corporations repurchase agreements 34 Capital Adequacy Management Recall once again that Capital 2 Assets Liabilities 2 Net Worth To understand the role played by bank capital consider two more examples 341 Example 1 Consider two banks one with high capital and the other with low capital Their balance sheets look like this HIGH CAPITAL BANK Assets Liabilities Reserves 10 Checkable Deposits 90 Loans 90 Capital 1 12 LOW CAPITAL BANK Assets Liabilities Reserves 10 Checkable Deposits 96 Loans 90 Capital 4 Now suppose that both of these banks have made 5 loans to a company that goes bankrupt The value of loans at both banks falls by 5 And since the value of their liabilities remains unchanged both banks also lose 5 in capital HIGH CAPITAL BANK Assets Liabilities Reserves 10 Checkable Deposits 90 Loans 85 Capital 5 LOW CAPITAL BANK Assets Liabilities Reserves 10 Checkable Deposits 96 Loans 85 Capital 1 The high capital bank still has positive net worth But the low capital bank is insolvent bankrupt This example shows how capital serves as a cushion against a drop in the value of the bank s assets 342 Example 2 1f capital is a cushion against a drop in the value of the bank s assets then why don t all banks have high capital To answer this question let s consider the high capital bank again before the 5 loan went bad HIGH CAPITAL BANK Assets Liabilities Reserves 10 Checkable Deposits 90 Loans 90 Capital 10 Suppose next that this bank receives 6 in new deposits but instead of holding the 6 as additional excess reserves loaning the money out or buying securities the bank decides to pay the 6 out as an extra dividend to its shareholders Now the bank s balance sheet is HIGH CAPITAL BANK Assets Liabilities Reserves 1 0 Checkable Deposits 96 Loans 90 Capital 4 This example shows that by lowering its level of capital the bank can pay more dividends to its shareholders Thus the bank faces a trade off By maintaining more capital it protects itself against a decline in the value of its assets But by maintaining less capital it can pay more dividends and thereby provide its shareholders with a better return on their investment 4 Conclusion By looking at a bank s balance sheet we can see how banks are involved in the process of asset transformation they sell liabilities with one set of characteristics and use the proceeds to acquire assets with a different set of characteristics By engaging in asset transformation the bank hopes to pro t by charging a higher interest rate on its assets than it must pay on its liabilities Thus a bank manager must be concerned with both asset management acquiring assets with the highest return and the lowest risk and liability management acquiring funds at the lowest cost But a bank manager has to additional concerns as well Liquidity management 2 making sure that the bank has enough cash to cover deposit out ows hold some excess reserves even though they do not pay interest Capital adequacy management 2 maintaining su icient capital as a cushion against a decline in the value of the bank s assets While still providing a decent return to the bank s shareholders