1、10-1CHAPTER 10THE LEVEL AND STRUCTUREOF INTEREST RATESTHEORY OF INTEREST RATESInterest is simply the price paid by a borrower to a lender for the use of funds during some interval. But there are two primary competing theories that determine the basic interest rate level: Fishers theory, which underl
2、ies the loanable funds theory, and Keynes liquidity preference theory. Fisher Classical ApproachClassical theory sees the interest rate as the interaction of supply and demand for savings. Supply is a function of time preference (whether to consume income now or a larger amount later), income (the h
3、igher the income the more funds saved), and the reward for saving in the form of higher interest rates. Demand for savings arises from the production function. As long as the marginal rate of return on an investment exceeds the cost of funds there will be a demand for more investment i.e. borrowing.
4、 The equilibrium rate of interest is then where supply equals demand. Under classical theory this rate did not change much in the short term, only in the long term on the basis of changes in the propensity to save and technological developments. The nominal (published) rate of interest equals the re
5、al rate plus an adjustment for inflation, which is justified to compensate the lender for loss of purchasing power.Decisions on saving and borrowing: Saving is the choice between current and future consumption of goods and services. There are several influences on savings: (1) marginal rate of time
6、preference, (2) income, (3) reward for saving. An important influence on the borrowing decision is the gain from investment. The gain from additional projects, as investments increase, is the marginal productivity of capital, which is negatively related to the amount of investment. Equilibrium in th
7、e market: The equilibrium rate of interest is determined by interaction of the supply and demand function. As a cost of borrowing and a reward for lending, the rate must reach the point where total supply of savings equals total demand for borrowing and investment. Real rate and nominal rate: There
8、is a distinction between the nominal rate of interest and the real rate of interest. The relationship between inflation and interest rate is set forth in Fishers Law: (1 + i) = (1 + r) x (1 + P) where i = nominal rate, r = real rate, and P = expected percentage change in the price level of goods and
9、 services. This equation is approximated as: i = r + P. Loanable Funds TheoryFishers theory does not consider the possibility that individuals and firms might invest in cash balances. Expanding Fishers theory to encompass these situations produces the loanable funds theory of interest rates. This th
10、eory proposes that the general level of interest rate is determined 10-2by the complex interactions of two forces: (1) the total demand for funds by firms, governments and households; (2) the total supply of funds by firms, governments, banks, and households. The intersection of the supply and deman
11、d functions sets the interest rate level and the level of loans. Liquidity Preference TheoryKeynes saw the equilibrium rate of interest as being where the demand for holding money equaled the supply of money. The later was controlled by the Fed, whereas the former was a function of income and intere
12、st rates themselves. Increases in income will create a greater demand for holding money. Likewise, at a low rate of interest, savers prefer to hold cash rather than invest in bonds, since they expect prices to decline in the near future.Demand, supply and equilibrium: The public holds money for seve
13、ral reasons: ease of transaction, precaution against unexpected events, and speculation about possible rises in the interest rate. Although money pays no interest, the demand for money is a negative function of the interest rate. For Keynes, the supply of money is fully under the control of the cent
14、ral bank. Moreover, the money supply is not affected by the level of the interest rate. Shifts in the rate of interest: The equilibrium rate of interest can change if there is a change in any variable affecting the demand or supply curves. On the demand side, Keynes recognized the importance of two
15、variables: (1) level of income, (2) level of prices for goods and services. Changes in the Money Supply and Interest Rates A change in the money supply has three different effects upon the level of the interest rate: (1) the liquidity effect, (2) the income effect, and (3) the price expectations eff
16、ect. Liquidity effect: When money supplied is more than that demanded, individuals will buy bonds, thereby pushing up prices and lowering yields;Income effect: The increased investment generates more income, and thereby a desire to hold more money, thus creating an upward pressure on yields;Price ex
17、pectations effect: If more money is supplied than demanded, and the economy is near full-employment, then inflationary price expectations will play a role driving up yields. There is no general guide to the relative size of the price expectations effect: it may be great enough to overwhelm the liqui
18、dity effect, or it may cancel only part of it. The magnitude of the income effect depends upon how much of the economys productive capacity it is utilizing when the money supply rises. In the U.S. economy, the price expectations effect was dominant in 1970s. However, during 1990s, this effect is ins
19、ignificant.10-3DETERMINANTS OF THE STRUCTURE OF INTEREST RATESFeatures of a BondThe term to maturity of a bond is the number of years during which the issuer has promised to meet the obligations. The maturity of a bond refers to the day the debt will cease to exist. The principal value of a bond is
20、the amount that the issuer agreed to repay at maturity. This amount is also called the par value, maturity value, redemption value, or face value. The coupon rate is the interest rate that the issuer agrees to pay each year. Yield on a BondBy bond yield is meant the interest and changes in price ove
21、r a stated period (usually annually) divided by purchase price. Yield to maturity (YTM) refers to annual income should the bond be held to maturity. This yield is consistent with the internal rate of return. The formula to calculate the yield to maturity is: P = C / (1 + y)1 + C / (1 + y)2 + . . . +
22、 (C + M) / (1 + y)Nwhere P = market price of the bond C = coupon payment M = principal N = time to maturity If at purchase the market price equals par, the YTM is the coupon rate. If market price is less than par, the YTM is greater than the coupon rate, and if market price is greater than par, the
23、YTM is less than the coupon.Some bonds pay annual coupon. Bonds in the US, however, pay semiannual coupon. To annualize the semiannual yield, the convention adopted in the bond market is to double the semiannual yield. The resulting yield is the bond-equivalent yield basis. The difference between th
24、e yields on any two bond issues is called a yield spread. Base Interest RateTreasury securities are backed by the full faith and credit of the US government. Thus, they are considered risk free. There are two categorizes of the US Treasury securities: (1) discount securities, and (2) coupon securiti
25、es. Discount securities pay only a contractually fixed amount at maturity. The most recently auctioned Treasury issues for each maturity are called on-the-run or current coupon issues. Issues auctioned before the current coupon issues are called off-the-run issues. The minimum interest rate or base
26、interest rate demanded by investors for non-Treasury securities is the yield offered on a comparable maturity on-the-run Treasury. The base interest rate is also called the benchmark interest rate. 10-4Risk PremiumThe interest offered on a non-US treasury security is the base rate plus a spread (ris
27、k premium).Interest Rate on Non-Treasury = Base Rate + Risk Premium Base Rate = Real Rate of Interest + Expected Rate of Inflation The base rate consists of the real rate expected inflation-rate with the introduction of TIPS, the yield on TIPS can be used as an estimate of the real rate of interest.
28、 In regard to the spread, these spreads must be interpreted relative to the benchmark interest rate used. This risk premium over and above the base rate depends upon several factors:Type of issuers: The bond market is classified by the type of issuer, and groups of securities of various kinds of iss
29、uers are referred to as market sectors. The spread between the interest rates offered in two sectors of the bond market is referred to as intermarket sector spread. The spread between two issuers within a market sector is called the intramarket sector spread. Perceived creditworthiness of issuer: De
30、fault risk refers to the risk that the issuer of a bond may be unable to meet its credit obligations. Bonds are typically rated by rating agencies. High grade means low risk. There is also medium grade, and high yield bonds. Bonds are classified into two categories: investment grade and noninvestmen
31、t grade. Term to maturity: The spread between any two maturity sectors of the market is called the maturity spread, or yield curve spread. The relationship between the yields on comparable securities but different maturities is called the term structure of interest rates. Inclusion of options: Bonds
32、 may have embedded options. Bonds can have call or put provisions, and may be convertible.Typically, the coupon on bonds is taxable income. Municipal bonds, however, are tax exempt. The yield that must be offered on a taxable bond issue to give the same after-tax yield as a tax-exempt issue is calle
33、d the equivalent taxable yield. Typically, the coupon on bonds is taxable income. Municipal bonds, however, are tax exempt. The yield that must be offered on a taxable bond issue to give the same after-tax yield as a tax-exempt issue is called the equivalent taxable yield.Expected liquidity of an is
34、sue: Bonds trade with different degrees of liquidity. The greater the expected liquidity, the lower is the yield. An important factor that affects the liquidity of an issue is the size of the issue. Swap Rate Yield Curve An interest rate swap is where a party swaps a floating rate for a fixed rate i
35、nterest payment. The fixed interest rate is called the swap rate. The relationship between the swap rate and maturity of a swap is the swap rate yield curve, also called the swap curve or LIBOR curve. 10-5There are several advantages of using a swap curve over a countrys government securities yield
36、curve. First, there may be technical reasons why within a government bond market some of the interest rates may not be representative of the true interest rate, but is instead biased by some technical or regulatory factors unique to that market. Second, a large number of maturities must be available
37、 to create a yield curve, and some government issues may have this feature. Lastly, the ability to compare government yields across countries is difficult because there are differences in the credit risk for every country.10-6ANSWERS TO QUESTIONS FOR CHAPTER 10(Questions are in bold print followed b
38、y answers.)1. Explain what these terms mean in Fishers theory of interest rates:a. marginal rate of time preferenceb. marginal productivity of capitalc. equilibrium interest ratea. The marginal rate of time preference refers to the preference for current over future consumption. Should that rate dec
39、line then savings will increase.b. The marginal productivity of capital is the return to additional investment. Should that rate go up, then the demand for investment capital increases.c. The equilibrium rate of interest is where the supply of savings curve intersects the demand for investments curv
40、e. It is the rate that “clears the market” or the point around which the rate of interest vacillates.2.a. How does the loanable funds theory expand Fishers theory of interest rate determination?b. How does a change in the governments deficit affect the equilibrium rate in the loanable funds theory?a
41、. The loanable funds theory takes into consideration the changes in the money supply as well as all sectors of the economy that supply savings and that have a demand to borrow funds (households, business, and government).b. An increase in the government deficit would have to be funded by additional
42、borrowing. So the government demand for loanable funds would drive up the interest rate. A decrease in the deficit would have the opposite effect.3.a. How do the assets, money, and bonds differ in Keyness liquidity preference theory?b. How does a change in income affect the equilibrium level of the
43、interest rate in Keyness theory?c. How does a change in the money supply affect that rate?a. Money (as demand deposits and cash) is considered the liquid asset that serves as a medium of exchange and a store of value. Such funds pay little or no interest. Bonds are not as liquid and do pay some inte
44、rest.b. In Keynesian theory, the rate of interest is determined by the demand to hold money (liquidity preference) and the money supply. An increase in income will lead to an increase in the demand for transactions purposes; hence an increase in the equilibrium rate of interest.c. An increase in the
45、 money supply will initially create a situation where more money exists than public wish to hold. They will then use these excess funds for investments, driving down interest rates.10-74.a. Explain these terms: the liquidity effect; the income effect; and the price expectations effect.b. How is it d
46、etermined which of these three effects on interest rates an increase in the money supply will have?a. The initial effect of an increase in the money supply is an increase in liquidity, which individuals will invest, thereby driving down interest rates. As incomes rise, however, the demand to hold mo
47、ney for transactions purposes will also go up, thereby raising the rate of interest. If the economy is near to the full employment, price expectations will take effect and the rate of interest will rise to reflect a higher premium for inflation.b. The level of economic activity or stage of business
48、cycle. If the economy is near full employment, price expectations effect would weigh stronger. However, in the U.S., in most recent years of late 1990s, productivity gains have lowered the role of price effect.5. Consider three bonds, all with a par value of $1,000:Bond Coupon Rate Market PriceA 8%
49、$1,100B 7 900C 9 1,000a. What is the yield to maturity of bond C?b. Is the yield to maturity of bond A greater than or less than 8%?c. Is the yield to maturity of bond B greater than or less than 9%?a. The yield to maturity of bond C is 9% because its market price is equal to the par value.b. The yield to maturity of bond A is less than 8% since it is selling at a premium over par. An investor will get the 8% coupon payments but only $1000 at maturity, less than the $1100 he had paid for it.c. Since bond B is selling at a discount, its yield is greater than the coupon rate, bu
