What Do Interest Rates Mean and What Is Their Role in Valuation? Dagmar Linnertová Measuring Interest Rates nDifferent debt instruments have very different streams of cash payments to the holders qCash flows nWith very different timing qThus, it is important to understand nHow we can compare the value of one kind of debt instrument with another before we see how interest rates are measured. qConcept of present value Present value nIt is base on simple idea qDollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. nThis is true because you can deposit a dollar in a saving account that earns interest and have more than dollar in one year. § § Present value qSimple loan nIn this loan, the lender provides the borrower with an amount of funds (principal) that must be repaid to the lender at the maturity date, along with an additional payment for the interest. §At the end of on n year, your 100 $ would turn into: § q qThe amounts you would have at the end of each year by making the 100 $ loan today can be seen in the following time line: Present value nThis time line tells you that qfor you is 100 in today equal as 110 in year 1 and equal as 121 in year 2, etc. n The process of calculation today’s value of dollars received in the future is called discounting of future: Present value nThe concept of present value is extremely useful because qYou are able to figure out today’s value of credit market instrument at a given simple interest rate i by adding up the present value of all the future cash flows received. qThe concept of present value allows you to compare the value of two instruments with very different timing of their cash flows. q Four Types of Credit Market Instruments nA simple loan qIn which lender provides the borrower with an amount of funds, which must be repaid to the lender at the maturity date along with an additional payments for the interest. qMoney markets instruments nCommercial loans to businesses n q n q Four Types of Credit Market Instruments nA fixed-payment loan (fully amortized loan) qThe lender provides the borrower with an amount of funds, which must be repaid by making the same payment every period (such a month), consisting of part of the principal and interest for a set of year. qMoney markets instruments nInstallment loans (such a auto loans) and mortgages q n Four Types of Credit Market Instruments nA coupon bond qIt pays the owner of the bond a fixed interest payment (coupon payment) every year until the maturity date when a specified final amount (face value) is repaid qThe coupon payment is so named because the bondholder used to obtain payment by clipping a coupon off the bond and sending it to the bond issuer who then sent the payment to the holder 486-269 Four Types of Credit Market Instruments nA coupon bond is identified by three pieces of information. nCorporation or government agency that issues bond nMaturity date of the bond nThe bond’s coupon rate expressed as a percentage of the face value of the bond qMoney markets instruments qTreasury bonds, corporate bonds Four Types of Credit Market Instruments nA discount bond (zero-coupon bond) qIt is bought at a price below its face value (at a discount) and the face value is repaid at the maturity date. qA discount bond does not make any interest payments, it just pays off the face value n Four Types of Credit Market Instruments nThese four types of instruments require payments at different times: qSimple loans and discount bonds make payment only at their maturity dates qPayments loans and coupon bonds have payments periodically until maturity Four Types of Credit Market Instruments nHow would you decide which of these instruments provides you with more income? qThey all seem so different because they make payments at different times. qTo solve this problem it is necessary to use the concept of present value. Yield to Maturity nThe most important way how to calculate interest rate qYield to maturity nThe interest equates the present value of cash flows received from a debt instrument qThis concept is considered to be one of the msot accurate measure of interest rates q Fixed-Payment loan nThis type of loan has the same cash flow payment every year throughout the life of the loan. nOn a fixed-rate mortgage, for example, the borrower makes the same payment to the bank every month until the maturity date, when the loan is completely paid off. nIt is necessary to equate today’s value of the loan with its present value. nBecause the fixed-payment loan involves more than one cash payment, the present value of the fixed-payment loan is calculated as the sum of the present values of all cash flows. Coupon Bond nThe calculate the yield to maturity for a coupon bond, follow the same strategy used for fixed-payment loan: qEquate today’s value of the bond with its present value. qBecause coupon bonds also have more than one cash flow payment, the present value of the bond is calculated as the sum of the present values of all the coupon payments plus the present value of the final payment of the face value of the bond. Coupon Bond nFor any coupon bond q Coupon Bond Coupon Bond n1. When the coupon bond is priced at its face value, the yield to maturity equals to coupon rate, n2. The price of coupon bond and the yield to maturity are negatively related, that is, as the yield to maturity rises, the price of the bond falls. If the yield to maturity falls, the price of the bond rises. n3. The yield to maturity is greater than the coupon rate when the bond price is below its face value. Perpetuity or consol nThere is one special case of a coupon bond that is worth discussing because its yield to maturity is particularly easy to calculate. nThis bond is called a perpetuity or a consol. qIt is a perpetual bond without any maturity and repayment of principal that makes fixed coupon payments of X $ forever. Perpetuity or consol nThe price of a perpetuity is simplifies to following: Perpetuity or consol Discount Bond nThe yield-to-maturity calculation for a discount bond is similar to that for the simple loan. nGenerally, for any one-year discount bond, the yield to maturity can be written as: Case of Japan nNormally interest rates must be always positive nNegative interest rates would imply that you are willing to pay more for a bond today than you will receive for it in the future nNegative interest rates therefore seem like an impossible because you would do better by holding cash that the same values in the future as it does today nIn November 1998, Japan, interest rate of Japanese six-months T-bills became negative, yielding an interest rate -0,004 %, with investors paying more for the bills than their face value. qWeakness of Japanse economy and a negative inflation rate have driven Japanese interest rate to low levels, but they can explain the negative rates nThe answer is that large investors find it more convenient to hold these six-months bills as a store of value rather than holding cash because the bills are denominated in large amounts and can be stored electronically. nThese advantages of the Japanese T-bills result in some investors being willing to hold them, given their negative rates, even though in monetary terms the investors would be better off holding cash. nClearly, the convenience of T-bills only goes so far and thus their interest rates can go only a little bit bellow zero. The Distinction Between Real and Nominal Interest Rates nSo far we have ignored the effects of inflation on the cost of borrowing. nReal vs. nominal interest rate nReal interest rate qAdjusted by expected changes in the price level nReflects the true cost of borrowing nEx ante interest rate qIt is adjusted for expected changes in the price level q“real” interest rate The Distinction Between Real and Nominal Interest Rates nFisher equation q q q qStates that the nominal interest rate is equal the real interest rate + the expected rate of inflation qWhen the real interest rate is low, there are greater incentives to borrow and fewer incentives to lend. qThe distinction between real and nominal interest rates is important because the real interest rate, which reflects the real cost of borrowing, is likely to be a better indicator of the incentives to borrow and lend. qIt is appear to be a better guide to how people will be affected by what is happening in credit markets. The Distinction Between Real and Nominal Interest Rates The Distinction Between Real and Nominal Interest Rates nU.S. Treasury bill, shows that nominal and real interest rates often do not move together. nIn particular qNominal rates were high in the 1970’s nReal rates were extremely low, often negative qBy the standard of nominal interest rates, you would thought that credit market conditions were tight in this period because it was expensive to borrow. qThe estimation of the real rates indicate that you would have been mistaken. In real terms, the cost of borrowing was actually quite low. n The Distinction Between Interest Rate and Returns n The Distinction Between Interest Rate and Returns The Distinction Between Interest Rate and Returns nTable calculates the one-year return on several 10% coupon rate bonds when interest rates on all these bonds rise from 10% to 20%. qThe only bond whose return equals the initial yield to maturity is one whose time to maturity is the same as the holding period qA rise in interest rates is associated with a fall in bond prices, resulting in capital losses on bond whose terms to maturity are longer than the holding period qThe more distant a bond’s maturity, the greater the size of the price change associated with an interest-rate change qThe more distant a bond’s maturity, the lower the rate of return that occurs as a result of the increase in the interest rate qEven though a bond has a substantial initial; interest rate, its return can turn out to be negative if interest rates rise The Distinction Between Interest Rate and Returns nA rise in the interest rate means that the price of a bond has fallen. nA rise in interest rates therefore means that a capital loss has occurred, and if this loss is large enough, the bond can be a poor investment indeed. Maturity and the Volatility of Bond Returns: Interest-rate Risk nThe findings that the price of longer-maturity bonds respond more dramatically to changes in interest rates helps explain an important fact about the behavior of bond markets: qPrice and returns for long-term bonds are more volatile than those for shorter-term bonds. n Maturity and the Volatility of Bond Returns: Interest-rate Risk nThe riskiness of an asset’s return that results from interest-rate changes qIs called interest-rate risk nAlthough long-term debt instruments have substantial interest-rate risk, short-term debt instruments do not. qBonds with a maturity that is as short as the holding period have no interest-rate risk. Summary nThe return on a bond, which tell you how good an investment it has been over the holding period, is equal to the yield to maturity in only one case: qWhen the holding period and the maturity of the bond are identical nBonds whose term to maturity is longer than the holding period are subject to interest-rate risk: qChanges in interest rates lead to capital gains and losses that produce differences between the return and the yield to maturity known as the time the bond is purchased. qInterest-rate risk is especially important for long-term bonds, where capital gains and losses can be substantial. nThis is why long-term bonds are not considered to be safe assets with a sure return over short holding periods.