货币金融学课件：chap04 understanding interest rates

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1、Copyright 2010 Pearson Addison-Wesley.All rights reserved.Chapter 4Understanding Interest RatesCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-2Present Value A dollar paid to you one year from now is less valuable than a dollar paid to you today Why?A dollar deposited today can earn inte

2、rest and become$1 x(1+i)one year from today.Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-3Discounting the Future23Let =.10In one year$100 X(1+0.10)=$110 In two years$110 X(1+0.10)=$121or 100 X(1+0.10)In three years$121 X(1+0.10)=$133or 100 X(1+0.10)In years$100 X(1+)niniCopyright 2010

3、 Pearson Addison-Wesley.All rights reserved.4-4Simple Present ValuenPV=todays(present)valueCF=future cash flow(payment)=the interest rateCFPV=(1+)iiCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-5Time Line$100$100Year01PV1002$100$100n100/(1+i)100/(1+i)2100/(1+i)nCannot directly compare

4、payments scheduled in different points in the time lineCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-6Four Types of Credit Market Instruments Simple Loan Fixed Payment Loan Coupon Bond Discount BondCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-7Yield to Maturity The inter

5、est rate that equates the present value of cash flow payments received from a debt instrument with its value todayCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-8Simple Loan1PV=amount borrowed=$100CF=cash flow in one year=$110=number of years=1$110$100=(1+)(1+)$100=$110$110(1+)=$100=0.1

6、0=10%For simple loans,the simple interest rate equniiiials theyield to maturityCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-9Fixed Payment Loan23The same cash flow payment every period throughout the life of the loanLV=loan valueFP=fixed yearly payment=number of years until maturityFP

7、FPFPFPLV=.+1+(1+)(1+)(1+)nniiiiCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-10Coupon Bond23Using the same strategy used for the fixed-payment loan:P=price of coupon bondC=yearly coupon paymentF=face value of the bond=years to maturity dateCCCCFP=.+1+(1+)(1+)(1+)(1nniiii+)niCopyright 2

8、010 Pearson Addison-Wesley.All rights reserved.4-11 When the coupon bond is priced at its face value,the yield to maturity equals the coupon rate The price of a coupon bond and the yield to maturity are negatively related The yield to maturity is greater than the coupon rate when the bond price is b

9、elow its face valueTable 1 Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years(Face Value=$1,000)Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-12Consol or Perpetuity A bond with no maturity date that does not repay principal but pays fixed coupon payments foreverconsol t

10、heofmaturity toyieldpaymentinterest yearly consol theof price/ccciCPiCPccPCi/:thisasequation above rewritecan For coupon bonds,this equation gives the current yield,an easy to calculate approximation to the yield to maturityCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-13Discount Bond

11、For any one year discount bondi=F-PPF=Face value of the discount bondP=current price of the discount bondThe yield to maturity equals the increasein price over the year divided by the initial price.As with a coupon bond,the yield to maturity is negatively related to the current bond price.Copyright

12、2010 Pearson Addison-Wesley.All rights reserved.4-14 2006 Pearson Addison-Wesley.All rights reserved1-14Other Measures of Interest RatesCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-15 2006 Pearson Addison-Wesley.All rights reserved1-15Current Yield、C ic=P Two Characteristics Is better

13、 approximation to yield to maturity,nearer price is to par and longer is maturity of bond Change in current yield always signals change in same direction as yield to maturityCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-16 2006 Pearson Addison-Wesley.All rights reserved1-16Yield on a D

14、iscount Basis (F P)360idb =x F (number of days to maturity)One year bill,P =$900,F=$1000$1000$900 360idb=x =0.099=9.9%$1000 365 Understates yield to maturity;longer the maturity,greater is understatement Change in discount yield always signals change in same direction as yield to maturityCopyright 2

15、010 Pearson Addison-Wesley.All rights reserved.4-17 2006 Pearson Addison-Wesley.All rights reserved1-17Bond Page of the NewspaperCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-18Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-19Rate of Return The payments to the owner plus t

16、he change in valueexpressed as a fraction of the purchase priceRET=CPt+Pt1-PtPtRET=return from holding the bond from time t to time t+1Pt=price of bond at time tPt1=price of the bond at time t+1C=coupon payment CPt =current yield=ic Pt1-PtPt=rate of capital gain=gCopyright 2010 Pearson Addison-Wesle

17、y.All rights reserved.4-20Rate of Return and Interest Rates The return equals the yield to maturity only if the holding period equals the time to maturity A rise in interest rates is associated with a fall in bond prices,resulting in a capital loss if time to maturity is longer than the holding peri

18、od The more distant a bonds maturity,the greater the size of the percentage price change associated with an interest-rate changeCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-21Rate of Return and Interest Rates(contd)The more distant a bonds maturity,the lower the rate of return the occ

19、urs as a result of an increase in the interest rate Even if a bond has a substantial initial interest rate,its return can be negative if interest rates rise Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-22Table 2 One-Year Returns on Different-Maturity 10%-Coupon-Rate Bonds When Interes

20、t Rates Rise from 10%to 20%Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-23Interest-Rate Risk Prices and returns for long-term bonds are more volatile than those for shorter-term bonds There is no interest-rate risk for any bond whose time to maturity matches the holding periodCopyrigh

21、t 2010 Pearson Addison-Wesley.All rights reserved.4-24Real and Nominal Interest Rates Nominal interest rate makes no allowance for inflation Real interest rate is adjusted for changes in price level so it more accurately reflects the cost of borrowing Ex ante real interest rate is adjusted for expec

22、ted changes in the price level Ex post real interest rate is adjusted for actual changes in the price levelCopyright 2010 Pearson Addison-Wesley.All rights reserved.4-25Fisher Equation=nominal interest rate=real interest rate=expected inflation rateWhen the real interest rate is low,there are greate

23、r incentives to borrow and fewer incentives to lend.The real intererreiiiiest rate is a better indicator of the incentives toborrow and lend.Copyright 2010 Pearson Addison-Wesley.All rights reserved.4-26FIGURE 1 Real and Nominal Interest Rates(Three-Month Treasury Bill),19532008Sources:Nominal rates

24、 from www.federalreserve.gov/releases/H15.The real rate is constructed using the procedure outlined in Frederic S.Mishkin,“The Real Interest Rate:An Empirical Investigation,”Carnegie-Rochester Conference Series on Public Policy 15(1981):151200.This procedure involves estimating expected inflation as a function of past interest rates,inflation,and time trends and then subtracting the expected inflation measure from the nominal interest rate.