货币银行学(2)

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 i

2、nterest 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 y

3、ears$100 X (1 + ) niniCopyright 2010 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$100n10

4、0/(1+i)100/(1+i)2100/(1+i)nCannot directly compare 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-Wesle

5、y. All rights reserved.4-7Yield to Maturity The interest 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 = $11

6、0 = number of years = 1$110$100 = (1 + )(1 + ) $100 = $110$110(1 + ) = $100 = 0.10 = 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

7、life of the loanLV = loan valueFP = fixed yearly payment = number of years until maturityFPFPFPFPLV = . . . +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 = yea

8、rly coupon paymentF = face value of the bond = years to maturity dateCCCCFP = . . . +1+(1+ )(1+ )(1+ )(1nniiii Copyright 2010 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

9、 the yield to maturity are negatively related The yield to maturity is greater than the coupon rate when the bond price is below 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.4-1

10、2Consol or Perpetuity A bond with no maturity date that does not repay principal but pays fixed coupon payments foreverconsol theofmaturity toyieldpaymentinterest yearly consol theof price/ccPCi/: thisasequation above rewritecan For coupon bonds, this equation gives the current yield, an easy to cal

11、culate approximation to the yield to maturityCopyright 2010 Pearson Addison-Wesley. All rights reserved.4-13Discount Bond 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 d

12、ivided by the initial price.As with a coupon bond, the yield to maturity is negatively related to the current bond price.Copyright 2010 Pearson Addison-Wesley. All rights reserved.4-14Rate of Return The payments to the owner plus the change in valueexpressed as a fraction of the purchase priceRET =

13、CPt + Pt Copyright 2010 Pearson Addison-Wesley. All rights reserved.4-15Rate 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 t

14、ime to maturity is longer than the holding period 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.4-16Rate of Return and Interest Rates (contd) The more distant a

15、bonds maturity, the lower the rate of return the occurs 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.4-17Table 2 One-Year Returns on

16、 Different-Maturity 10%-Coupon-Rate Bonds When Interest Rates Rise from 10% to 20%Copyright 2010 Pearson Addison-Wesley. All rights reserved.4-18Interest-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 w

17、hose time to maturity matches the holding periodCopyright 2010 Pearson Addison-Wesley. All rights reserved.4-19Real 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 b

18、orrowing Ex ante real interest rate is adjusted for expected 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.4-20Fisher Equation = nominal interest rate = real interest rate = expected inflation rateWhen the real interest rate is low,there are greater incentives to borrow and fewer incentives to lend.The real intererreiiii Co