货币金融学(全英)Charpter4

1、UnderstandingInterest Rateschapter 4Copyright 2003 Addison WesleyTM 4- 2Key points 1. yield to maturity 2. current yield 3. yield on a discount basis 4. return rateCopyright 2003 Addison WesleyTM 4- 34 types of credit instruments1. Simple loan（普通贷款）（普通贷款）In which the lender provides the borrower wit

2、h an amount of funds, which must be repaid to the lender at the maturity date along with an additional payment for the interest.2.Fixed-payment loan（ 固定支付贷款）（固定支付贷款）（full amortized loan分期偿还债务）分期偿还债务）In which the lender provides the borrower with an amount of funds, which must be repaid by making the

3、 same payment every period.Copyright 2003 Addison WesleyTM 4- 4 3. Coupon bond（息票债券）（息票债券） In which pays the owner of the bond a fixed interest payment every year until the maturity date, when a specified final amount is repaid. Coupon rate: the dollar amount of the yearly coupon payment expressed a

4、s a percentage of the face value of the bond. 4. Discount bond （zero-coupon bond零息债券）零息债券） Which is bought at a price below its face value, and the face value is repaid at the maturity date.Copyright 2003 Addison WesleyTM 4- 5Present ValueConcept of Present ValueSimple loan of $1 at 10% interestYear

5、123 n$110$121$133 $100 x(1 + i)n $1PV of future $1 = (1 + i)nCopyright 2003 Addison WesleyTM 4- 6Example What is the present value of $450 to be paid in 3 years if the interest rate is 20%? What is the present value of $250 to be paid in 2years if the interest rate is 15%?Copyright 2003 Addison Wesl

6、eyTM 4- 7Yield to Maturity: LoansYield to maturity = interest rate that equates todays value with present value of all future payments1. Simple Loan (i = 10%)$100 = $110/(1 + i) $110 $100 $10i = = 0.10 = 10%$100 $1002. Fixed Payment Loan (i = 12%) $126$126$126$126$1000 = + + + . + (1+i) (1+i)2 (1+i)

7、3 (1+i)25 FP FP FP FPLV = + + + . + (1+i) (1+i)2 (1+i)3 (1+i)nCopyright 2003 Addison WesleyTM 4- 8 1. if you take out a loan from a bank, you need pay $900 as the yearly payment to the bank for 15 years, how much you borrowed from the bank? (an interest rate of 5%) 2. you decide to purchase a new ho

8、use and need a $100,000 mortgage. You take out a loan from the bank that has an interest rate of 7%. What is the yearly payment to the bank to pay off the loan in twenty years?Copyright 2003 Addison WesleyTM 4- 9Yield to Maturity: Bonds4. Discount Bond (P = $900, F = $1000)$1000$900 =(1+i)$1000 $900

9、i = 0.111 = 11.1%$900F Pi =P3. Coupon Bond (Coupon rate = 10% = C/F)$100$100$100$100$1000P = + + + . + +(1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10C C C C FP = + + + . + +(1+i) (1+i)2 (1+i)3 (1+i)n (1+i)nConsol: Fixed coupon payments of $C foreverCCP = i =iPCopyright 2003 Addison WesleyTM 4- 10Relationship

10、Between Price and Yield to MaturityThree Interesting Facts in Table 11. When bond is at par, yield equals coupon rate2. Price and yield are negatively related3. Yield greater than coupon rate when bond price is below par valueCopyright 2003 Addison WesleyTM 4- 11Coupon bond Write the formula of calc

11、ulating the yield to maturity of a ten-year 8%coupon bond, face value is $3000, selling price is $2800. Find the price of a 10% coupon bond with a face value of $1000, a 12.25% yield to maturity, and eight years to maturity.Copyright 2003 Addison WesleyTM 4- 12Current Yield C ic = PTwo Characteristi

12、cs1. Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond2. Change in current yield always signals change in same direction as yield to maturityYield on a Discount Basis(F P)360idb = xF(number of days to maturity)One year bill, P = $900, F = $1000$1000

13、$900360idb = x=0.099 = 9.9%$10003651. Understates yield to maturity; longer the maturity, greater is understatement2. Change in discount yield always signals change in same direction as yield to maturityCopyright 2003 Addison WesleyTM 4- 13Bond Page of the NewspaperCopyright 2003 Addison WesleyTM 4-

14、 14Distinction Between Interest Rates and ReturnsRate of ReturnC + Pt+1 PtRET = ic + gPtCwhere: ic = = current yieldPtPt+1 Ptg = capital gainPtThe rate of return is defined as thepayments to the owner plus the change in its value, expressed as a fraction of its purchaseprice.Copyright 2003 Addison W

15、esleyTM 4- 15Key facts about RelationshipBetween Interest Rates and ReturnsCopyright 2003 Addison WesleyTM 4- 16Maturity and the Volatility of Bond ReturnsKey Findings from Table 21. Only bond whose return = yield is one with maturity = holding period2. For bonds with maturity holding period, i P im

16、plying capital loss3. Longer is maturity, greater is price change associated with interest rate change4. Longer is maturity, more return changes with change in interest rate5. Bond with high initial interest rate can still have negative return if i Conclusion from Table 2 Analysis1. Prices and retur

17、ns more volatile for long-term bonds because have higher interest-rate risk2. No interest-rate risk for any bond whose maturity equals holding periodCopyright 2003 Addison WesleyTM 4- 17Distinction Between Real and Nominal Interest RatesReal Interest RateInterest rate that is adjusted for expected changes in the price levelir = i e1. Real interest rate more acc