茲維博迪金融學(xué)第二版課件Chapter08

1、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall1Chapter 8 Contents 8.1 Using Present Value Formulas to Value Known Flows 8.2 The Basic Building Blocks: Pure Discount Bonds 8.3 Coupon Bonds, Current Yield, and Yield-to-Maturity 8.4 Reading Bond Listings 8.5 Why Yields for the same

2、Maturity Differ 8.6 The Behavior of Bond Prices Over Time第1頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall28.1 Using Present Value Formulas to Value Known Flows You have been offered the opportunity to purchase a mortgage. It was originally part of a creative financing packa

3、ge where the original owner financed the buyer The remaining life of the mortgage is 60 months, with payment of $400. Your required rate of return is 1.5% / month第2頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall3Calculation Using the present value of an annuity formula discu

4、ssed in chapter 4, you will pay no more than11.752,15$015. 111015. 040011160niipmtPV第3頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall4Financial Calculator Alternatively, using your financial calculator (remember to set the correct defaults) you obtainNIPVPMTFV601.5%?15,752.1

5、1-4000第4頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall5Change in Required Rate If your required rate of return increased to 1.6% / monthNIPVPMT FV60 1.6% ?15,354.66-400 0第5頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall6Using Present Value Formulas

6、to Value Known Flows Observe that the maximum you would pay for the bond has decreased An increase in the required rate of return always leads to a decrease in the value of a fixed income security The proof is very easy第6頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall7Bond P

7、rices Rise as the Interest Rates Fall Write the PV of the fixed income security as the sum termsnnnnnjjjipmtipmtipmtipmtipmtPV11*11*.11*11*11*1122111第7頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall8Bond Prices Rise as the Interest Rates Fall If i goes up, 1+i goes up, 1/(1+

8、i) goes down for i -1, (1/(1+i)j goes down for i 0. So if the payments are positive, then the sum must also go down Similarly, i down - PV up第8頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall9Bond Prices Rise as the Interest Rates Fall Basic principle in evaluating known flow

9、s A change in market interest rates causes a change in the opposite direction in the market values of all existing contracts promising fixed payments in the future第9頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall10Note Volatile market rates imply volatile market values第10頁/共

10、57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall11Finding the Correct Discount Rate Bond analysis is not as easy as this analysis appears to imply We need an interest rate to use in the formula We saw in Chapter 2 that interest rates are a function of time-to-maturity Two defaul

11、t-free bonds with identical maturities may have different YTMs第11頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall12Yield Curve A typical yield curve:第12頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall138.2 The Basics Building Blocks: Pure Discount Bond

12、s We can always analyze any fixed income contract into a sum of pure discount bonds A pure discount bond is a security that promises to pay a specified single cash payment (face value or par value) at a specified date called its maturity date第13頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing

13、 as Prentice Hall14Pure Discount Bonds Note There is no cash flow associated with interest Pure discount bonds are purchased at a discount from their face or par value第14頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall15Pure Discount Bonds The pure discount bond is an example

14、 of the present value of a lump sum equation we analyzed in Chapter 4 Solving this, the yield-to-maturity on a pure discount bond is given by the relationship:111nnPFiiPF第15頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall16Pure Discount Bonds111nnPFiiPF In this equation, P is

15、 the present value or price of the bond F is the face or future value n is the investment period i is the yield-to-maturity第16頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall17Pure Discount Bonds Example You can purchase a pure discount bond for $9,000, and it matures in two

16、years with a face value of $10,000 What is the ytm?第17頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall18Pure Discount Bonds%41. 519000100001211nPFiNIPVPMTFV2?5.41%9,0000-10,000第18頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall198.3 Coupon Bonds, Curre

17、nt Yield, and Yield to Maturity A coupon bond obligates the issuer to make periodic payments of interest (called coupon payments) to the bond holder until the bond matures at which time the face value of the bond is also paid to the bond holder and the contract is satisfied第19頁/共57頁Copyright 2009 Pe

18、arson Education, Inc. Publishing as Prentice Hall20Coupon Rate The coupon rate is the interest rate applied to the face value to compute the coupon payment A bond with a face value of $1,000 and a coupon rate of 10% pays an annual coupon of $100 At maturity, the payment is $1,000+$100第20頁/共57頁Copyri

19、ght 2009 Pearson Education, Inc. Publishing as Prentice Hall21Cash Flows for 10% $1,000 Coupon Bond第21頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall22Par, premium, and Discount Bonds A coupon bond with its current price equal to its par value is a par bond If it is trading

20、below par it is a discount bond If it is trading above par it is a premium bond (not to be confused with the U.K. lottery bond of the same name!)第22頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall23Bonds Trading at Par Bond Pricing Principle #1: (Par Bonds) If a bonds price e

21、quals its face value, then its yield-to-maturity = current yield = coupon rate. Proof:FipmtPiipmtiPFPiFiipmtPnnnn111111&11111第23頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall24Coupon Bonds, Current Yield, and Yield-to-Maturity The yield-to-maturity is the discount rate

22、that makes the present value of the cash flows from the bond equal to the current price of the bond An excellent way to compute the ytm is given in Chapter 4第24頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall25Using Pure Discount Bonds to Value other Bonds Value a bond that p

23、ays its $100 coupon at the end of each year for 3-years, and its par value of $1,000 in 3-years You have discovered three pure discount bonds (each with a $1,000 par value) that mature in 1, 2, and 3 years, and that are trading at $960, $890, and $810 respectively第25頁/共57頁Copyright 2009 Pearson Educ

24、ation, Inc. Publishing as Prentice Hall26First Solution Method00.1076$1001000100081010010008901001000960PP第26頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall27Second Solution Method91.075, 1$0728. 110010000600. 11000417. 1100%28. 71810000, 1%00. 61890000, 1%17. 41960000, 1323

25、13 , 0212, 0111 , 0PPiii第27頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall28Conclusion The first method uses the fact that a coupon bond is the sum of pure discount bonds it is fast and direct The second method first determines the yields-to-maturity of each discount bond ca

26、sh flows are then evaluated using them第28頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall29The YTM of the Coupon Bond We have the price of the coupon bond, and the timing and magnitude of its future cash flows, so we can determine its YTM We use the financial calculator, but

27、a numerical method was provided in chapter 4 for this class of problems第29頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall30The YTM of the Coupon BondNIPVPMTFV3?7.10%-1076 1001000第30頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall31Observation The yiel

28、d to maturity on the 3-year pure discount bond was 7.28% and the yield-to-maturity on the 3-year coupon bond was 7.10% The yield-curve for default-free bonds is not a unique value第31頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall32Bond Pricing Principle #2 & 3 Bond Princ

29、iple # 2: Premium Bondsbond price face value ytm current yield coupon rate Bond Principle # 3: Discount Bondsbond price current yield coupon rate第32頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall33Proof of Relationship between YTM and Current Yield For coupon bonds, we have

30、the following relationships Note the (sensible) restrictions on the variable ranges Note that 1/(1+i)n - 1) is always positive第33頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall3401111&11111110&0&0&11111nnnnnnippfippfpxfipixixniifiixp第34頁/共57頁Copyright 2009 Pe

31、arson Education, Inc. Publishing as Prentice Hall35Proof of Relationship between Current and Coupon Yields For coupon bonds, we have the following relationship derived from the bond formula Note that the differences between the reciprocals have the same sign, so the actual differences also have the

32、same sign Note that size relationship is determined by the discount factor which is always 1第35頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall36 ytm1yieldcoupon 1ytm1ytm1yieldcurrent 1111110&0&0&11111nfxnpxnniiixniifiixp第36頁/共57頁Copyright 2009 Pearson Education,

33、Inc. Publishing as Prentice Hall37How to Remember Principles Imagine that the bond was issued at par the yield-to-maturity moves from the coupon yield in the opposite direction to price the coupon rate is unchanging This diagram may help:第37頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as

34、Prentice Hall38Yield Relationships00.020.040.060.080.10.120.140.160.180.2600.00800.001000.001200.001400.001600.001800.00PriceYieldcoupon_ycurrent_yy_t_m第38頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall39High Yield T-Bond Funds Yield curves with large positive slopes make lo

35、nger-term T-bonds tempting because, like T-bills, they are default-free The above diagram was based on: par = $1000, coupon = $100, n = 10-years, flat Observe the large effect of modest changes in interest on capital A close up is given below第39頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing

36、 as Prentice Hall40Yield Relationships0.070.090.110.13800.001000.001200.00PriceYieldcoupon_ycurrent_yy_t_m第40頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall41Clarification The last example used a flat yield curve Let us look at an example with short-term rates remaining fixe

37、d longer-term rates rising on increased expectation of a general rise in interest rates第41頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall42Two Yield Curves (Pure Discount)0.00%1.00%2.00%3.00%4.00%5.00%6.00%7.00%8.00%9.00%05101520Years to MaturityYield to Maturiry第42頁/共57頁Cop

38、yright 2009 Pearson Education, Inc. Publishing as Prentice Hall43Investment Implications Assume a 20-year bond with a coupon rate of 6% Purchase for $1016.54 when the lower curve prevails When yield curve rises, the bond is worth only $814.05 This is a massive capital risk Additionally, long-term ra

39、tes are more volatile than short-term rates第43頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall448.4 Reading Bond Listings There are traditions for reporting yields and computing earned interest that need to be understood before trading Coupon bonds are often quoted in terms o

40、f the annual rate compounded semi-annually T-bills are often quoted on a discount basis e.g., a 1 year T-bill has 364 days outstanding, but a year has only 360 days(it gets nasty)第44頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall45Reading Bond Listings Take care that the fra

41、ctional part of a number is understood Is it 16ths, 32nds, 64ths, 100ths or some other convention? Ask price: dealers selling price Bid price: dealers buying price第45頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall468.5 Why Yields for the same Maturity Differ The fundamental

42、building block of bonds is the pure discount bond: Coupon bonds may be viewed as a portfolio of discount bonds The rule of one price applies to bonds through pure discount bonds It is a mistake to assume that coupon bonds with the same life have the same yield-their coupon rates differ, leading to a

43、 different % mix of discount bonds第46頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall47Movement of a Pure Discount Bonds Price over Time第47頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall488.6 The Behavior of Bond Prices Over Time The expected price of

44、 pure discount bonds rises exponentially to the face value with time, and the actual price never exceeds par Coupon bonds are more complex, and their price may exceed their par value, but at maturity they reach their par value第48頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hal

45、l49Bond Prices at Alternative Yields第49頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall50Bond Price Sensitivity to Yield Changes第50頁/共57頁Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall51Bond Price Trajectory The following diagram shows the dynamic nature of the yield curve as it passes through time Think of a y