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Debt Investments 1. The best technique to analyze the ability of a corporation to pay its debt service is: A. Traditional ratio analysis B. A forecast of the firm’s profitability C. The DuPont model D. An analysis and projection of discretionary cash flow. 1. D :Ultimately, a firm must service its debt from cash 2. In which of the following cases would estimated changes to portfolio’s value, which are based on the portfolio’s effective duration only, be most likely to be appropriate? I. There is a small, parallel shift in the yield curve. II. On average interest rates change very little, with long-term rates rising 50 basis points and short-term rates falling 50 basis points. III. Interest rates fall substantially in parallel fashion over the next year. 2. A :For III the convexity effect may be important. Neither duration nor convexity deals with nonparallel shifts (II). A. I only B. II only C. III only D. I and II (七)、修正的存續期間與價格存續期間： 除了 Macaulay 的存續期間用來衡量債券價格的利率彈性之外，還有 修正的存續期間與價格存續期間 1.修正的存續期間（Modified Duration, Dmod） P 公式： Dm od D mac P y y 1 m m 表示當殖利率微小變動時，債券價格變動的比例；即利率微小變動時， 債券價格的變動幅度。 2.價格存續期間（Dollar Duration, Ddol） P 公式： Ddol P y Dm od m 由此公式可以計算出殖利率微小變動時，對債券價格「金額」上的影響 程度。 (八)、存續期間之應用： 例子：有一張 3 年期的零息債券，每年付息一次，殖利率為 8％，面額 100 萬。若殖利率下降 10 個基本點，則債券之價格波動比例為何？波動 的金額為何？ 解答：796041 – 793832=2209.18 步驟 1：求算 Dmac 0 1 0 2 0 3 PV 1,000 ,000 3 D mac 3 3 3 PV t 1 t PV t 1 t PV t 1 t 1,000,000 3 P 1.08 3 3 3 P 1,000,000 y 1.08 3 m y 1 m ＊由此計算結果亦可得知：零息債券的存續期間等於到期期間。 步驟 2：求算 Dmod D mac 3 2.78 D mod y 1.08 1 m 故當殖利率下降 0.1％時，債券價格將上漲的比例＝2.78×0.1％＝0.278％。 y P 0.001 3 3 m .00278 P y 8% 1 1 m 1 1,000,000 步驟 3：原債券價格 P 793,832.24 10.08 3 步驟 4：Ddol＝Dmod×P＝2.78×＄793,832.24＝＄2,206,853 0.1％×＄2,206,853=＄2,206 故當殖利率下降 0.1％時，債券價格將上漲 2,206 元。 P .00278 P P .00278 793842 .00278 2206 P 793832 796041P 2209.18 3. A ten-year 8% coupon bond issued by ABC Corp. is selling at 95.00, with a yield to maturity of 8.76%. Your bond valuation model indicates that a 50 bp decrease in rates will result in an increase in the price from 95.00 to 97.75, whereas a 50 bp increase in rates will result in a decrease in the price from 95.00 to 92.75. What is the price value of a basis point change in this bond? A. $5.26 B. $1.05 C. $0.05 3. C:Duration = (97.75-92.75)/ (2*95*50 bp) = 5.2632,PVBP = 5.26 * 1bp *95 = 0.05 P PB PS 97.75 92.25 50000 DMO 5.2632, Dadj P 2 PM Y 2 95 50bp 2 95 50 Y 1 P Y Dadj P 95 P Dadj P PVBP P WHEN Y 1BP Y 1 1 C. $0.06 4. Given the 2-year spot rate of 4% and knowing the market expects a 3-year security two years from now to yield 5%. Calculate the current 5-year spot rate. A. 2.3% B. 4.6% 4. B : (1+S5)5 = (1+S2)2 * (1+ 2f3)3 ,S5 = 4.6% 1.04^2= 1.0816 1.05^3= 1.157625 1.04^2*1.05^3= 1.2520872 1.252087^0.2= 1.045988513 1.0459-1= 0.0459 5. Ken Cambie owns a barbell portfolio consisting of equal investments in two bonds: A 5-year bond with a modified duration of 4.0 and a 10-year bond with modified duration of 8.0. If the yield curve inverts so that the yields on 5-year maturities increase 100 basis points, and the yields on 10-year maturities decrease by 100 basis points, the return on Cambie’s portfolio will be: P P P P P 8 100BP, D A 4 P 4 100BP, DB 8 Y P Y P 1 1 5. C : price change= -WA * DA * Interest rate change A – WB * DB * Interest rate change B = -0.5 * 4 * 100 bp – 0.5* 8 * (-100 bp) = 2% C. +2% D. –2% P P DMO Dadj P Dadj Y Y P 1 P D4 : Dadj Y 4 (.01) .04 P P D8 : Dadj Y 8 (.01) .08 P .5D4 .5D8 .02 95.42029 (4.57971) -0.045797072 109.47130 9.47130 0.094713045 0.5*B1+0.5*B2= 2.445798672 0.024458 0.5*C1+0.5*C2 0.024457987 0.5*C1+0.5*C2 99.5045 (.4955) 100.5025 .5025 0.5*B1+0.5*B2= . 00350246 6. What is the fair price to pay for a 5.25% coupon, 2-year corporate bond, callable at 100.25 consistent with the binomial interest rate tree for this corporate issuer shown below? (Assume annual compounding) 6. a- NH = 105.25/ 1.0597 = 99.32 NL = 105.25/ 1.0489 = 100.34 > 100.25 = call price N0 = 0.5* (99.32+5.25)/ 1.054 + 0.5* (100.25+5.25)/ 1.054 = 99.65 100.00 price NHH 5.25 coupon 5.25% NH 5.97% 100.00 price N0 5.4% NHL 5.25 coupon 5.7% NL 4.89% 100.00 price NLL 5.25 coupon 4.67% A. 99.65 B. 99.69 C. 99.98 D. 100.25 EXHIBIT 14-10 Finding the One-Year Forward Rates for Year 11Using EXHIBIT 14-10 Finding the One-Year Forward Rates for Year Using the Two-Year 4% On-the-Run：First Trial the Two-Year 4% On-the-Run：First Trial V=100 ● V=100 ● C=4.00 NHH C=4.00 NHH r2,HH=? r2,HH=? V=98.582 ● V=98.582 ● C=4.00 NH C=4.00 NH r1,H=5.496% r1,H=5.496% V=99.567 V=99.567 V=100 ● C=0 ● V=100 ● C=0 ● C=4.00 N r0r=3.500 NHL C=4.00 N 0=3.500 NHL r2,HL=? % r2,HL=? % V=99.522 ● V=99.522 ● C=4.00 NL C=4.00 NL r1,L=4.500% r1,L=4.500% V=100 ● V=100 ● C=4.00 NLL C=4.00 NLL r2,LL=? r2,LL=? 3a. The bond’s value two years from now must be determined. In our example this is simple. We are using a two-year bond, so the bond’s value is its maturity value ($100) Plus its final coupon payment ($4). Thus, it is $104. 3b. Calculate the present value of the bond's value found in 3a using the higher rate. In our example the appropriate discount rate is the one-year higher forward rate, 5.496%. The present value is $98.582 (= $104/1.05496). This is the value of VH that we referred to earlier. PVH=（VH+C）/（1+r1,H）=（100+4）/ （1+5.496%） =$98.582 3c. Calculate the present value of the bond’s value found in 3a using the lower rate. The discount rate used is then the lower one-year forward rate, 4.5%. The value is $99.522(= $104/1.045) and is the value of VL. PVL=（VL+C）/（1+r1,L）=（100+4）/（1+4.5%） =$99.522 3d. Add the coupon to VH and VL to get the cash flow at NH and NL, respectively. In our example we have $102.582 for the higher rate and $103.522 for the lower rate. 3e. Calculate the present value of the two values using the one-year forward rate using r*. At this point in the valuation, r* is the root rate, 3.50%. EXHIBIT 14-10 Finding the One-Year Forward Rates for Year 1 Using EXHIBIT 14-10 Finding the One-Year Forward Rates for Year 1 Using the Two-Year 4% On-the-Run：First Trial the Two-Year 4% On-the-Run：First Trial V=100 ● V=100 ● C=4.00 NHH C=4.00 NHHr2,HH=? r2,HH=? V=98.582 ● V=98.582 ● C=4.00 NH C=4.00 NH r1,H=5.496% r1,H=5.496% V=99.567 V=99.567 V=100 ● C=0 ● V=100 ● r =3.500 C=0 ● C=4.00 N 0 NHL C=4.00 N r0=3.500 NHLr2,HL=? % r2,HL=? % V=99.522 ● V=99.522 ● C=4.00 NL C=4.00 NL r1,L=4.500% r1,L=4.500% V=100 ● V=100 ● C=4.00 NLL C=4.00 NLLr2,LL=? r2,LL=? 在N點： VH C $102 .582 PVH $99 .113 1 r* 1.035 VL C $103 .522 PVL $100 .021 1 r* 1.035 Step 4: Calculate the average present value of the two cash flows in step 3. This is the value we referred to earlier as 1 V H C V C value at a node = L 2 1 r* 1 r* value at a node = 1/2【($99.113 + $100.021)】= $99.567 Step 5: Compare the value in step 4 with the bond's market value. If the two values are the same, the r1 used in this trial is the one we seek. This is the one-year forward rate that would then be used in the binomial interest-rate tree for the lower rate, and the corresponding rate would be for the higher rate. If, instead, the value found in step 4 is not equal to the market value of the bond, this means that the value r1 in this trial is not the one-period forward rate that is consistent with： In this example, when r1 is 4.5% we get a value of $99.567 in step 4, which is less than the observed market value of $l00. Therefore, 4.5% is too large and the five steps must be repeated, trying a lower value for r1. Let's jump right to the correct value for r1 in this example and rework steps l through 5. This occurs when r1,L is 4.074%; The corresponding binomial interest-rate tree is shown in Exhibit 14-11. 99.113 100.021 199.134 99.567 EXHIBIT 14-10 Finding the One-Year Forward Rates for Year 11Using EXHIBIT 14-10 Finding the One-Year Forward Rates for Year Using the Two-Year 4% On-the-Run：First Trial the Two-Year 4% On-the-Run：First Trial V=100 ● V=100 ● C=4.00 NHH C=4.00 NHH r2,HH=? r2,HH=? V=98.582 ● V=98.582 ● C=4.00 NH C=4.00 NH r1,H=5.496% r1,H=5.496% V=99.567 V=99.567 V=100 ● ● C=0 C=0 ● V=100 ● C=4.00 NN r0=3.500 r0=3.500 NHL C=4.00 NHL r2,HL=? % r2,HL=? % V=99.522 ● V=99.522 ● C=4.00 NL C=4.00 NL r1,L=4.500% r1,L=4.500% V=100 ● V=100 ● C=4.00 NLL C=4.00 NLL r2,LL=? r2,LL=? EXHIBIT 14-11 One-Year Forward Rates for Year 1 Using EXHIBIT 14-11 One-Year Forward Rates for Year 1 Using the Two-Year 4% On-the-Run：Issue the Two-Year 4% On-the-Run：Issue V=100 V=100 ●● C=4.00 NHH C=4.00 NHH r2,HH=? r2,HH=? V=99.071 V=99.071 ●● C=4.00 NH C=4.00 NH r1,H=4.976% r1,H=4.976% V=100 V=100 V=100 V=100 ● C=0 ●● C=4.00 ● C=0 N NHL C=4.00 NHL r2,HL=? N r0=3.500% r0=3.500% r2,HL=? V=99.929 V=99.929 ●● C=4.00 NL C=4.00 NL r1,L=4.074% r1,L=4.074% V=100 V=100 ●● C=4.00 NLL C=4.00 NLL r2,LL=? r2,LL=? 99.071 103.071 99.58551 99.929 103.929 100.4145 1.035 200 1.035 100 Step 1：In this trial we select a value of 4.074% for r 1,L. Step 2：The corresponding value for the higher one-year forward rate is 4.976%(= 4.074% e2*0.10). r1,H= r1,L*e2= 4.074%*e2*0.1=4.976 Step 3：The bond’s value one year from now is determined as follows: 3a. The bond’s value two years from now is $104, just as in the first trial. 3b. The present value of the bond's value found in 3a for the higher rate, VH, is $99.071(= $104/1.04976). PVH=（VH+C）/（1+r1,H）=（100+4）/（1+4.976%） =$99.071 3c. The present value of the bond's value found in 3a for the lower rate, VL, is $99.929(= $104/1.04074). PVL=（VL+C）/（1+r1,L）=（100+4）/（1+4.074%） =$99.929 3d. Adding the coupon to VH and VL, we get $103.071 as the cash flow for the higher rate and $103.929 as the cash flow for the lower rate. 3e. The present value of the two cash flows using the one-year forward rate at the node to the left, 3.5%, gives 在N點： VH C $103 .071 PV H $99 .586 1 r* 1.035 VL C $103 .929 PVL $100 .414 1 r* 1.035 Step 4: The average present value is $100, which is 1 V C the value at the node V1 rC H 2 1 r * L * the value at the node 1 VH C VL C value at a node = 2 1 r* 1 r* value at a node = 1/2【($99.586 + $100.414)】= $100 Step 5: Because the average present value is equal to the observed market value of $100, r1 is 4.074%. 7. Comparing expected yield and risk on agency and non-agency mortgage passthroughs, you would expect: A. Agencies to have the highest yield and risk B. Agencies to have the lowest yield and risk C. Agencies to have the lowest yield and highest risk D. Agencies to have the highest yield and lowest risk 7. b- 8. If you expect interest rates to rise, how would IO and PO prices respond? http://www.ginniemae.gov/investors/strips_press.asp?Section=Investors A. Both will drop B. Both will rise C. The PO will drop and the IO would rise or fall D. The IO will rise and the PO could rise or fall 8. c- The interest rate rise reduces the PV of the cash flows for the PO and its price drops. This is also true for the IO, but prepays also slow, so total cash flows increase and the price could rise or fall. 9. As the economy slips into a recession, it is typical for the yield curve to: A. Shift upward in a parallel manner B. Shift downward in a parallel manner C. Shift downward and flatten or invert D. Shift downward and steepen 9. d – As the economy slips into recession, the yield curve usually shift downward because rates will be cut to spur activity, but long-term rates won’t fall as much as investors will still need a premium to invest in long-term assets. 10. The advantage of using implied yield volatility to forecast future interest rate volatility is: A. It is calculated from the long-term history of interest rate moves B. It puts more weight on recent interest rate movement C. It best captures the market consensus for future interest rate movement D. It is computed from an equal weighting of each of these items. 10. c- a and b are historical methods. Since implied volatility is based on the current prices of bond and options, it should reflect the market’s expectations of future interest rate. 11. As interest rates become more volatile, the price of a putable bond will tend to: a. Decrease b. Increase c. Remain unchanged d. It could increase or decrease 12. All of the following would tend to affect mortgage prepayment 預付款項 speeds 提前還 本速度 except: a. The cost of refinancing 重新貸款 existing mortgages b. The pace of homes sales c. The age of the mortgages d. The call premium paid by the mortgage servicer. 12. d- 及時償付本息風險(Timely Payment of Interest and Principal)、提前還本風險(Prepayment Risk) 提前還本風險:不論何種房貸轉付證券，投資人都必須承擔提前還本風險。 13. For a new 30-year $10,000,000 passthrough with 6% coupon, calculate the expected prepayment 預付款項 amount for the first month. The CPR is 10% a. 0 b. $59,955 c. $87,313 d. $99,925 13. c- PMT = 59,955 ( N =30*12 = 360; I = 6/12 = 0.5; PV = 10,000,000; comp PMT = -59,955.05) 14. During the lockout period on a credit card asset-backed securities: a. The investor receives coupon interest but no principal. b. The credit card holder may not pay down their principal. c. The investor may not resell their holding. d. All of the above are true. 14. a- 15. Internal credit enhancements for an asset-backed security can be provided with a: I. Third-party guarantee II. Cash reserve set aside III. Over collateralization(超額擔保) IV. Senior subordinate structure V. Bank line of credit a. All of the above b. II, III, IV, V c. II, III, IV d. I, V 15. c- I and V are external credit enhancements 16. Which of the following statements is correct? a. Option-free bonds must be evaluated on both their OAS and zero-volatility spread b. Asset-backed securities whose prepayments vary with the level of interest rates should be evaluated on their Z-spreads c. Asset-backed securities whose prepayments are affected by interest rates and “burnout” should be evaluated with Monte Carlo- based OAS d. Asset-backed securities whose prepayments are affected by interest rates and “burnout” can be evaluated with Monte Carlo or binomial based OAS 16. c- For ABSs which cashflow are interest rate path dependent, Monte Carlo- based OAS should be used. Answers for Bonus Questions: Debt Investments 1. d- Ultimately, a firm must service its debt from cash 2. a- For III the convexity effect may be important. Neither duration nor convexity deals with nonparallel shifts (II). 3. c- Duration = (97.75-92.75)/ (2*95*50 bp) = 5.2632 PVBP = 5.26 * 1bp *95 = 0.05 4. b- (1+S5)5 = (1+S2)2 * (1+ 2f3)3 S5 = 4.6% 5. c- price change = -WA * DA * Interest rate change A – WB * DB * Interest rate change B = -0.5 * 4 * 100 bp – 0.5* 8 * (-100 bp) = 2% 6. a- NH = 105.25/ 1.0597 = 99.32 NL = 105.25/ 1.0489 = 100.34 > 100.25 = call price N0 = 0.5* (99.32+5.25)/ 1.054 + 0.5* (100.25+5.25)/ 1.054 = 99.65 7. b- 8. c- The interest rate rise reduces the PV of the cash flows for the PO and its price drops. This is also true for the IO, but prepays also slow, so total cash flows increase and the price could rise or fall. 9. d – As the economy slips into recession, the yield curve usually shift downward because rates will be cut to spur activity, but long-term rates won’t fall as much as investors will still need a premium to invest in long-term assets. 10. c- a and b are historical methods. Since implied volatility is based on the current prices of bond and options, it should reflect the market’s expectations of future interest rate. 11. b- Vputable bond = V option-free bond + Vput option Interest rate volatility Vput option Vputable bond 12. d- 13. c- PMT = 59,955 ( N =30*12 = 360; I = 6/12 = 0.5; PV = 10,000,000; comp PMT = -59,955.05) Interest portion = 10,000,000*6%/12 = 50,000 Principal portion = 59,955 – 50,000 = 9,955 CPR = 10%, SMM = 1- (1-CPR)1/12 = 0.874% Expected prepayment = 0.874%*(10,000,000 – 9,955) *0.874% = 87,313 14. a- 15. c- I and V are external credit enhancements 16. c- For ABSs which cashflow are interest rate path dependent, Monte Carlo- based OAS should be used. 98.588+5.25=103.838 1.04976 103.838/1.04976=98.91594 99.732+5.25=104.982 1.04976 104.982/1.04976=100.0057 99.46083 104.982 1.04074 104.982/1.04074=100.8725 100.689+5.25=105.939 1.04074 105.939/1.04074=101.7920 101.3322 Application to Valuing an Option-Free Bond 無選擇權債券評價 To illustrate how to use the binomial interest-rate tree, consider a 5.25% corporate bond that has two years remaining to maturity and is option-free. Exhibit 14-13 shows the various values in the discounting process and produces a bond value of $102.075. This clearly demonstrates that the valuation model is consistent with the standard valuation model for an option-free bond. EXHIBIT 14-13 Valuing Option-Free Corporate Bond with Three EXHIBIT 14-13 Valuing Option-Free Corporate Bond with Three Years to Maturity and aaCoupon Rate of 5.25% Years to Maturity and Coupon Rate of 5.25% V=98.588 ● V=98.588 ● C=5.25 NHH C=5.25 NHH r2,HH=6.757% r2,HH=6.757% V=99.461 ● V=99.461 ● C=5.25 NH C=5.25 NH r1,H=4.976% r1,H=4.976% V=102.07 V=102.07 V=99.732 ● 55 C=0 ● C=0 ● V=99.732 ● C=5.25 N r0=3.500 N r0=3.500 NHL C=5.25 NHL r2,HL=5.532% % r2,HL=5.532% % V=101.333 ● V=101.333 ● C=5.25 NL C=5.25 NL r1,L=4.074% r1,L=4.074% V=100.689 ● V=100.689 ● C=5.25 NLL C=5.25 NLL r2,LL=4.530% r2,LL=4.530% The valuation process proceeds in the same fashion as in the case of an option-free bond. One exception: When the call option may be exercised by the issuer, the bond value at a node must be changed to reflect the lesser of its value if it is not called. For example, consider a 5.25% corporate bond with three years remaining to maturity that is callable in one year at $100. The discounting process is identical to that shown in Exhibit 14-13 except that at two nodes, NL and NLL, the values from the recursive valuation formula ($101.3322 at NL and $100.689 at NLL) exceed the call price ($100) and therefore have been struck out and replaced with $100. The value for this callable bond is $101.432. EXHIBIT 14-14 Valuing a Callable Corporate Bond with Three Years to Maturity, a Coupon Rate of 5.25% and Callable in One Year at 100 V=98.588 ● C=5.25 NHH r2,HH=6.757% V=99.461 ● C=5.25 NH r1,H=4.976% V=101.432 V=99.732 ● ● C=0 C=5.25 N NHL r0=3.500% r2,HL=5.532% V=100(100.001 ● ) C=5.25 NL r1,L=4.074% V=100(100.689) ● C=5.25 NLL r2,LL=4.530% Value of a call option = value of a noncallable bond – value of a callable bond. Value of a noncallable bond （$102.075） - ） Value of a callable bond （$101.432） Value of a call option （$0.643） The value of the noncallable bond is $102.075 and the value of the callable bond is $101.432, so the value of the call option is $0.643. Extension to Other Embedded Options 其他嵌入式選擇權的延伸 Other embedded options, such as put options, caps and floors on floating-rate notes. For example, let's consider a putable bond. Suppose that a 5.25% corporate bond with three years remaining to maturity is putable in one year at par $100. The bond values altered at two nodes (N HHand NLH) because the bond values at these two nodes exceed $100, the value at which the bond can be put. The value of this putable bond is $102.523. EXHIBIT 14-15 Valuing a Putable Corporate Bond with Three EXHIBIT 14-15 Valuing a Putable Corporate Bond with Three Years to Maturity, a Coupon Rate of 5.25% Years to Maturity, Year at 100 and Putable in One a Coupon Rate of 5.25% and Putable in One Year at 100 V=100(98.588 價值不足100 ● V=100(98.588 價值不足100 ●) NHH ) C=5.25 C=5.25 時 r NHH 2,HH=6.757% 時 r2,HH=6.757% 以100折現 V=100.261 價值不足100 以100折現 ● V=100.261 C=5.25 價值不足100 ● C=5.25 NH r1,H=4.976 時 NH r1,H=4.976 % 時 % 以100折現 V=102.52 V=102.52 以100折現 V=100(99.732 ● 3 C=0 ● V=100(99.732 N● r0=3.500 3 C=0 ●) NHL C=5.25 r C=5.25 ) =5.532% N% r0=3.500 NHL 2,HL r2,HL=5.532% % V=101.461 V=101.461 ● C=5.25 ● C=5.25 NL r1,L=4.074 NL r1,L=4.074 % % V=100.689 ● V=100.689 ● C=5.25 NLL C=5.25 NLLr2,LL=4.530% r2,LL=4.530% Value of a put option = value of a nonputable bond – value of a putable bond. Value of a noncallable bond - ） Value of a callable bond Value of a call option The value of the putable bond is $102.523 and the value of the corresponding nonputable bond is $102.075, the value of the put option is -$0.448. The negative sign indicates that the issuer has sold the option, or equivalently, the investor has purchased the option. EXHIBIT 14-15 Valuing a Putable Corporate Bond with Three Years to Maturity, a Coupon Rate of 5.25% and Putable in One Year at 100 V=100(98.588) v 價值不足 100 時 ● C=5.25 NHH r2,HH=6.757% 以 100 折現 v 價值不足 100 時 V=100.261 ● C=5.25 NH 以 100 折現 r1,H=4.976% V=102.523^ V=100(99.732) ● ● C=0 C=5.25 N NHL r0=3.500% r2,HL=5.532% V=101.461 ● C=5.25 NL r1,L=4.074% EXHIBIT 14-13 Valuing Option-Free Corporate Bond with Three EXHIBIT 14-13 Valuing Option-Free Corporate Bond with Three Years to Maturity and a Coupon Rate of 5.25% Years to Maturity and a Coupon Rate of 5.25% ● V=98.588 V=98.588 V=100.689 ●C=5.25 NHH r C=5.25 NHH2,HH=6.757% ● r2,HH=6.757% C=5.25 ● V=99.461 V=99.461 NLL C=5.25 NH● C=5.25 NH 1,H=4.976% r r2,LL=4.530% r1,H=4.976% V=102.07 V=99.732 ● 5 V=102.07 C=0 ● V=99.732 N ●r0=3.500 5 C=0 ●C=5.25 NHL N% r0=3.500 r C=5.25 NHL2,HL=5.532% r2,HL=5.532% % V=101.333 ● V=101.333 C=5.25 NL● C=5.25 NLr1,L=4.074% r1,L=4.074% V=100.689 ● V=100.689 C=5.25 NLL● C=5.25 r NLL2,LL=4.530% r2,LL=4.530% EXHIBIT 14-15 Valuing a Putable Corporate Bond with Three EXHIBIT 14-15 Valuing a Putable Corporate Bond with Three Years to Maturity, a Coupon Rate of 5.25% Years to Maturity, Year at 100 and Putable in One a Coupon Rate of 5.25% and Putable in One Year at 100 V=100(98.588 ● V=100(98.588 ●) NHH ) C=5.25 C=5.25 r NHH 2,HH=6.757% r2,HH=6.757% V=100.261 V=100.261 ● C=5.25 ● r C=5.25 NH 1,H=4.976 NH r1,H=4.976 % V=102.52 % V=102.52 V=100(99.732 ● 3 C=0 ● V=100(99.732 ● r =3.500 N 0 3 C=0 ●) NHL ) C=5.25 C=5.25 N %r0=3.500 NHLr2,HL=5.532% r2,HL=5.532% % V=101.461 V=101.461 ● C=5.25 ● C=5.25 NL r1,L=4.074 NL r1,L=4.074 % % V=100.689 ● V=100.689 ● C=5.25 NLL C=5.25 NLLr2,LL=4.530% r2,LL=4.530% 105.25 1.04976 100.2610 105.25 1.04976 100.2610 100.2610 98.588+5.25+100= 1.04976 105.25/1.04976=100.261 98.588+5.25+101= 1.04976 105.25/1.04976=100.261 100.261 105.25 1.04074 101.1299652 105.25/1.04074= 105 100.689+5.25=105.939 1.04074 101.7919942 105.939/1.04074 105.939 101.4609797 100.261+5.25= 101.4609797 105.511 1.035 101.9430 106.711 1.035 103.1024 101.461+5.25= 0.5(101.943+103.1024)= ^102.5227

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