Download presentation

Presentation is loading. Please wait.

Published byNicolas Pape Modified over 3 years ago

1
Lecture 9

2
2 3 10 8.04 6.00 4.84

3
Maturity (years)YTM 13.0% 53.5% 103.8% 154.1% 204.3% 304.5% The Pure Term Structure or Pure Yield Curve are comprised of zero-coupon bonds These are often only found in the form of US Treasury Strips. http://online.wsj.com/mdc/public/page/2_3 020-tstrips.html?mod=topnav_2_3000

4
01230123 Rates f 3-1 R n = spot rates f n = forward rates year

5
R2R3R2R3 f 3 f 3-2 f2f2 0 1 2 3 year

6
example 1000=1000 (1+R 3 ) 3 (1+f 1 )(1+f 2 )(1+f 3 )

7
Forward Rate Computations (1+ R n ) n = (1+R 1 )(1+f 2 )(1+f 3 )....(1+f n )

8
Continuous Compounding Warning: Answers in book will be slightly different than calculator.

9
Bond Value = C 1 + C 2 + C 3 (1+r)(1+r) 2 (1+r) 3 Example $1,000 bond pays 8% per year for 3 years. What is the price at a YTM of 6% 1053.46 = 80 + 80 + 1080 (1+.06)(1+.06) 2 (1+.06) 3

10
Bond Value Bond Value = C 1 + C 2 + C 3 e r e r2 e r3 Example $1,000 bond pays 8% per year for 3 years. What is the price at a YTM of 6% 1048.39 = 80 + 80 + 1080 e. 06 e.06x2 e.06x3

11
YTM Example zero coupon 3 year bond with YTM = 6% and par value = 1,000 Price = 1000 / (1 +.06) 3 = 839.62

12
YTM Example zero coupon 3 year bond with YTM = 6% and par value = 1,000

13
Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995% 3 year zero treasury YTM = 9.660%

14
Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995% 3 year zero treasury YTM = 9.660% Answer FV of principal @ YTM 2 yr1000 x (1.08995) 2 = 1187.99 3 yr1000 x (1.09660) 3 = 1318.70 IRR of ( FV= 1318.70 & PV= -1187.99) = 11%

15
example (using previous example ) f 3 = 11% Q: What is the 2 year forward price on a 1 yr bond? A: 1 / (1+.11) =.9009

16
Example Two years from now, you intend to begin a project that will last for 5 years. What discount rate should be used when evaluating the project? 2 year spot rate = 5% 7 year spot rate = 7.05%

17
Example (previous example) 2 yr spot = 5% 7 yr spot = 7.05% 5 yr forward rate at year 2 = 7.88% Q: What is the price on a 2 year forward contract if the underlying asset is a 5year zero bond? A: 1 / (1 +.0788) 5 =.6843

18
coupons paying bonds to derive rates Bond Value = C 1 + C 2 (1+r)(1+r) 2 Bond Value = C 1 + C 2 (1+R 1 )(1+f 1 )(1+f 2 ) d1 = 1 d2 = 1 (1+R 1 )(1+f 1 )(1+f 2 )

19
Example – How to create zero strips 8% 2 yr bond YTM = 9.43% 10% 2 yr bond YTM = 9.43% What is the forward rate? Step 1 value bonds 8% = 975 10%= 1010 Step 2 975 = 80d1 + 1080 d2 -------> solve for d1 1010 =100d1 + 1100d2 -------> insert d1 & solve for d2

20
example continued Step 3 solve algebraic equations d1 = [975-(1080)d2] / 80 insert d1 & solve = d2 =.8350 insert d2 and solve for d1 = d1 =.9150 Step 4 Insert d1 & d2 and Solve for f 1 & f 2..9150 = 1/(1+f 1 ).8350 = 1 / (1.0929)(1+f 2 ) f 1 = 9.29% f 2 = 9.58% PROOF

21
Continuous Compounding Warning: Answers in book will be slightly different than calculator.

22
Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995% 3 year zero treasury YTM = 9.660%

23
Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995% 3 year zero treasury YTM = 9.660% Answer FV of principal @ YTM IRR of ( FV= 1336.16 & PV= -1197.10) = 10.99% Trick: Use 365 days to get a near continuous compounding rate. Then multiply by 365

24
example (using previous example ) f 3 = 10.99% Q: What is the 2 year forward price on a 1 yr bond? A:

25
Example Two years from now, you intend to begin a project that will last for 5 years. What discount rate should be used when evaluating the project? 2 year spot rate = 5% 7 year spot rate = 7.05%

26
Example (previous example) 2 yr spot = 5% 7 yr spot = 7.05% 5 yr forward rate at year 2 = 7.87% Trick: Use 365 x 5 days to approximate continuous compounding when calculating IRR. Q: What is the price on a 2 year forward contract if the underlying asset is a 5year zero bond? A:

27
coupons paying bonds to derive rates

28
Example – How to create zero strips 8% 2 yr bond YTM = 9.43% 10% 2 yr bond YTM = 9.43% What is the forward rate? Step 1 value bonds 8% = 975 10%= 1010 Step 2 975 = 80d1 + 1080 d2 -------> solve for d1 1010 =100d1 + 1100d2 -------> insert d1 & solve for d2

29
example continued Step 3 solve algebraic equations d1 = [975-(1080)d2] / 80 insert d1 & solve = d2 =.8350 insert d2 and solve for d1 = d1 =.9150 Step 4 Insert d1 & d2 and Solve for f 1 & f 2. f 1 = 8.89% f 2 = 9.15% PROOF

Similar presentations

OK

Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Inflation & Time Value.

Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Inflation & Time Value.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Run ppt on tv Ppt on petroleum industry in india download Ppt on individual taxation in india Ppt on personality development and grooming Ppt on wireless communication network Ppt on protein energy malnutrition with its management Ppt on trial and error examples Ppt on self development goals Ppt on new invention of computer technology Ppt on condition monitoring training