Lecture 9. 2 3 10 8.04 6.00 4.84 Maturity (years)YTM 13.0% 53.5% 103.8% 154.1% 204.3% 304.5% The...

29
Derivatives Lecture 9

TAGS:

Transcript of Lecture 9. 2 3 10 8.04 6.00 4.84 Maturity (years)YTM 13.0% 53.5% 103.8% 154.1% 204.3% 304.5% The...

Page 1: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

DerivativesLecture 9

Page 2: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Term Structure & Spots Rates

2 3 10

8.04

6.00

4.84

Page 3: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Pure Term StructureMaturity (years) YTM

1 3.0%5 3.5%10 3.8%15 4.1%20 4.3%30 4.5%

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_3020-tstrips.html?mod=topnav_2_3000

http://online.wsj.com/mdc/public/page/2_3020-tstrips.html?mod=topnav_2_3000
http://online.wsj.com/mdc/public/page/2_3020-tstrips.html?mod=topnav_2_3000
Page 4: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Forward rates

0 1 2 3

Rates

f3-1

Rn = spot rates

fn = forward rates

year

Page 5: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Spot/Forward rates

R2

R3

f3

f3-2

f2

0 1 2 3 year

Page 6: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

example

1000 = 1000 (1+R3)3 (1+f1)(1+f2)(1+f3)

Spot/Forward rates

Page 7: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Forward Rate Computations

(1+ Rn)n = (1+R1)(1+f2)(1+f3)....(1+fn)

Spot/Forward rates

Page 8: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Continuous Compounding

rtt

tt

e

C

r

C

)1(

Warning:

Answers in book will be slightly different than calculator.

Page 9: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Bond Value

Bond Value = C1 + C2 + C3

(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

Page 10: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Bond Value

Bond Value = C1 + C2 + C3

er er2 er3

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

Page 11: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

YieldsYTM

Examplezero coupon 3 year bond with YTM = 6% andpar value = 1,000Price = 1000 / (1 +.06)3 = 839.62

Page 12: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

YieldsYTM

Examplezero coupon 3 year bond with YTM = 6% andpar value = 1,000

27.835

1000Price

306.

e

Page 13: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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

Spot/Forward rates

Page 14: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

ExampleWhat 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 yr 1000 x (1.08995)2 = 1187.99

3 yr 1000 x (1.09660)3 = 1318.70

IRR of ( FV= 1318.70 & PV= -1187.99) = 11%

Spot/Forward rates

Page 15: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

example (using previous example )f3 = 11%Q: What is the 2 year forward price on a 1 yr bond?A: 1 / (1+.11) = .9009

Forward rates & Prices

Page 16: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

ExampleTwo 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%

Spot/Forward rates

Page 17: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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

Forward rates & Prices

Page 18: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

coupons paying bonds to derive rates

Spot/Forward rates

Bond Value = C1 + C2

(1+r) (1+r)2

Bond Value = C1 + C2

(1+R1) (1+f1)(1+f2)

d1 = 1 d2 = 1

(1+R1) (1+f1)(1+f2)

Page 19: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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 1value bonds 8% = 975 10%= 1010

Step 2 975 = 80d1 + 1080 d2 -------> solve for d11010 =100d1 + 1100d2 -------> insert d1 & solve for d2

Spot/Forward rates

Page 20: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

example continuedStep 3 solve algebraic equationsd1 = [975-(1080)d2] / 80insert d1 & solve = d2 = .8350insert d2 and solve for d1 = d1 = .9150

Step 4

Insert d1 & d2 and Solve for f1 & f2.

.9150 = 1/(1+f1) .8350 = 1 / (1.0929)(1+f2)

f1 = 9.29% f2 = 9.58%

PROOF

Spot/Forward rates

Page 21: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

Continuous Compounding

rtt

tt

e

C

r

C

)1(

Warning:

Answers in book will be slightly different than calculator.

Page 22: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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

Spot/Forward rates

Page 23: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

ExampleWhat 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

Spot/Forward rates

16.133610003

10.119710002309660.

208995.

eyr

eyr

Page 24: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

example (using previous example )f3 = 10.99%Q: What is the 2 year forward price on a 1 yr bond?

A:

Forward rates & Prices

8959.

1Price

11099.

e

Page 25: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

ExampleTwo 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%

Spot/Forward rates

Page 26: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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:

Forward rates & Prices

6747.

1Price

50787.

e

Page 27: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

coupons paying bonds to derive rates

Spot/Forward rates

221 Value Bondrr e

C

e

C

211

21 Value Bond fff ee

C

e

C

1

1 d1fe

21

12d

ff ee

Page 28: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

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 1value bonds 8% = 975 10%= 1010

Step 2 975 = 80d1 + 1080 d2 -------> solve for d11010 =100d1 + 1100d2 -------> insert d1 & solve for d2

Spot/Forward rates

Page 29: Lecture 9. 2 3 10 8.04 6.00 4.84 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.

example continuedStep 3 solve algebraic equationsd1 = [975-(1080)d2] / 80insert d1 & solve = d2 = .8350insert d2 and solve for d1 = d1 = .9150

Step 4

Insert d1 & d2 and Solve for f1 & f2.

f1 = 8.89% f2 = 9.15%

PROOF

Spot/Forward rates

1

1 .9150 fe

20889.

18350. fee


Pure Hearts… Pure Thoughts …

Pure Hearts… Pure Thoughts …

QWIK-PURE 200 QWIK-PURE 350

QWIK-PURE 200 QWIK-PURE 350

Pure WATER. Pure PLEASURE. - Swimming-Teich

Pure WATER. Pure PLEASURE. - Swimming-Teich

First Oak Brook Bancshares, Inc. · $204.3 MIL $1,847.8MIL Assets $1.57 $30.01 Stock Price $0.20 $1.5 MIL $11.8 MIL $1.87 $18.4 MIL $120.9 MIL Earnings per share (Diluted) Equity

First Oak Brook Bancshares, Inc. · $204.3 MIL $1,847.8MIL Assets $1.57 $30.01 Stock Price $0.20 $1.5 MIL $11.8 MIL $1.87 $18.4 MIL $120.9 MIL Earnings per share (Diluted) Equity

PURE-LAND ZEN ZEN PURE-LAND - BuddhaNet

PURE-LAND ZEN ZEN PURE-LAND - BuddhaNet

PRODUCT OVERVIEW 2017 · video montage installation nomastyl® pure ne1 nomastyl® pure ne2 nomastyl® pure ne3 nomastyl® pure ne4 new nomastyl® pure 19 nomastyl® pure is a new

PRODUCT OVERVIEW 2017 · video montage installation nomastyl® pure ne1 nomastyl® pure ne2 nomastyl® pure ne3 nomastyl® pure ne4 new nomastyl® pure 19 nomastyl® pure is a new

fraser.stlouisfed.orgFeb 13, 1970  · 158.4 163.7 168.3 166.9 168.6 168.0 156.8 167.5 171.7 174.1 170.7 164.3| 159.0 166.1 171.3 170.9 169.9 172.7 161.4 176.7 177.5 178.6 165.4 154.1

fraser.stlouisfed.orgFeb 13, 1970  · 158.4 163.7 168.3 166.9 168.6 168.0 156.8 167.5 171.7 174.1 170.7 164.3| 159.0 166.1 171.3 170.9 169.9 172.7 161.4 176.7 177.5 178.6 165.4 154.1

Results Presentation Half-year ended 31 December 2015€¦ · FY2015 ($ Million) Net profit after tax attributable to shareholders $8.9 $16.7 Total assets $204.3 $179.6 Equity $123.0

Results Presentation Half-year ended 31 December 2015€¦ · FY2015 ($ Million) Net profit after tax attributable to shareholders $8.9 $16.7 Total assets $204.3 $179.6 Equity $123.0

Manitoba Hydro Electric Energy and Natural Gas - …...Demand Side Management NA 9.7 10.3 11.7 10.8 10.8 10.9 10.4 10.6 10.4 10.6 10.3 106.8 204.3 NATURAL GAS CAPITAL & DSM FORECAST

Manitoba Hydro Electric Energy and Natural Gas - …...Demand Side Management NA 9.7 10.3 11.7 10.8 10.8 10.9 10.4 10.6 10.4 10.6 10.3 106.8 204.3 NATURAL GAS CAPITAL & DSM FORECAST

PURE-LA BODY FRESHNER PURE-LA - BUG&DUST ...shop.inx-networks.com/popdate/ss_6.pdfPURE-LA BODY FRESHNER PURE-LA - BUG&DUST GUARD PURE-LA - BIO VANISH PURE-LA - BIO VANISH-TR PURE-LA

PURE-LA BODY FRESHNER PURE-LA - BUG&DUST ...shop.inx-networks.com/popdate/ss_6.pdfPURE-LA BODY FRESHNER PURE-LA - BUG&DUST GUARD PURE-LA - BIO VANISH PURE-LA - BIO VANISH-TR PURE-LA

A Productions and Operations Management Business Plan Pure adaptation, pure ease, pure convenience, sheer genius.

A Productions and Operations Management Business Plan Pure adaptation, pure ease, pure convenience, sheer genius.

C:Documents and SettingsAll UsersDocumentiArchivio .......146.4 _141.3 155.3' ; 141.8 .142.6 145.5 .141.4 .137.8 146.4 141.4 .136.3 143.9 152.9 h 130.9 .150.9 .154.1\. 151.0 .144_4

C:Documents and SettingsAll UsersDocumentiArchivio .......146.4 _141.3 155.3' ; 141.8 .142.6 145.5 .141.4 .137.8 146.4 141.4 .136.3 143.9 152.9 h 130.9 .150.9 .154.1\. 151.0 .144_4

CHRONOS iDOCK - PURE Help Centre · CHRONOS iDock, textSCAN, PURE, le logo PURE, PURE Digital, le logo PURE Digital, EcoPlus, le logo EcoPlus, Imagination Technologies et le logo

CHRONOS iDOCK - PURE Help Centre · CHRONOS iDock, textSCAN, PURE, le logo PURE, PURE Digital, le logo PURE Digital, EcoPlus, le logo EcoPlus, Imagination Technologies et le logo

Dinner4Two Pure / Dinner4All Pure · 2020. 4. 30. · Dinner4Two Pure / Dinner4All Pure 01.104020.01.001 / 01.104040.01.001 ... (voor klasse I-apparaten). •WAARSCHUWING: Indien

Dinner4Two Pure / Dinner4All Pure · 2020. 4. 30. · Dinner4Two Pure / Dinner4All Pure 01.104020.01.001 / 01.104040.01.001 ... (voor klasse I-apparaten). •WAARSCHUWING: Indien

PURE Prosperityimages.genesispure.com/web/pdf/GP_PURE_Prosperity.pdfPURE Prosperity 1 PURE Prosperity: The PURE Compensation Plan PURE Prosperity offers Independent Business Owners

PURE Prosperityimages.genesispure.com/web/pdf/GP_PURE_Prosperity.pdfPURE Prosperity 1 PURE Prosperity: The PURE Compensation Plan PURE Prosperity offers Independent Business Owners

PURE GENIUS AN IN N9 PURE

PURE GENIUS AN IN N9 PURE

UGANDA COUNTRY BRIEF P RIGHTS AND LAND … ·  · 2003-08-154.1 Contemporary Customary Tenure 10 4.2 The Land ... interventions and its impacts in Uganda. The preparation of this

UGANDA COUNTRY BRIEF P RIGHTS AND LAND … ·  · 2003-08-154.1 Contemporary Customary Tenure 10 4.2 The Land ... interventions and its impacts in Uganda. The preparation of this

XII ICSMFE, RIO 89-CONTRIBUTION IN SPECIAL LECTURE …victorfbdemello.com.br/arquivos/Publicacoes/154.1 - XII ICSMFE, RI… · pressures Cerro Pelado Darn, Cordoba, Argentina. Because

XII ICSMFE, RIO 89-CONTRIBUTION IN SPECIAL LECTURE …victorfbdemello.com.br/arquivos/Publicacoes/154.1 - XII ICSMFE, RI… · pressures Cerro Pelado Darn, Cordoba, Argentina. Because

2013 Product guide - Pure Health Pure Oil

2013 Product guide - Pure Health Pure Oil

PURE SESAME OIL(Dark) 170g PURE SESAME OIL(Dark) 1650g · PURE SESAME OIL(Dark) 170g PURE SESAME OIL(Dark) 1650g PURE SESAME OIL(Dark) 6.2floz (US market packaging design) PURE SESAME

PURE SESAME OIL(Dark) 170g PURE SESAME OIL(Dark) 1650g · PURE SESAME OIL(Dark) 170g PURE SESAME OIL(Dark) 1650g PURE SESAME OIL(Dark) 6.2floz (US market packaging design) PURE SESAME