Chapter 5. Interest Rate Term Structure and Arbitrage-Free Valuation
|
|
|
- Adelia Hodges
- 7 years ago
- Views:
Transcription
1 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Chaper 5. Ineres Rae Term Srucure and Arbirage-Free Valuaion Yield curve Spo raes Forward raes Term Srucure Theories Secion I. The yield curve (La courbe des aux de rendemen A. Definiion Graphical depicion of he relaionship beween he mauriy and he yield o mauriy on securiies of he same credi risk: Curve ( ; y( Treasury yield curve Example US Treasury yield curve February 8, 00 Mauriy Yield monh.68% monhs.7% 6 monhs.8% year.09% years.9% 5 years 4.8% 0 years 4.88% 0 years 5.8% Example con d US Treasury yield curve February 8, % 5.00% 4.88% 5.8% Yield o mauriy 4.00%.00%.00%.68%.7%.8%.09%.9% 4.8%.00% 0.00% monh monhs 6 monhs year years 5 years 0 years 0 years Mauriy
2 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example US Treasury yield curve December 000 and December % 5.50% 5.5% 5.48% 5.00% 5.% 4.99% 5.% 5.04% Yield o mauriy 4.50% 4.00%.50% 4.4%.00%.05% End of 000 End of 00.50% years 5 years 0 years 0 years Mauriy 4 Example con d German bund yield curve December 000 and December % 5.50% 5.4% 5.9% Yield o mauriy 5.00% 4.50% 4.46% 4.5% 4.4% 4.99% 4.85% 4.00% End of 000 End of 00.66%.50% years 5 years 0 years 0 years Mauriy 5 Example con d Japanese governmen bond yield curve December 000 and December 00.50%.%.00%.0% Yield o mauriy.50%.00% 0.97%.65%.7% 0.50% 0.48% 0.54% End of 000 End of % 0.% years 5 years 0 years 0 years Mauriy 6
3 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example con d UK gil yield curve December 000 and December % 5.50% End of 000 End of 00 Yield o mauriy 5.00% 5.6% 4.76% 5.6% 5.% 5.05% 4.88% 4.70% 4.50% 4.% 4.00% years 5 years 0 years 0 years Mauriy 7 Example con d French OAT yield curve December 000 and December % 5.50% 5.44% Yield o mauriy 5.00% 4.50% 4.00% 4.5% 4.59% 4.5% 5.06% 5.00%.7%.50% End of 000 End of 00.00% years 5 years 0 years 0 years Mauriy 8
4 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences B. Common shapes of he yield curve (Formes usuelles des courbes de aux de rendemen Yield Normal Yield Invered / (Inversée Mauriy Mauriy Yield Humped / (Bombée Yield Fla / (Plae Mauriy Mauriy 0 C. Missing mauriies and inerpolaion y = yield for mauriy y = yield for mauriy y = yield for mauriy < < No Treasury issue available for mauriy Linear inerpolaion o approximae y = ŷ y + y Example Mauriy Yield 6 monhs.8% year no issue years.9% years no issue 4 years no issue 5 years 4.8% 4
5 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example con d Linear inerpolaion For he -year mauriy 0.5 ŷ ˆ( year =.8% +.9% =.8%.5.5 For he -year mauriy ŷ ( year =.9% + 4.8% =.% For he 4-year mauriy ŷ ( 4 year =.9% + 4.8% =.76% Example con d Inerpolaed yield curve Yield 4.50% 4.00%.50%.00%.50%.00%.50%.00% 4.8% 76%.76%.%.9%.8%.8% 6 monhs year years years 4 years 5 years Mauriy 4 D. Yield spreads (Ecars de aux de rendemen Yield spread = Yield (bond X Yield (benchmark bond Yield spread = Yield ( -mauriy bond Yield ( -mauriy Treasury issue Compensaion for Credi risk Illiquidiy Opion risk 5 5
6 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences D. Yield spreads con d Absolue yield spread / Nominal spread = Yield(bond X Yield (benchmark bond Relaive yield spread = ( Yield(bond X Yield (benchmark bond / Yield (benchmark bond Yield raio = Yield(bond X / Yield (benchmark bond 6 Example 4 Mauriy Issuer Raing Yield Absolue Relaive Yield yield yield raio spread spread 5 years US Treasury Aaa/AAA 4.8% years General Elecric Aaa/AAA 4.9% 75 bp 7.94%.79 5 years Verizon Communicaions A/A+ 5.% 9 bp.5%. 7 Secion II. The spo rae curve (La courbe des aux zéro-coupon A. A bond is a package of zero-coupon bonds bond pays a series of annual cash flows ( CF T = Equivalen o a package of T zero-coupon bonds -year zero-coupon bond CF -year zero-coupon bond CF -year zero-coupon bond CF T-year zero-coupon bond CF T 8 6
7 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences No-arbirage heory CF = V marke value of a bond paying ( T Z marke value of a zero-coupon bond paying CF in year Z marke value of a zero-coupon bond paying CF in years Z marke value of a zero-coupon bond paying CF in years Z T marke value of a zero-coupon bond paying CF T in T years 9 No-arbirage heory con d Arbirage-free values T V = Z + Z Z Z Suppose V ( Z Z... Z... Z T = Ω > 0 Suppose Arbirage sraegy Sell he coupon bond Buy he zero-coupon bonds 0,000 imes Risk-free profi = 0,000 Ω 0 The spo rae curve Marke value of a zero-coupon bond z = spo rae Z CF = z Spo rae curve = graphical depicion of he relaionship beween he mauriy and he Treasury spo rae for ha mauriy: Curve ( ; z 7
8 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences B. Boosrapping (Méhode iéraive Marke value of N-year coupon securiy = N N N V = + N CF ( y Marke values of uni zero-coupon securiies T Z =,..., Z =,..., Z = z z zt T Arbirage-free values N N N V = CF Z = N N N N CF CF = = yn = z B. Boosrapping con d Deriving spo raes from yields CF CF = y z CF CF + CF = CF + y ( + ( + y z z... N CF CF = y z =... T CF CF = y z = N N T T N = T = N T Example 5 4 on-he-run Treasury issues Annual-pay bonds Nex coupon dae: year from now Bulle mauriy Mauriy Coupon rae Marke price year.50% 00 years 4.0% 00 years 4.70% 00 4 years 5.0%
9 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example 5 con d Yield curve Mauriy Yield year.50% years 4.0% years 4.70% 4 years 5.0% 5 Example 5 Boosrapping Deermining he -year spo rae = z = y =.50% y z Deermining he -year spo rae = + y ( y ( z + + z = z z z = 04.0 = 4.48% z 6 Example 5 Boosrapping Deermining he -year spo rae = + + y ( y ( y ( z z z = z z z z = = 4.75% ( z + z 7 9
10 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example 5 Boosrapping Deermining he 4-year spo rae y 4 4 y4 y4 y = z 4 z z z = z 4 z z z z4 = = 5.706% ( z + z z 8 Example 5 con d Mauriy Yield Spo rae year.50%.5000% years 4.0% 4.48% years 4.70% 4.75% 4 years 5.0% 5.706% 9 Pracice quesion Trading dae: April 0, 006 Selemen dae: April 5, 006 Four bonds raded ex-coupon OAT 5.5% 5% 007 OAT 5.5% 008 OAT 4% 009 OAT 5.5% 00 Each OAT pays annual coupons every 5h of April. Bulle redempion a par Nex coupon: year from now 0 0
11 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Pracice quesion con d Prices in he marke Securiy Mauriy dae Coupon rae Price OAT 5.5% 007 5/04/ % 0.75 OAT 5.5% 008 5/04/ % 0.8 OAT 4% 009 5/04/ % OAT 5.5% 00 5/04/ % 04.5 Deermine he yield curve. Deermine he spo rae curve. Pracice quesion con d Pracice quesion con d
12 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Pracice quesion con d 4 Pracice quesion con d 5 Pracice quesion Trading dae: November 0, 006 Selemen dae: December 5, 006 Four bonds raded cum-coupon OAT 5.5% 5% 007 OAT 5.5% 008 OAT 4% 009 OAT 5.5% 00 Each OAT pays annual coupons every 5h of April. Bulle redempion a par 6
13 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Pracice quesion con d Prices Securiy Mauriy dae Coupon rae Clean price OAT 5.5% 007 5/04/ % OAT 5.5% 008 5/04/ % 0.0 OAT 4% 009 5/04/ % OAT 5.5% 00 5/04/ % Deermine he spo rae curve from o years. 7 Pracice quesion con d 8 Pracice quesion con d 9
14 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Pracice quesion con d 40 Pracice quesion con d 4 Pracice quesion con d 4 4
15 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Pracice quesion con d 4 Pracice quesion con d 44 Pracice quesion con d 45 5
16 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences C. Spread measures relaive o a spo rae curve (Marges par rappor aux aux zéro-coupon N-year corporae bond V marke value, y yield Nominal spread (relaive o he yield curve s such ha N CF V = = N Treasury y = yn + s Treasury y + s 46 C. Spread measures relaive o a spo rae curve con d Zero-volailiy spread / Z-spread / Saic spread s such ha CF CF CF V = N ( + z + s' z + s' zn + s' N Opion-adjused spread (OAS s such ha CF ( z CF ( z V = z + s'' z + s'' CFN ( zn z + s'' N N 47 C. Spread measures relaive o a spo rae curve con d Spread measure Benchmark Compensaion for Nominal spread Yield curve Credi risk, illiquidiy, opion risk Z-spread Spo rae curve Credi risk, illiquidiy, opion risk OAS Spo rae curve Credi risk, illiquidiy Nominal spread Z-spread OAS = Z-spread ± opion cos Z-spread > OAS if opion graned o issuer Z-spread < OAS if opion graned o bondholder 48 6
17 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences D. Valuing using spo raes (Evaluaion par les aux zéro-coupon ( ; z, =,,T spo rae curve New Treasury issue X Annual coupon = c, firs coupon in one year N-year mauriy, bulle mauriy Similar liquidiy as oher Treasury issues Marke value V X? Corporae bond A: marke Annual coupon = c A, firs coupon in one year N A -year mauriy, bulle mauriy Z-spread s A Marke value V A? 49 D. Valuing using spo raes con d Arbirage-free value of he new Treasury issue X V c c c c + 00 = z ( + z ( + z ( + z N N Arbirage-free value of bond A A V = A c A c A c A c A z + s A A N ( ( A ( A + z + s + z + s + z A N + s 50 Example 6 Spo rae curve of Example 5 Corporaion Xra issue bonds Coupon rae = 6% 4-year mauriy, bulle mauriy Opion-free s coupon in one year Z-spread compensaing for credi risk and liquidiy risk = 0 bp Price Xra s bond using he arbirage-free approach. 5 7
18 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example 6 con d Spo rae curve z =.5%, z = 4.48%, z = 4.75%, z4 = 5.706% Arbirage-free value Xra V 6 6 = + +.5% +.% 4.48% +.% % +.% 5.706% +.% = Secion III. Forward raes (Les aux à erme A. Definiion Forward rae = spo rae prevailing a a fuure dae for a given mauriy sf s-year forward rae years from now spo rae deermined oday, prevailing in years for an s-year mauriy f -year forward rae year from now f -year forward rae years from now f -year forward rae years from now 5 B. Deriving forward raes z, z : spo raes f: -year forward rae year from now Alernaive Buy a -year zero coupon bond Buy a -year zero coupon bond, hen buy anoher one in year from now Amoun invesed a dae 0: X Indifferen oward he sraegies if same amoun in years 54 8
19 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Accrued amoun in years Invesing in he -year bond X ( + z ² Invesing wice in he -year bond X ( + z ( + f Indifferen if ( + z ( + f = ( + z ² f = [ ( + z ² / ( + z ] 55 -year implied forward raes General formula zm+ ( + z m+ fm = m m -year forward-rae curve ( m ; T f m m= T = longes mauriy of he spo rae curve 56 Example 7 Treasury spo rae curve of Example 5 -year forward-rae curve? Mauriy Yield Spo rae Forward rae year.50%.5000% --- years 4.0% 4.48%? years 4.70% 4.75%? 4 years 5.0% 5.706%? 57 9
20 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Example 7 con d -year implied forward rae in year z ( 4.48% f + = = = 4.945% z.5000% -year implied forward rae in years z ( 4.75% f + = = = 5.788% z 4.48% -year implied forward rae in years 4 4 z ( 5.706% f 4 + = = = 6.89% z 4.75% 58 Example 7 con d Shor-erm forward-rae curve Mauriy Yield Spo rae Forward rae year.50%.5000% --- years 4.0% 4.48% 4.945% years 4.70% 4.75% 5.788% 4 years 5.0% 5.706% 6.89% 59 C. Relaionship beween shor-erm forward raes and spo raes Implied forward-rae verify ( + z f = z ( ( ( + z + f = + z M z f = z z f = z M T z f = z T T T + + T 60 0
21 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences C. Relaionship beween shor-erm forward raes and spo raes con d z f = z z f f = z M z f f... f = z z f f... f f = z M z f f... f = z T T T C. Relaionship beween shor-erm forward raes and spo raes con d ( z f f... f = ( z z = z f f... f z = m= z f m 6 Example 7 Compuing z from forward raes = z f =.5% 4.945% 4.48% z = Compuing z from forward raes z = z f f =.5% 4.945% 5.788% = 4.75% Compuing z 4 from forward raes z 4 4 = z f f f = 4.5% 4.945% 5.788% 6.89% = 5.706% 6
22 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences D. Valuing using forward raes (Evaluaion par les aux à erme Arbirage-free valuaion wih spo raes = N CF V = z Relaionship beween spo raes and forward raes z ( ( ( ( 44 = + z f f f spo discoun facor forward discoun facor Arbirage-free valuaion wih forward raes V = N CF = z f m= m 64 Example 8 Forward rae curve of Example 5 Value a Treasury issue Coupon = 4 Firs coupon in one year -year mauriy 4 4 V = + +.5%.5% 4.945% % 4.945% 5.788% = E. Compuing any forward rae s f s-year forward rae in years from now mauring in +s years s+ ( + z = z f s s+ sf = s s zs+ z s + 66
23 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Secion IV. The deerminans of he ineres rae erm srucure A. Shor rae deerminaion Moneary policy implemened by he CB European Cenral Bank in he EMU Federal Reserve bank (Fed in he U.S. Tools Rae a which banks borrow funds o he CB Open marke operaions Bank reserve requiremens 67 B. Relaing shor-erm and longerm raes Theories explaining he erm srucure of ineres raes Expecaions Pure expecaions Theory (Luz, 940; Meiselman, 96 Liquidiy preference heory (Hicks, 946 Marke segmenaion Segmenaion Theory (Culberson, 957 Preferred habia heory (Modigliani & Such, The pure expecaions heory (La héorie des anicipaions non biaisées Pure or unbiased expecaions heory = for a given mauriy, he spo rae resuls from he expeced shor-erm ineres raes unil he considered mauriy dae -year rae such ha reurn (-year bond = reurn (-year bond & expeced reurn (-year bond purchased year from oday -year rae such ha reurn (-year bond = reurn (--year bond & expeced reurn (-year bond purchased - years from oday or reurn (-year bond = reurn (-year bond & expeced reurns (-year bond each year from year o - 69
24 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences. The pure expecaions heory con d Relaionship beween he spo discoun facor and he forward discoun facor z = z f... fm... f According o his heory, shor-erm forward raes are unbiased marke expecaions of fuure shor-erm spo raes fm = E0( z~ ( m where z~ ( m year spo rae prevailing in m years 70 Implicaions The erm srucure conains informaion. Pure expecaions Shape of he erm srucure Implicaion of he heory upward sloping raes expeced o rise downward sloping raes expeced o decline fla raes no expeced o change humped raes expeced o rise firs, hen fall 7. The liquidiy preference heory (La héorie de la préférence pour la liquidié According o his heory, implied forward raes are deermined by marke expecaions abou fuure shor-erm spo raes rae premium for greaer ineres rae risk / longer fund non-availabiliy f m = E0( z~ ( m + Lm Term srucure resuling from z = z E0( z( + L... E0( z( m + Lm... E0( z( + L wih L L... Lm... L 7 4
25 Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Implicaions Upward sloping erm srucure = mos frequenly observed ype The informaion conained in he erm srucure is biased by liquidiy premia. Liquidiy preference Shape of he erm srucure upward sloping downward sloping fla humped Implicaion of he heory raes expeced o rise, or fall, or remain unchanged raes expeced o decline raes expeced o decline raes expeced o fall in he long run bu unclear in he shor run 7. Marke segmenaion heory (La héorie de la segmenaion Each mauriy = independen marke secor Supply / demand ineres rae for each mauriy Any shape of he erm srucure possible Preferred habia heory (La héorie de l habia préféré Invesors prefer paricular mauriy secors Shif ou if given an inducemen = rae premium f m = E 0 ( z~ ( m + H m Term srucure resuling from z = z E0( z( + H... E0( z( m + Hm... E0( z( + H Any curve shape possible Informaion conained in he erm srucure biased 75 5
Chapter 9 Bond Prices and Yield
Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value
4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
Chapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Long-erm deb-loosely, bonds wih a mauriy of one year or more Shor-erm deb-less han a year o mauriy, also called unfunded deb Bond-sricly
The yield curve, and spot and forward interest rates Moorad Choudhry
he yield curve, and spo and forward ineres raes Moorad Choudhry In his primer we consider he zero-coupon or spo ineres rae and he forward rae. We also look a he yield curve. Invesors consider a bond yield
11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge
Pricing Single Name Credit Derivatives
Pricing Single Name Credi Derivaives Vladimir Finkelsein 7h Annual CAP Workshop on Mahemaical Finance Columbia Universiy, New York December 1, 2 Ouline Realiies of he CDS marke Pricing Credi Defaul Swaps
Fixed Income Analysis: Securities, Pricing, and Risk Management
Fixed Income Analysis: Securiies, Pricing, and Risk Managemen Claus Munk This version: January 23, 2003 Deparmen of Accouning and Finance, Universiy of Souhern Denmark, Campusvej 55, DK-5230 Odense M,
Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
Interest Rate Parity, Money Market Basis Swaps, and Cross-Currency Basis Swaps
Fixed Income Liquid Markes Research June 23 Ineres Rae Pariy, Money Marke Basis Swaps, and Cross-Currency Basis Swaps Bruce uckman, Pedro Porfirio Because he classic ineres rae pariy condiion requires
13. a. If the one-year discount factor is.905, what is the one-year interest rate?
CHAPTER 3: Pracice quesions 3. a. If he one-year discoun facor is.905, wha is he one-year ineres rae? = DF = + r 0.905 r = 0.050 = 0.50% b. If he wo-year ineres rae is 0.5 percen, wha is he wo-year discoun
BALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
Equities: Positions and Portfolio Returns
Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi
Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis
Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work
INSTITUTE OF ECONOMIC STUDIES
INIU O CONOMIC UDI aculy of social sciences of Charles Universiy uures Conracs Lecurer s Noes No. Course: inancial Marke Insrumens I eacher: Oldřich Dědek I. BAIC AUR O ORWARD AND UUR CONRAC. Classificaion
Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012
Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing Time-Varying Equiy Risk Premium The Japanese Sock Marke 1980-2012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA
Morningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
Chapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
ARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
Diagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
An Introductory Note on Two Curve Discounting 1
An Inroducory Noe on Two Curve Discouning LCH.Clearne Ld (LCH.Clearne), which operaes he world s leading ineres rae swap (IRS) clearing service, SwapClear, is o begin using he overnigh index swap (OIS)
Real Return Bonds, Inflation Expectations, and the Break-Even Inflation Rate Ian Christensen, Frédéric Dion, and Christopher Reid
Bank of Canada Banque du Canada Working Paper 2004-43 / Documen de ravail 2004-43 Real Reurn Bonds, Inflaion Expecaions, and he Break-Even Inflaion Rae by Ian Chrisensen, Frédéric Dion, and Chrisopher
The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
FORWARD AND FUTURES CONTRACTS
Page1 C H A P T E R 2 FORWARD AND FUTURES CONTRACTS 2.1 INTRODUCTION The main purpose of forward and fuures conracs is he managemen of risk. The exposure o risk as a resul of ransacing in he spo marke
Return Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
Chapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
I. Basic Concepts (Ch. 1-4)
(Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
Nikkei Stock Average Volatility Index Real-time Version Index Guidebook
Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying
Option Put-Call Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
The impact of Federal Reserve asset purchase programmes: another twist 1
Jack Meaning jm583@ken.ac.uk eng Zhu feng.zhu@bis.org The impac of ederal Reserve asse purchase programmes: anoher wis 1 This aricle examines he effeciveness of recen ederal Reserve asse purchase programmes.
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
OpenGamma Quantitative Research Multi-curves: Variations on a Theme
OpenGamma Quaniaive Research Muli-curves: Variaions on a Theme Marc Henrard marc@opengamma.com OpenGamma Quaniaive Research n. 6 Ocober 2012 Absrac The muli-curves framework is ofen implemened in a way
Term Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:
Pricing Fixed-Income Derivaives wih he Forward-Risk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK-8 Aarhus V, Denmark E-mail: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs
Cointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
Risk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
Description of the CBOE S&P 500 BuyWrite Index (BXM SM )
Descripion of he CBOE S&P 500 BuyWrie Index (BXM SM ) Inroducion. The CBOE S&P 500 BuyWrie Index (BXM) is a benchmark index designed o rack he performance of a hypoheical buy-wrie sraegy on he S&P 500
Are European Corporate Bond and Default Swap Markets Segmented?
Are European Corporae Bond and Defaul Swap Markes Segmened? Didier COSSIN IMD Inernaional Hongze LU IMD Inernaional HEC Universiy of Lausanne Research Paper N 33 March 005 FAME - Inernaional Cen er for
AP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
When Do TIPS Prices Adjust to Inflation Information?
When Do TIPS Prices Adjus o Inflaion Informaion? Quenin C. Chu a, *, Deborah N. Piman b, Linda Q. Yu c Augus 15, 2009 a Deparmen of Finance, Insurance, and Real Esae. The Fogelman College of Business and
Markit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual
PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
The Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
Introduction to Arbitrage Pricing
Inroducion o Arbirage Pricing Marek Musiela 1 School of Mahemaics, Universiy of New Souh Wales, 252 Sydney, Ausralia Marek Rukowski 2 Insiue of Mahemaics, Poliechnika Warszawska, -661 Warszawa, Poland
The Term Structure of Interest Rates CHAPTER 13
The Term Structure of Interest Rates CHAPTER 13 Chapter Summary Objective: To explore the pattern of interest rates for different-term assets. The term structure under certainty Forward rates Theories
MSCI Index Calculation Methodology
Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...
SHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013
SHB Gas Oil Index Rules v1.3 Version as of 1 January 2013 1. Index Descripions The SHB Gasoil index (he Index ) measures he reurn from changes in he price of fuures conracs, which are rolled on a regular
Capital budgeting techniques
Capial budgeing echniques A reading prepared by Pamela Peerson Drake O U T L I N E 1. Inroducion 2. Evaluaion echniques 3. Comparing echniques 4. Capial budgeing in pracice 5. Summary 1. Inroducion The
S&P GSCI Crude Oil Covered Call Index Methodology
S&P GSCI Crude Oil Covered Call Index Mehodology July 2014 S&P Dow Jones Indices: Index Mehodology Table of Conens Inroducion 3 Highlighs 3 The S&P GSCI Crude Oil Covered Call Index Mehodology 3 Definiions
The Interest Rate Risk of Mortgage Loan Portfolio of Banks
The Ineres Rae Risk of Morgage Loan Porfolio of Banks A Case Sudy of he Hong Kong Marke Jim Wong Hong Kong Moneary Auhoriy Paper presened a he Exper Forum on Advanced Techniques on Sress Tesing: Applicaions
Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities
Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao and Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics Previous Draf: 27 January 28 This Draf: 27 April 29
S&P 500 Dynamic VIX Futures Index Methodology
S&P 500 Dynamic VIX Fuures Index Mehodology April 2014 S&P Dow Jones Indices: Index Mehodology Table of Conens Inroducion 2 Highlighs 2 Family 2 Index Consrucion 3 Consiuens 3 Allocaions 3 Excess Reurn
Puttable and Extendible Bonds: Developing Interest Rate Derivatives for Emerging Markets
WP/03/01 Puable and Exendible Bonds: Developing Ineres Rae Derivaives for Emerging Markes Salih N. Nefci and André O. Sanos 003 Inernaional Moneary Fund WP/03/01 IMF Working Paper IMF Insiue Puable and
INDEX RULE BOOK Leverage, Short, and Bear Indices
INDEX RULE BOOK Leverage, Shor, and Bear Indices Version 14-01 Effecive from 1 June 2014 indices.euronex.com Index 1. Index Summary 1 2. Governance and Disclaimer 6 2.1 Indices 6 2.2 Compiler 6 2.3 Cases
Curve Building and Swap Pricing in the Presence of Collateral and Basis Spreads SIMON GUNNARSSON
Curve Building and Swap Pricing in he Presence of Collaeral and Basis Spreads SIMON GUNNARSSON Maser of Science Thesis Sockholm, Sweden 2013 Curve Building and Swap Pricing in he Presence of Collaeral
S&P/Valmer Indices Methodology
S&P/Valmer Indices Mehodology S&P Dow Jones Indices: Mehodology January 2016 Table of Conens Inroducion 4 Families 4 Eligibiliy Crieria 6 Eligible Securiies 6 Pricing 7 Timing of Changes 7 Sub- Rules 8
Lecture Note on the Real Exchange Rate
Lecure Noe on he Real Exchange Rae Barry W. Ickes Fall 2004 0.1 Inroducion The real exchange rae is he criical variable (along wih he rae of ineres) in deermining he capial accoun. As we shall see, his
Liquidity, Default, Taxes and Yields on Municipal Bonds
Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Liquidiy, Defaul, axes and Yields on Municipal Bonds Junbo Wang, Chunchi
Hedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures
Present Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
Chapter Four: Methodology
Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
The Determinants of Trade Credit: Vietnam Experience
Proceedings of he Second Asia-Pacific Conference on Global Business, Economics, Finance and Social Sciences (AP15Vienam Conference) ISBN: 978-1-63415-833-6 Danang, Vienam, 10-12 July 2015 Paper ID: V536
Conceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100...
Normal (Gaussian) Disribuion Probabiliy De ensiy 0.5 0. 0.5 0. 0.05 0. 0.9 0.8 0.7 0.6? 0.5 0.4 0.3 0. 0. 0 3.6 5. 6.8 8.4 0.6 3. 4.8 6.4 8 The Black-Scholes Shl Ml Moel... pricing opions an calculaing
One dictionary: Native language - English/English - native language or English - English
Faculy of Social Sciences School of Business Corporae Finance Examinaion December 03 English Dae: Monday 09 December, 03 Time: 4 hours/ 9:00-3:00 Toal number of pages including he cover page: 5 Toal number
SEB Commodity Sector Index Series. Index Rules January 2014
EB Commodiy ecor ndex eries ndex Rules January 2014 PART A 1. nroducion 1.1 ndex Descripion The EB Commodiy ecor ndex eries (The ndices ) is a family of benchmark indices ha covers all he major commodiy
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is
Fifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance
Fifh Quaniaive Impac Sudy of Solvency II (QIS 5) Naional guidance on valuaion of echnical provisions for German SLT healh insurance Conens 1 Inroducion... 2 2 Calculaion of bes-esimae provisions... 3 2.1
FUTURES AND OPTIONS. Professor Craig Pirrong Spring, 2007
FUTURES AND OPTIONS Professor Craig Pirrong Spring, 2007 Basics of Forwards and Fuures A forward conrac is an agreemen beween a buyer and a seller o ransfer ownership of some asse or commodiy ( he underlying
The Allocation of Interest Rate Risk and the Financial Sector
The Allocaion of Ineres Rae Risk and he Financial Secor Juliane Begenau Sanford Monika Piazzesi Sanford & NBER May 2012 Marin Schneider Sanford & NBER Absrac This paper sudies US banks exposure o ineres
Vector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians
Modeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling
Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se
Betting Against Beta
Being Agains Bea Andrea Frazzini and Lasse Heje Pedersen * This draf: May 10, 2013 Absrac. We presen a model wih leverage and margin consrains ha vary across invesors and ime. We find evidence consisen
Market Models for Inflation
Marke Models for Inflaion Ferhana Ahmad Lady Margare Hall Universiy of Oxford A hesis submied for he degree of Msc. in Mahemaical and Compuaional Finance Triniy 2008 This work is dedicaed o my family,
Outline. Role of Aggregate Planning. Role of Aggregate Planning. Logistics and Supply Chain Management. Aggregate Planning
Logisics and upply Chain Managemen Aggregae Planning 1 Ouline Role of aggregae planning in a supply chain The aggregae planning problem Aggregae planning sraegies mplemening aggregae planning in pracice
The determinants of credit spread changes in Japan
Bank of Japan Working Paper Series The deerminans of credi spread changes in Japan Shinsuke Ohyama * shinsuke.ooyama@bo.or.p Takuya Sugimoo ** No.07-E-4 February 007 Bank of Japan -1-1 Nihonbashi Hongoku-cho,
Liquidity Risk in the Sovereign Credit Default Swap Market
Liquidiy Risk in he Sovereign Credi Defaul Swap Marke Rob Sperna Weiland Absrac In his repor, which is an adapaion of a sudy we conduced a Rabobank, one of he larges financial insiuions in he Neherlands,
A Note on Construction of Multiple Swap Curves with and without Collateral
A Noe on Consrucion of Muliple Swap Curves wih and wihou Collaeral Masaaki Fujii, Yasufumi Shimada, Akihiko Takahashi Absrac There are now available wide variey
Heterogeneous Expectations and Bond Markets
Heerogeneous Expecaions and Bond Markes Wei Xiong and Hongjun Yan January 2008 Absrac This paper presens a dynamic equilibrium model of bond markes in which wo groups of agens hold heerogeneous expecaions
Inflation Expectations and the Evolution of U.S. Inflation
No. -4 Inflaion Expecaions and he Evoluion of U.S. Inflaion Jeffrey C. Fuhrer Absrac: Much recen commenary has cenered on he imporance of well-anchored inflaion expecaions as he foundaion of a well-behaved
Mortgage Convexity. Samuel G. Hanson. Harvard Business School shanson@hbs.edu. This draft: January 2014 First draft: July 2012.
Morgage Convexiy Samuel G. Hanson Harvard Business School shanson@hbs.edu This draf: January 214 Firs draf: July 212 Absrac Mos home morgages in he Unied Saes are fixed-rae loans wih an embedded prepaymen
LIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
CRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis
CRISES AND THE FLEXIBLE PRICE MONETARY MODEL Saranis Kalyviis Currency Crises In fixed exchange rae regimes, counries rarely abandon he regime volunarily. In mos cases, raders (or speculaors) exchange
Yield to Maturity Outline and Suggested Reading
Yield to Maturity Outline Outline and Suggested Reading Yield to maturity on bonds Coupon effects Par rates Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading
Contrarian insider trading and earnings management around seasoned equity offerings; SEOs
Journal of Finance and Accounancy Conrarian insider rading and earnings managemen around seasoned equiy offerings; SEOs ABSTRACT Lorea Baryeh Towson Universiy This sudy aemps o resolve he differences in
Methodology brief Introducing the J.P. Morgan Emerging Markets Bond Index Global (EMBI Global)
Mehodology brief Emerging Markes Bond Index The EMBI Global, which currenly includes 27 counries, has been creaed in response o invesor demand for a broader emerging markes deb benchmark The EMBI Global
Development Centre RESEARCH MEMORANDUM. Banking sector output measurement in the euro area a modified approach. Antonio Colangelo and Robert Inklaar
Universiy of Groningen Groningen Growh and Developmen Cenre Banking secor oupu measuremen in he euro area a modified approach Research Memorandum GD-117 Anonio Colangelo and Rober Inklaar RESEARCH MEMORANDUM
LEASING VERSUSBUYING
LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss
Chapter 8 Student Lecture Notes 8-1
Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
Chapter 6 Interest Rates and Bond Valuation
Chapter 6 Interest Rates and Bond Valuation Solutions to Problems P6-1. P6-2. LG 1: Interest Rate Fundamentals: The Real Rate of Return Basic Real rate of return = 5.5% 2.0% = 3.5% LG 1: Real Rate of Interest
Sovereign debt management and fiscal vulnerabilities
Sovereign deb managemen and fiscal vulnerabiliies Alessandro Missale 1 Absrac A wide consensus has emerged on he role of deb managemen in reducing fiscal vulnerabiliy by providing insurance agains macroeconomic
An Interest Rate Swap Volatility Index and Contract
Anonio Mele QUASaR Yoshiki Obayashi Applied Academics LLC Firs draf: November 10, 2009. This version: June 26, 2012. ABSTRACT Ineres rae volailiy and equiy volailiy evolve heerogeneously over ime, comoving
Chapter 7. Response of First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
Monetary Policy & Real Estate Investment Trusts *
Moneary Policy & Real Esae Invesmen Truss * Don Bredin, Universiy College Dublin, Gerard O Reilly, Cenral Bank and Financial Services Auhoriy of Ireland & Simon Sevenson, Cass Business School, Ciy Universiy
Financial Reporting for Employee Stock Options: Liabilities or Equity?
Financial Reporing for Employee Sock Opions: Liabiliies or Equiy? Mary E. Barh Sanford Universiy mbarh@sanford.edu Leslie D. Hodder Indiana Universiy lhodder@indiana.edu Sephen R. Subben The Universiy
Chapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how