YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.


 Dinah Tyler
 1 years ago
 Views:
Transcription
1 . Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure of ineres raes. A. There are hree reasons ha bonds wih he same ime o mauriy have differen YTM s. i. Differen probabiliy of defaul ii. Liquidiy iii. Taxes B. Bonds wih defaul risk will always have a posiive risk premium. i. Define he risk premium here as he difference (spread) beween he ineres raes on bonds wih defaul risk and he ineres rae on defaul free bonds. a) Treasuries are essenially defaul risk free. b) Bu corporae bonds and municipals are cerainly no defaul risk free. () How do we know how much defaul risk a corporae bond has? (2) There are wo major firms ha rank he deb of corporaions based on defaul risk. Moody s and S&P. (a) The bes bonds (leas likely o defaul) are hose raed AAA, hen here are AA, A, BBB, and anyhing raed below BBB is considered junk. C. Liquidiy should obviously have an affec on ineres raes. The harder i is o sell he bond he higher he ineres rae mus be o compensae invesors. i. Noe ha Treasuries are he mos liquid of bonds. They have he mos acive and larges marke. I is easy and fas o sell a Tbond. ii. The same canno be said for corporae bonds or muni s. These markes are much hinner and i akes much more ime o conver a bond in hese markes ino cash. D. Taxes if a bond ges special ax reamen hen i may have a lower ineres rae han bonds of similar risk, liquidiy, and mauriy. i. Muni s are exemp from federal axes ii. Flower bonds reasuries ha can be cashed in a par value o pay esae axes if he owner dies. E. Hence, YTM is posiively relaed o defaul risk. YTM is posiively relaed o liquidiy risk. YTM is negaively relaed o special ax reamen. 3. So, why do bonds wih differen imes o mauriy, bu similar risk characerisics have differen YTM s?
2 A. Anoher way o pu he same quesion is: Why does he yield curve (erm srucure) have a given shape? 4. Wha is he yield curve? A. The yield curve is also called he erm srucure of ineres raes B. The yield curve is simply a plo of yields o mauriy versus imes o mauriy. i. The ime o mauriy is also called he erm hence he name erm srucure of ineres raes. ii. Curve is usually drawn for bonds of equal qualiy a) Like Treasuries b) AAA or Junk (bonds wih raings below BBB) for corporae bonds. iii. Here is he erm srucure for Treasury securiies from yeserdays WSJ. iv. How do you read his? a) For Treasuries wih 3 monhs lef o mauriy he yield o mauriy is jus below 2%. For Treasuries wih 2 monhs lef o mauriy he yield o mauriy is abou.75%. For Treasuries wih 0 years lef o mauriy he yield o mauriy is jus below 5%. C. How does one draw a yield curve? 2
3 i. The way he WSJ has done i is o ake he YTM of he Treasury closes o he mauriy. Plo he poins and connec he dos. ii. The way he book does i is a bi more sophisicaed. a) Here hey calculae all he YTM s and imes o mauriies for all available Treasuries. b) Then fi a nonlinear spline hrough he daa. This is probably more accurae bu is cerainly no he only way o esimae a curve hrough he daa. D. Typically, he yield curve is upward sloping ha is long raes are ypically higher hen shor raes. Why? 5. Three heories o explain he erm srucure A. Expecaions hypohesis B. Marke segmenaion heory C. Liquidiy preference or Preferred habia heory. D. Expecaions hypohesis: Ineres raes on long erm bonds will equal an average of shorerm ineres raes ha people expec o occur. i. This heory assumes ha bonds of differen mauriy are perfec subsiues. ii. I.E. invesors are indifferen beween: a) Buying a oneyear bond and holding i o mauriy, hen buying anoher oneyear bond. b) Buying a woyear bond. iii. If hese porfolios are perfec subsiues hen he ineres rae on he woyear bond should be he average ineres rae of he wo oneyear bonds. i + i 2 e i 2 = + iv. And we could exend his ou for longererm bonds oo. v. Noice wha his implies hough. a) If he yield curve slopes up, hen shorraes are going o rise b) The yield curve ypically slopes up. c) Tha means if his hypohesis is correc hen we would ypically see shor raes increasing. Since shor raes ofen go up as well as go down, hen we have a problem wih his heory. 6. Marke segmenaion heory (he oher exreme) A. Marke for differen mauriy bonds are compleely separae. B. Bonds of differen mauriies are no subsiues a all. i. Here, people are assumed o only wan o purchase bonds ha mach heir invesmen horizon.  Maybe because hey are immunizing heir porfolio we will ge o his shorly. ii. A each mauriy he supply and demand for bonds deermines he ineres rae for ha mauriy. 3
4 iii. More demand for shor bonds implies higher prices of bonds and ha implies lower ineres raes. iv. Here we have a heory ha is consisen wih an upward sloping yield curve ha does no sugges ha shorerm raes will always be rising. C. BUT in his heory here is no reason for bonds of differen mauriies o be relaed a all. So, why do long raes ypically move up when shor raes move up? i. This heory canno accoun for he fac ha ineres raes a differen mauriies are relaed. 7. Liquidiy preference heory (preferred habia) A. This heory is a combinaion of he wo heories above. B. Ineres raes on longerm bonds are an average of expeced shorerm raes PLUS a erm or liquidiy premium ha depends on he supply and demand for bonds a ha mauriy. i + i 2 e + 2 = + k2 i 8. Here, if an invesor prefers he one period habia hey will normally buy one period bonds, bu if he premium for he woperiod bond is big enough hen hey can be induced o subsiue a woyear bond for a oneyear bond. 9. Now we have a heory ha explains why raes move ogeher and we can explain why he erm srucure ypically slopes up wihou he need o say ha shor raes mus be expeced o increase. A. The problem wih his heory is wha exacly deermines he erm premium. ) Wha is duraion? D = P = T ( + R) = P = R V c T = D = P ( + R ) c T ( + R ) ( + ) R = P R c 2) Well ha's nice bu wha does i mean? a) D = presenvalue weighed average of he mauriy of each cash flow. b) D measures he effec of unexpeced changes in ineres raes on an asse's rae of reurn. c) Think of i like his. i) Toal risk = marke risk plus unique (idiosyncraic) risk ii) The risk premium depends on marke risk, no unique risk 4
5 iii) Sandard deviaion measures oal risk iv) Bea measures marke risk which is nohing more hen changes in he rae of reurn of an asse due o unexpeced changes in general economic condiions such as naional income or ineres raes. v) Duraion is he par of bea ha depends on unexpeced changes in ineres raes. 3) Duraion is simply a measure of he ineres rae sensiiviy of an asse (or liabiliy). a) Large D means ha he price of ha asse is highly sensiive o changes in ineres raes. b) In fac, i is common o see he following approximaion. dp P dr D + R which says ha he percenage change in price is equal o he percenage change in he ineres rae imes negaive duraion. 4) A reasonable quesion o ask is jus how accurae is ha approximaion? a) The answer is i depends on he size of he ineres rae change or shock as i is someimes called. b) Duraion accuraely measures he price sensiiviy of fixedincome securiies for ineres rae changes on he order of one basis poin. Is ha good enough for mos ineres rae changes? i) The approximaion is definiely good enough for he ypical movemens in ineres raes. ii) Bu wha if Federal Reserve Chairman Greenspan decides o up he Fed Funds rae? These changes are almos always 25 or 50 basis poin changes. iii) For large ineres rae increases, duraion will over predic he fall in bond prices. iv) For large ineres rae decreases, duraion will under predic he increase in bond prices. 5) Pu differenly, for rae increase he capial loss effec ends o be smaller han he capial gain effec from rae decreases. i) This phenomenon is known as convexiy. ii) Le's look a an example. Suppose we have an 8%, $000 bond selling a par wih six years ill mauriy and paying annual coupons. This informaion is in he firs row of Table. 6) I used he Excel duraion funcion o calculae D = a) Wha happens o he price as he ineres rae changes? 7) This can be seen in he firs wo columns of Table. a) If he ineres rae suddenly goes o zero hen he price will become $480. 5
6 b) If he ineres rae jumps o 4% hen he price will become $ These prices are based on he sandard bond pricing equaion: he presen value of level sream of cash flows and he presen value of he face. c) The las column of he able shows he percenage change in he price given he changes in ineres raes. d) Remember ha we are looking a he change in price when he ineres rae changes from 8%. Table : Duraion Approximaion N Coupon Rae Price Duraion 6 $ % $, New Rae New Price D*dR/(+R) New Duraion based price dr/(+r) Duraion dp/p True dp/p 0.0% $, $, % $, $, % $, $, % $, $, % $, $, % $, $, % $, $, % $, $, % $ $ % $ $ % $ $ % $ $ % $ $ % $ $ % $ $
7 Duraion Approximaion vs. True Price 0.33 Dp/p DR/(+R) e) We can also esimae ha percenage change in price using he duraion formula above. i) Column 3 has he percenage change in price given he change in he ineres rae in column. ii) Again I used he Excel funcion for duraion. f) The prices based on he duraion approximaion are in column 4. 8) Already you can see ha he prices implied by he duraion approximaion are differen from he rue price changes. a) The las hree columns of he able have he percenage change in he ineres rae, he percenage change in price according o duraion, and he rue percenage change in price respecively. b) The figure plos he duraion esimaed percenage change in price and he acual percenage change in price agains he percenage change in ineres raes. c) In he graph i is easy o see ha he larger he ineres rae change he worse he esimae of price change prediced by D. 9) Remember he curved or convex line is he ruh here. 0) The amoun of curvaure in he line wha we mean by he erm convexiy. a) Aribues of convexiy i) Convexiy is a good hing. () The greaer he convexiy of a securiy or a porfolio of securiies, he more ineres rae proecion agains ineres rae increases and he greaer he gains for ineres rae decreases. (2) The higher he level of convexiy, he bigger he error made by using he duraion approximaion. 7
8 b) All fixed income securiies exhibi convexiy. c) Convexiy increases wih mauriy d) Longer erm bonds have more convexiy i) This is a posiive aribue of long erm bonds e) Convexiy varies wih coupon i) For wo bonds ha are exacly alike excep one has a lower coupon, he lower coupon bond will have more convexiy and higher duraion ii) For wo bonds wih equal duraion and yields, he lower coupon bond will have less convexiy. 8
Convexity. Concepts and Buzzwords. Dollar Convexity Convexity. Curvature, Taylor series, Barbell, Bullet. Convexity 1
Deb Insrumens and Markes Professor Carpener Convexiy Conceps and Buzzwords Dollar Convexiy Convexiy Curvaure, Taylor series, Barbell, Bulle Convexiy Deb Insrumens and Markes Professor Carpener Readings
More informationChapter 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
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO
Profi Tes Modelling in Life Assurance Using Spreadshees, par wo PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Erik Alm Peer Millingon Profi Tes Modelling in Life Assurance Using Spreadshees,
More informationDuration 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 UVAF38 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
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationFIN 472 FixedIncome Securities Approximating Price Changes: From Duration to Convexity Professor Robert B.H. Hauswald Kogod School of Business, AU
FIN 47 FixedIncome Securiies Approximaing rice Changes: From Duraion o Convexiy rofessor Rober B.H. Hauswald Kogod School of Business, AU Bond rice Volailiy Consider only IR as a risk facor Longer M means
More informationA 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
More informationMorningstar 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
More informationDerivatives. Forwards and Futures. Forward. Futures. Options. Initial Cost
Derivaives Forwards and Fuures A derivaive securiy is a securiy whose value depends on he values of oher more basic underlying variables. Forward The mos common derivaive securiies are forward, fuures
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder 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
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS 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 cuingedge
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More information4. 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
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationTREASURY BILL VERSUS PRIVATE MONEY MARKET YIELD CURVES
TREASURY BILL VERSUS PRIVATE MONEY MARKET YIELD CURVES Timohy D. Rowe, Thomas A. Lawler* and Timohy Q. Cook The relaionship beween ime o mauriy and yield on securiies is of widespread ineres o financial
More informationNewton's second law in action
Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In
More informationPart 1: White Noise and Moving Average Models
Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical
More informationWhat is a swap? A swap is a contract between two counterparties who agree to exchange a stream of payments over an agreed period of several years.
Currency swaps Wha is a swap? A swap is a conrac beween wo counerparies who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiyindexlinked
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationCVA calculation for CDS on super senior ABS CDO
MPRA Munich Personal RePEc Archive CVA calculaion for CDS on super senior AS CDO Hui Li Augus 28 Online a hp://mpra.ub.unimuenchen.de/17945/ MPRA Paper No. 17945, posed 19. Ocober 29 13:33 UC CVA calculaion
More informationTable 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
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationEntropy: From the Boltzmann equation to the Maxwell Boltzmann distribution
Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
More informationFair games, and the Martingale (or "Random walk") model of stock prices
Economics 236 Spring 2000 Professor Craine Problem Se 2: Fair games, and he Maringale (or "Random walk") model of sock prices Sephen F LeRoy, 989. Efficien Capial Markes and Maringales, J of Economic Lieraure,27,
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationChapter 5. Interest Rate Term Structure and ArbitrageFree Valuation
Universié ParisDauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Chaper 5. Ineres Rae Term Srucure and ArbirageFree Valuaion Yield curve Spo
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes  ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he kvalue for he middle erm, divide
More informationChapter 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
More informationPROFIT 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
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationHedging 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 buyside of a forward/fuures
More informationChapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Longerm debloosely, bonds wih a mauriy of one year or more Shorerm debless han a year o mauriy, also called unfunded deb Bondsricly
More informationTechnical Description of S&P 500 BuyWrite Monthly Index Composition
Technical Descripion of S&P 500 BuyWrie Monhly Index Composiion The S&P 500 BuyWrie Monhly (BWM) index is a oal reurn index based on wriing he nearby ahemoney S&P 500 call opion agains he S&P 500 index
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More informationEquities: 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
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More information2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity
.6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) 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
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationThe 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
More informationChapter 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
More informationVector 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), 101115. Macroeconomericians
More informationDiagnostic 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)
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 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
More informationTopic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING?
Chaper 10: THE BASICS OF CAPITAL BUDGETING Should we build his plan? Topic Overview Projec Types Capial Budgeing Decision Crieria Payback Period Discouned Payback Period Ne Presen Value () Inernal Rae
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More information11. Tire pressure. Here we always work with relative pressure. That s what everybody always does.
11. Tire pressure. The graph You have a hole in your ire. You pump i up o P=400 kilopascals (kpa) and over he nex few hours i goes down ill he ire is quie fla. Draw wha you hink he graph of ire pressure
More information1. Explain why the theory of purchasing power parity is often referred to as the law of one price.
Chaper Review Quesions. xplain why he heory of purchasing power pariy is ofen referred o as he law of one price. urchasing ower ariy () is referred o as he law of one price because he deerminaion of he
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationLecture III: Finish Discounted Value Formulation
Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More information4. The Poisson Distribution
Virual Laboraories > 13. The Poisson Process > 1 2 3 4 5 6 7 4. The Poisson Disribuion The Probabiliy Densiy Funcion We have shown ha he k h arrival ime in he Poisson process has he gamma probabiliy densiy
More information1. Fund types and population covered
Performance and financial overview of invesmen funds  France 1 March 016 The Banque de France draws up he following informaion for invesmen funds: 1 monhly saisics on fund ousandings and flows, and on
More informationCapital 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
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationComplex Fourier Series. Adding these identities, and then dividing by 2, or subtracting them, and then dividing by 2i, will show that
Mah 344 May 4, Complex Fourier Series Par I: Inroducion The Fourier series represenaion for a funcion f of period P, f) = a + a k coskω) + b k sinkω), ω = π/p, ) can be expressed more simply using complex
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationThe 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 zerocoupon or spo ineres rae and he forward rae. We also look a he yield curve. Invesors consider a bond yield
More informationReturn 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
More informationChapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )
Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationDuration Outline and Reading
Deb Isrumes ad Markes Professor Carpeer Duraio Oulie ad Readig Oulie Ieres Rae Sesiiviy Dollar Duraio Duraio Buzzwords Parallel shif Basis pois Modified duraio Macaulay duraio Readig Tuckma, Chapers 5
More informationChapter 8 Student Lecture Notes 81
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
More informationPricing 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
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationChapter 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
More informationCredit Index Options: the noarmageddon pricing measure and the role of correlation after the subprime crisis
Second Conference on The Mahemaics of Credi Risk, Princeon May 2324, 2008 Credi Index Opions: he noarmageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo  Join work
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationDefault Risk in Equity Returns
Defaul Risk in Equiy Reurns MRI VSSLOU and YUHNG XING * BSTRCT This is he firs sudy ha uses Meron s (1974) opion pricing model o compue defaul measures for individual firms and assess he effec of defaul
More informationThe Identification of the Response of Interest Rates to Monetary Policy Actions Using MarketBased Measures of Monetary Policy Shocks
The Idenificaion of he Response of Ineres Raes o Moneary Policy Acions Using MarkeBased Measures of Moneary Policy Shocks Daniel L. Thornon Federal Reserve Bank of S. Louis Phone (314) 4448582 FAX (314)
More informationChapter 8 Copyright Henning Umland All Rights Reserved
Chaper 8 Copyrigh 19972004 Henning Umland All Righs Reserved Rise, Se, Twiligh General Visibiliy For he planning of observaions, i is useful o know he imes during which a cerain body is above he horizon
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationIf You Are No Longer Able to Work
If You Are No Longer Able o Work NY STRS A Guide for Making Disabiliy Reiremen Decisions INTRODUCTION If you re forced o sop working because of a serious illness or injury, you and your family will be
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationFifth 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 besesimae provisions... 3 2.1
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationMath 201 Lecture 12: CauchyEuler Equations
Mah 20 Lecure 2: CauchyEuler Equaions Feb., 202 Many examples here are aken from he exbook. The firs number in () refers o he problem number in he UA Cusom ediion, he second number in () refers o he problem
More informationTerm 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 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationand Decay Functions f (t) = C(1± r) t / K, for t 0, where
MATH 116 Exponenial Growh and Decay Funcions Dr. Neal, Fall 2008 A funcion ha grows or decays exponenially has he form f () = C(1± r) / K, for 0, where C is he iniial amoun a ime 0: f (0) = C r is he rae
More informationGraduate Macro Theory II: Notes on Neoclassical Growth Model
Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.
More informationHANDOUT 14. A.) Introduction: Many actions in life are reversible. * Examples: Simple One: a closed door can be opened and an open door can be closed.
Inverse Funcions Reference Angles Inverse Trig Problems Trig Indeniies HANDOUT 4 INVERSE FUNCTIONS KEY POINTS A.) Inroducion: Many acions in life are reversible. * Examples: Simple One: a closed door can
More informationFixed 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, DK5230 Odense M,
More informationStochastic Calculus, Week 10. Definitions and Notation. TermStructure Models & Interest Rate Derivatives
Sochasic Calculus, Week 10 TermSrucure Models & Ineres Rae Derivaives Topics: 1. Definiions and noaion for he ineres rae marke 2. Termsrucure models 3. Ineres rae derivaives Definiions and Noaion Zerocoupon
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationWhen 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
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationSupplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect RiskTaking?
Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec RiskTaking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF
More informationMarkit 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 Semiannual
More informationChapter 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
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationChapter 6. First Order PDEs. 6.1 Characteristics The Simplest Case. u(x,t) t=1 t=2. t=0. Suppose u(x, t) satisfies the PDE.
Chaper 6 Firs Order PDEs 6.1 Characerisics 6.1.1 The Simples Case Suppose u(, ) saisfies he PDE where b, c are consan. au + bu = 0 If a = 0, he PDE is rivial (i says ha u = 0 and so u = f(). If a = 0,
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More information