Introduction to Financial Derivatives
|
|
- Geraldine Allison
- 5 years ago
- Views:
Transcription
1 Itroductio to Fiacial Derivatives Determiig Prices for Forwards ad Futures Week of October 1, 01 Where we are Last week: Itroductio to Iterest Rates, Future Value, Preset Value ad FRAs (Chapter 4, OFOD) This week: Revisit FRAs ad the we look at the Determiatio of Forward ad Futures Prices - Value (Chapter 5, OFOD) Next week: Iterest Rate Futures (Chapter 6, OFOD) Assigmet Assigmet For This Week (October 1 st ) Read: Hull Chapter 5 Problems (Due October 1 st ) Chapter 4: 5, 8, 9, 11, 1, 14, 16, ; 3 Chapter 4 (7e): 5, 8, 9, 11, 1, 14, 16, ; 7 Problems (Due October 8 th ) Chapter 5:, 4, 6, 7, 1, 16, 17, 0; 4 Chapter 5 (7e):, 4, 6, 7, 1, 16, 17, 0; For Next Week (October 8 th ) Read: Hull Chapter 6 Problems (Due October 8 th ) Chapter 5:, 4, 6, 7, 1, 16, 17, 0; 4 Chapter 5 (7e):, 4, 6, 7, 1, 16, 17, 0; 4 Problems (Due October 17 th ) Chapter 6: 4, 6, 9, 11, 14, 1; 6, 7 Chapter 6 (7e): 4, 6, 9, 11, 14, 1; 3, 4 Exams Midterm: October 1 th, 011 Fial: Thurs., Dec. 15 th, 9am 1oo 1.4 1
2 Pla for This Week Forward Rate Agreemet Look at FRAs (today, the:) Determiatio of Forward & Futures Prices Ivestmet Asset vs. Cosumptio Asset Forward Price for a Ivestmet Asset Whe the Ivestmet Asset has Icome/Divided Yield Value of Forward Cotracts Forward vs. Futures Pricig Forward ad Futures o Currecies Futures o Commodities Futures Details (carry, embedded optios) A forward rate agreemet (FRA) is a agreemet that a certai rate will apply to a specified pricipal, L, durig a certai future time period ( T 1 to T ) A FRA is equivalet to a agreemet where iterest at a predetermied rate, R K, is exchaged for iterest at the market rate, R M, If R K is received (paid), receiver (payer) value at T is L( R ( ) K RM)( T T1) L( RM RK)( T T1) FRAs are settled (w/payoff) at T 1 rather tha T : L( R R )( T T) L( R R )( T T) ( M K 1 ) 1 R ( T T) Futures Price vs. Expected Future Spot 1.5 M 1 M K M 1 1 R ( T T) Forward Rate Agreemet A FRA ca be preset valued by assumig that the forward iterest rate is certai to be realized A dealer who writes the FRA ca lock-i the forward rate to be paid or received at essetially o cost To receive, borrow to T 1 ad ivest to T Borrow $100 util T 1 ad ivest it to T T1 R 1 At T 1 you pay 100e T T R ad at T you receive 100e T Ad ormalizig, a deposit of 100 at T 1 returs (at T ): T RT T1 R T1 F T1, T T T1 100e 100e Hece, by defiitio of the forward rate, this rate o a ivestmet (to receive) has bee locked-i for the period T 1 to T Similarly, the dealer ca lock-i his borrowig cost from T 1 to T by borrowig util T ad ivestig to T Forward Rate Agreemet A FRA ca be preset valued by assumig that the forward iterest rate is certai to be realized Sice the dealer ca lock-i the forward rate, a cliet that wats to receive a fixed rate ca have the forward rate agreemet at the curret market forward rate at o cost (there is a fee charged by the dealer) The dealer just eters ito the trade o the last slide, ad o the cotract date ca deliver the cotract rate o the agreed upo pricipal to the cliet If the cliet wats a rate other tha the curret forward rate, he has to settle the differetial PV, up-frot this is how we establish the PV of the FRA for R K 1.8
3 FRA Valuatio Formulas PV of FRA where a fixed rate R K will be received o a pricipal L betwee times T 1 ad T is RT L( RK RF )( T T1 ) e PV of FRA where a fixed rate is paid is RT L( RF RK )( T T1 ) e R F is the forward rate for the period ad R is the zero rate for maturity T What compoudig frequecies are used i these formulas for R K, R F, ad R? R K & R F are defied by the period of the forward T T T 1 R is the cotiuously compouded rate 1.9 Duratio Bod Duratio is the (value-weighted) average time to receipt of cash Duratio, D, of a bod that provides cash flow c i at time t i is yt i c i e D t i i 1 B yti with price B cie ad (cotiuously compouded) yield y i 1 Sice a small chage i yield, y, leads to a chage i price as B db dy y ad yt B i So B y citie ad D y i 1 B The percetage chage i price is egatively related to a chage i yield. db dy i 1 c t e yti i i 1.10 Duratio Covexity Whe the yield y is expressed with compoudig m times per year BD y D B B y 1 y m y m 1 / The expressio D D* 1 y m defies D* ad it is referred to as Modified Duratio Duratio measures are importat for risk maagemet B D * y B Which exhibits the well kow characteristic for bods that yield ad price move i opposite directio Note that for cotiuous compoudig, duratio does t have to be modified The covexity of a bod is defied as 1 B C B y so that i 1 c t e yti i i B 1 D y C( y) B A useful result to show the limitatio of duratio hedgig as yield chages become larger the effect of the oliearity of the price-yield relatioship B 1.1 3
4 The Ed for Last Week Pla for This Week Questios? Now for this week 1.13 Determiatio of Forward & Futures Prices Ivestmet Asset vs. Cosumptio Asset Short Sellig & Arbitrage Forward Price for a Ivestmet Asset Whe the Ivestmet Asset has Icome/Divided Yield Value of Forward Cotracts Forward vs. Futures Pricig Forward ad Futures o Currecies Futures o Commodities Futures Details (carry, embedded optios) Futures Price vs. Expected Future Spot 1.14 Cosumptio vs. Ivestmet Assets Short Sellig Ivestmet assets are assets held by sigificat umbers of people purely for ivestmet purposes (Examples: gold, silver, stocks, bods) Cosumptio assets are assets held primarily for cosumptio (Examples: copper, oil, hogs, OJ) Ivestmet assets readily admit arbitrage ad therefore permit ratioal pricig of futures ad forwards from spot prices Cosumptio assets are slightly more ivolved Short sellig ivolves sellig securities you do ot ow Your broker borrows the securities from aother cliet ad sells them i the market i the usual way Margi accout provides protectio
5 Short Sellig (cotiued) At some stage you must buy the securities back so they ca be replaced i the accout of the cliet You must pay divideds ad other beefits the ower of the securities receives Notatio for Valuig Futures ad Forward Cotracts S 0 : Spot price today F 0 : Futures or forward price today T: Time util delivery date r: Risk-free iterest rate for maturity T (lets thik r ( T) 0 ) Whe Iterest Rates are Measured with Cotiuous Compoudig Arbitrage Example F 0 = S 0 e rt This equatio relates the forward price ad the spot price for ay ivestmet asset that provides o icome ad has o storage costs The relatioship is govered by the term, T, to the forward date ad the time value of moey, expressed through the term spot rate,
6 Whe a Ivestmet Asset Provides a Kow Dollar Icome Arbitrage Example F 0 = (S 0 I )e rt Where I is the preset value (at t = t 0 ) of the icome durig life of forward cotract Whe a Ivestmet Asset Provides a Kow Yield F 0 = S 0 e (r q )T Where q is the average yield, durig the life of the cotract (expressed with cotiuous compoudig), provided by the asset 1.3 Valuig a Forward Cotract Suppose that K is delivery price i a forward cotract ad F 0 is forward price that would apply to the cotract today (at t 0 ) The value of a log forward cotract, ƒ, o a asset w/o icome ad with delivery price K is rt f ( F0 K) e rt rt rt ( Se 0 Ke ) S0 Ke Similarly, for kow icome ad divided yield q f S0 I Ke rt ad qt rt f Se 0 Ke 1.4 6
7 Forward vs. Futures Prices Forward & futures prices usually assumed equal Whe iterest rates are ucertai they are, i theory, slightly differet: A strog positive correlatio betwee iterest rates ad the asset price implies that the futures price should be slightly higher tha the forward price A strog egative correlatio implies the reverse: futures price should be slightly lower tha forward price The differece is usually small eough to be igored for short dated futures Stock Idex Ca be viewed as a ivestmet asset payig a divided yield The futures price ad spot price relatioship is therefore F 0 = S 0 e (r q )T where q is the average divided yield o the portfolio represeted by the idex durig life of cotract The textbook will assume they are the same Stock Idex Idex Arbitrage For the formula to be true it is importat that the idex represet a ivestmet asset I other words, chages i the idex must correspod to chages i the value of a tradable portfolio The Nikkei idex viewed as a dollar umber does ot represet a ivestmet asset (See Busiess Sapshot 5.3, page 113) If S is value of Nikkei 5; the CME futures is 5xS We ca oly ivest i a PF worth 5xQxS (Q:$valueY) 1.7 Whe F 0 > S 0 e (r-q)t a arbitrageur buys the stocks uderlyig the idex ad sells futures Whe F 0 < S 0 e (r-q)t a arbitrageur buys futures ad shorts or sells the stocks uderlyig the idex 1.8 7
8 Idex Arbitrage Futures ad Forwards o Currecies Idex arbitrage ivolves simultaeous trades i futures ad may differet stocks Very ofte a computer is used to geerate the trades Occasioally (e.g., o Black Moday) simultaeous trades are ot possible ad the theoretical o-arbitrage relatioship betwee F 0 ad S 0 does ot hold A foreig currecy is aalogous to a security providig a divided yield The cotiuous divided yield is the foreig risk-free iterest rate It follows that if r f is the foreig risk-free iterest rate ( F S e r r f ) T Why the Relatio Must Be True Futures o Cosumptio Assets r T 1000e f uits of foreig currecy at time T r T 1000F f 0 e dollars at time T 1000 uits of foreig currecy at time zero 1000S 0 dollars at time zero rt 1000S 0 e dollars at time T F 0 S 0 e (r+u )T where u is the storage cost per uit time as a percet of the asset value. Alteratively, F 0 (S 0 +U )e rt where U is the preset value of the storage costs. Storage costs act as egative icome We might fid the iequality surprisig, but ot so for cosumptio commodities vs. ivestmet commodities (gold, silver): the iequality may hold!
9 The Cost of Carry The cost of carry, c, is the storage cost plus the iterest costs less the icome eared c=r for a o-divided payig stock c=r-q for a idex w/yield q (c=r-r f ) c=r-q+u w/storage rate u For a ivestmet asset F 0 = S 0 e ct For a cosumptio asset F 0 S 0 e ct The coveiece yield o the cosumptio asset, y, is defied so that F 0 = S 0 e (c y )T If c>y beefit of holdig < tha carry; short: deliver early Ear the iterest o moey received If c<y coveiece is better tha carry; short: deliver later 1.33 Futures Prices & Expected Future Spot Prices Suppose k is the expected retur required by ivestors o a asset We ca ivest F 0 e r T at the risk-free rate ad eter ito a log futures cotract so that there is a cash iflow of S T at maturity This shows that, with the required retur k rt kt ( Fe 0 ) E( ST ) e or ( r k) T F E( S ) e 0 T 1.34 Futures Prices & Future Spot Prices (cotiued) If the asset has o systematic risk, the k = r ad F 0 is a ubiased estimate of S T positive systematic risk (positively correlated with stocks), the k > r ad F 0 < E (S T ) ormal backwardatio egative systematic risk (egatively correlated with stocks), the k < r ad F 0 > E (S T ) cotago
Binomial Model. Stock Price Dynamics. The Key Idea Riskless Hedge
Biomial Model Stock Price Dyamics The value of a optio at maturity depeds o the price of the uderlyig stock at maturity. The value of the optio today depeds o the expected value of the optio at maturity
More informationCHAPTER 2 PRICING OF BONDS
CHAPTER 2 PRICING OF BONDS CHAPTER SUARY This chapter will focus o the time value of moey ad how to calculate the price of a bod. Whe pricig a bod it is ecessary to estimate the expected cash flows ad
More informationSection 3.3 Exercises Part A Simplify the following. 1. (3m 2 ) 5 2. x 7 x 11
123 Sectio 3.3 Exercises Part A Simplify the followig. 1. (3m 2 ) 5 2. x 7 x 11 3. f 12 4. t 8 t 5 f 5 5. 3-4 6. 3x 7 4x 7. 3z 5 12z 3 8. 17 0 9. (g 8 ) -2 10. 14d 3 21d 7 11. (2m 2 5 g 8 ) 7 12. 5x 2
More informationSubject CT1 Financial Mathematics Core Technical Syllabus
Subject CT1 Fiacial Mathematics Core Techical Syllabus for the 2018 exams 1 Jue 2017 Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig
More information1 The Power of Compounding
1 The Power of Compoudig 1.1 Simple vs Compoud Iterest You deposit $1,000 i a bak that pays 5% iterest each year. At the ed of the year you will have eared $50. The bak seds you a check for $50 dollars.
More informationChapter Four Learning Objectives Valuing Monetary Payments Now and in the Future
Chapter Four Future Value, Preset Value, ad Iterest Rates Chapter 4 Learig Objectives Develop a uderstadig of 1. Time ad the value of paymets 2. Preset value versus future value 3. Nomial versus real iterest
More informationad covexity Defie Macaulay duratio D Mod = r 1 = ( CF i i k (1 + r k) i ) (1.) (1 + r k) C = ( r ) = 1 ( CF i i(i + 1) (1 + r k) i+ k ) ( ( i k ) CF i
Fixed Icome Basics Cotets Duratio ad Covexity Bod Duratios ar Rate, Spot Rate, ad Forward Rate Flat Forward Iterpolatio Forward rice/yield, Carry, Roll-Dow Example Duratio ad Covexity For a series of cash
More informationChapter Four 1/15/2018. Learning Objectives. The Meaning of Interest Rates Future Value, Present Value, and Interest Rates Chapter 4, Part 1.
Chapter Four The Meaig of Iterest Rates Future Value, Preset Value, ad Iterest Rates Chapter 4, Part 1 Preview Develop uderstadig of exactly what the phrase iterest rates meas. I this chapter, we see that
More informationChapter Six. Bond Prices 1/15/2018. Chapter 4, Part 2 Bonds, Bond Prices, Interest Rates and Holding Period Return.
Chapter Six Chapter 4, Part Bods, Bod Prices, Iterest Rates ad Holdig Period Retur Bod Prices 1. Zero-coupo or discout bod Promise a sigle paymet o a future date Example: Treasury bill. Coupo bod periodic
More informationChapter 4: Time Value of Money
FIN 301 Class Notes Chapter 4: Time Value of Moey The cocept of Time Value of Moey: A amout of moey received today is worth more tha the same dollar value received a year from ow. Why? Do you prefer a
More information2. The Time Value of Money
2. The Time Value of Moey Problem 4 Suppose you deposit $100 i the bak today ad it ears iterest at a rate of 10% compouded aually. How much will be i the accout 50 years from today? I this case, $100 ivested
More information1 Savings Plans and Investments
4C Lesso Usig ad Uderstadig Mathematics 6 1 Savigs las ad Ivestmets 1.1 The Savigs la Formula Lets put a $100 ito a accout at the ed of the moth. At the ed of the moth for 5 more moths, you deposit $100
More informationChapter 3. Compound interest
Chapter 3 Compoud iterest 1 Simple iterest ad compoud amout formula Formula for compoud amout iterest is: S P ( 1 Where : S: the amout at compoud iterest P: the pricipal i: the rate per coversio period
More informationFirst determine the payments under the payment system
Corporate Fiace February 5, 2008 Problem Set # -- ANSWERS Klick. You wi a judgmet agaist a defedat worth $20,000,000. Uder state law, the defedat has the right to pay such a judgmet out over a 20 year
More information7 Swaps. Overview. I have friends in overalls whose friendship I would not swap for the favor of the kings of the world. Thomas A.
7 Swaps I have frieds i overalls whose friedship I would ot swap for the favor of the kigs of the world. Thomas A. Ediso Overview Mechaics of iterest rate swaps Day cout issues (Cofirmatios skip) The comparative-advatage
More informationFixed Income Securities
Prof. Stefao Mazzotta Keesaw State Uiversity Fixed Icome Securities FIN4320. Fall 2006 Sample First Midterm Exam Last Name: First Name: Studet ID Number: Exam time is: 80 miutes. Total poits for this exam
More information1 Basic Growth Models
UCLA Aderso MGMT37B: Fudametals i Fiace Fall 015) Week #1 rofessor Eduardo Schwartz November 9, 015 Hadout writte by Sheje Hshieh 1 Basic Growth Models 1.1 Cotiuous Compoudig roof: lim 1 + i m = expi)
More informationUsing Math to Understand Our World Project 5 Building Up Savings And Debt
Usig Math to Uderstad Our World Project 5 Buildig Up Savigs Ad Debt Note: You will have to had i aswers to all umbered questios i the Project Descriptio See the What to Had I sheet for additioal materials
More informationFixed Income Securities
Prof. Stefao Mazzotta Keesaw State Uiversity Fixed Icome Securities Sample First Midterm Exam Last Name: First Name: Studet ID Number: Exam time is: 80 miutes. Total poits for this exam is: 400 poits Prelimiaries
More informationAPPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES
APPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES Example: Brado s Problem Brado, who is ow sixtee, would like to be a poker champio some day. At the age of twety-oe, he would
More informationCourse FM/2 Practice Exam 1 Solutions
Course FM/2 Practice Exam 1 Solutios Solutio 1 D Sikig fud loa The aual service paymet to the leder is the aual effective iterest rate times the loa balace: SP X 0.075 To determie the aual sikig fud paymet,
More informationCAPITAL PROJECT SCREENING AND SELECTION
CAPITAL PROJECT SCREEIG AD SELECTIO Before studyig the three measures of ivestmet attractiveess, we will review a simple method that is commoly used to scree capital ivestmets. Oe of the primary cocers
More informationWhere a business has two competing investment opportunities the one with the higher NPV should be selected.
Where a busiess has two competig ivestmet opportuities the oe with the higher should be selected. Logically the value of a busiess should be the sum of all of the projects which it has i operatio at the
More informationClass Sessions 2, 3, and 4: The Time Value of Money
Class Sessios 2, 3, ad 4: The Time Value of Moey Associated Readig: Text Chapter 3 ad your calculator s maual. Summary Moey is a promise by a Bak to pay to the Bearer o demad a sum of well, moey! Oe risk
More informationNPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE)
NPTEL DEPARTMENT OF INDUSTRIAL AND MANAGEMENT ENGINEERING IIT KANPUR QUANTITATIVE FINANCE END-TERM EXAMINATION (2015 JULY-AUG ONLINE COURSE) READ THE INSTRUCTIONS VERY CAREFULLY 1) Time duratio is 2 hours
More informationKEY INFORMATION DOCUMENT CFD s Generic
KEY INFORMATION DOCUMENT CFD s Geeric KEY INFORMATION DOCUMENT - CFDs Geeric Purpose This documet provides you with key iformatio about this ivestmet product. It is ot marketig material ad it does ot costitute
More informationChapter 13 Binomial Trees. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull
Chapter 13 Biomial Trees 1 A Simple Biomial Model! A stock price is curretly $20! I 3 moths it will be either $22 or $18 Stock price $20 Stock Price $22 Stock Price $18 2 A Call Optio (Figure 13.1, page
More informationThe Time Value of Money in Financial Management
The Time Value of Moey i Fiacial Maagemet Muteau Irea Ovidius Uiversity of Costata irea.muteau@yahoo.com Bacula Mariaa Traia Theoretical High School, Costata baculamariaa@yahoo.com Abstract The Time Value
More informationCourse FM Practice Exam 1 Solutions
Course FM Practice Exam 1 Solutios Solutio 1 D Sikig fud loa The aual service paymet to the leder is the aual effective iterest rate times the loa balace: SP X 0.075 To determie the aual sikig fud paymet,
More informationFinancial Analysis. Lecture 4 (4/12/2017)
Fiacial Aalysis Lecture 4 (4/12/217) Fiacial Aalysis Evaluates maagemet alteratives based o fiacial profitability; Evaluates the opportuity costs of alteratives; Cash flows of costs ad reveues; The timig
More information2013/4/9. Topics Covered. Principles of Corporate Finance. Time Value of Money. Time Value of Money. Future Value
3/4/9 Priciples of orporate Fiace By Zhag Xiaorog : How to alculate s Topics overed ad Future Value Net NPV Rule ad IRR Rule Opportuity ost of apital Valuig Log-Lived Assets PV alculatio Short uts ompoud
More informationModels of Asset Pricing
APPENDIX 1 TO CHAPTER 4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More informationModels of Asset Pricing
APPENDIX 1 TO CHAPTER4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More information43. A 000 par value 5-year bod with 8.0% semiaual coupos was bought to yield 7.5% covertible semiaually. Determie the amout of premium amortized i the 6 th coupo paymet. (A).00 (B).08 (C).5 (D).5 (E).34
More information0.07. i PV Qa Q Q i n. Chapter 3, Section 2
Chapter 3, Sectio 2 1. (S13HW) Calculate the preset value for a auity that pays 500 at the ed of each year for 20 years. You are give that the aual iterest rate is 7%. 20 1 v 1 1.07 PV Qa Q 500 5297.01
More informationSTRAND: FINANCE. Unit 3 Loans and Mortgages TEXT. Contents. Section. 3.1 Annual Percentage Rate (APR) 3.2 APR for Repayment of Loans
CMM Subject Support Strad: FINANCE Uit 3 Loas ad Mortgages: Text m e p STRAND: FINANCE Uit 3 Loas ad Mortgages TEXT Cotets Sectio 3.1 Aual Percetage Rate (APR) 3.2 APR for Repaymet of Loas 3.3 Credit Purchases
More informationSIMPLE INTEREST, COMPOUND INTEREST INCLUDING ANNUITY
Chapter SIMPLE INTEREST, COMPOUND INTEREST INCLUDING ANNUITY 006 November. 8,000 becomes 0,000 i two years at simple iterest. The amout that will become 6,875 i years at the same rate of iterest is:,850
More informationLecture 16 Investment, Time, and Risk (Basic issues in Finance)
Lecture 16 Ivestmet, Time, ad Risk (Basic issues i Fiace) 1. Itertemporal Ivestmet Decisios: The Importace o Time ad Discoutig 1) Time as oe o the most importat actors aectig irm s ivestmet decisios: A
More informationDate: Practice Test 6: Compound Interest
: Compoud Iterest K: C: A: T: PART A: Multiple Choice Questios Istructios: Circle the Eglish letter of the best aswer. Circle oe ad ONLY oe aswer. Kowledge/Thikig: 1. Which formula is ot related to compoud
More informationModels of Asset Pricing
4 Appedix 1 to Chapter Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More informationWe learned: $100 cash today is preferred over $100 a year from now
Recap from Last Week Time Value of Moey We leared: $ cash today is preferred over $ a year from ow there is time value of moey i the form of willigess of baks, busiesses, ad people to pay iterest for its
More informationClass Notes for Managerial Finance
Class Notes for Maagerial Fiace These otes are a compilatio from:. Class Notes Supplemet to Moder Corporate Fiace Theory ad Practice by Doald R. Chambers ad Nelso J. Lacy. I gratefully ackowledge the permissio
More informationFINANCIAL MATHEMATICS
CHAPTER 7 FINANCIAL MATHEMATICS Page Cotets 7.1 Compoud Value 116 7.2 Compoud Value of a Auity 117 7.3 Sikig Fuds 118 7.4 Preset Value 121 7.5 Preset Value of a Auity 121 7.6 Term Loas ad Amortizatio 122
More informationBond Valuation. Structure of fixed income securities. Coupon Bonds. The U.S. government issues bonds
Structure of fixed icome securities Bod Valuatio The Structure of fixed icome securities Price & ield to maturit (tm) Term structure of iterest rates Treasur STRIPS No-arbitrage pricig of coupo bods A
More informationCalculation of the Annual Equivalent Rate (AER)
Appedix to Code of Coduct for the Advertisig of Iterest Bearig Accouts. (31/1/0) Calculatio of the Aual Equivalet Rate (AER) a) The most geeral case of the calculatio is the rate of iterest which, if applied
More informationAppendix 1 to Chapter 5
Appedix 1 to Chapter 5 Models of Asset Pricig I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy a asset, we are
More informationDriver s. 1st Gear: Determine your asset allocation strategy.
Delaware North 401(k) PLAN The Driver s Guide The fial step o your road to erollig i the Delaware North 401(k) Pla. At this poit, you re ready to take the wheel ad set your 401(k) i motio. Now all that
More informationof Asset Pricing R e = expected return
Appedix 1 to Chapter 5 Models of Asset Pricig EXPECTED RETURN I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy
More informationLecture 2. Tuesday Feb 3 rd. Time Value of Money 1
Lecture 2. Tuesday Feb 3 rd Time Value of Moey 1 What is Moey? Moey is a promise A Eglish Bakote says: I promise to pay the Bearer o demad the sum of twety pouds Ad it is siged by the Chief Cashier of
More informationMark to Market Procedures (06, 2017)
Mark to Market Procedures (06, 207) Risk Maagemet Baco Sumitomo Mitsui Brasileiro S.A CONTENTS SCOPE 4 2 GUIDELINES 4 3 ORGANIZATION 5 4 QUOTES 5 4. Closig Quotes 5 4.2 Opeig Quotes 5 5 MARKET DATA 6 5.
More informationChapter 11 Appendices: Review of Topics from Foundations in Finance and Tables
Chapter 11 Appedices: Review of Topics from Foudatios i Fiace ad Tables A: INTRODUCTION The expressio Time is moey certaily applies i fiace. People ad istitutios are impatiet; they wat moey ow ad are geerally
More informationInstitute of Actuaries of India Subject CT5 General Insurance, Life and Health Contingencies
Istitute of Actuaries of Idia Subject CT5 Geeral Isurace, Life ad Health Cotigecies For 2017 Examiatios Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which
More informationCAPITAL ASSET PRICING MODEL
CAPITAL ASSET PRICING MODEL RETURN. Retur i respect of a observatio is give by the followig formula R = (P P 0 ) + D P 0 Where R = Retur from the ivestmet durig this period P 0 = Curret market price P
More informationMATH : EXAM 2 REVIEW. A = P 1 + AP R ) ny
MATH 1030-008: EXAM 2 REVIEW Origially, I was havig you all memorize the basic compoud iterest formula. I ow wat you to memorize the geeral compoud iterest formula. This formula, whe = 1, is the same as
More informationHighest Daily Lifetime Seven SM Spousal Highest Daily Lifetime Seven SM
Optioal Icome beefits Highest Daily Lifetime Seve SM Spousal Highest Daily Lifetime Seve SM Daily Opportuities to Capture Greater Lifetime Icome HD Lifetime Seve ad Spousal HD Lifetime Seve Offer:» Miimum
More informationof Asset Pricing APPENDIX 1 TO CHAPTER EXPECTED RETURN APPLICATION Expected Return
APPENDIX 1 TO CHAPTER 5 Models of Asset Pricig I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy a asset, we are
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS This set of sample questios icludes those published o the iterest theory topic for use with previous versios of this examiatio.
More informationWhen you click on Unit V in your course, you will see a TO DO LIST to assist you in starting your course.
UNIT V STUDY GUIDE Percet Notatio Course Learig Outcomes for Uit V Upo completio of this uit, studets should be able to: 1. Write three kids of otatio for a percet. 2. Covert betwee percet otatio ad decimal
More informationOnline appendices from Counterparty Risk and Credit Value Adjustment a continuing challenge for global financial markets by Jon Gregory
Olie appedices from Couterparty Risk ad Credit Value Adjustmet a APPENDIX 8A: Formulas for EE, PFE ad EPE for a ormal distributio Cosider a ormal distributio with mea (expected future value) ad stadard
More information2. Find the annual percentage yield (APY), to the nearest hundredth of a %, for an account with an APR of 12% with daily compounding.
1. Suppose that you ivest $4,000 i a accout that ears iterest at a of 5%, compouded mothly, for 58 years. `Show the formula that you would use to determie the accumulated balace, ad determie the accumulated
More informationSubject CT5 Contingencies Core Technical. Syllabus. for the 2011 Examinations. The Faculty of Actuaries and Institute of Actuaries.
Subject CT5 Cotigecies Core Techical Syllabus for the 2011 Examiatios 1 Jue 2010 The Faculty of Actuaries ad Istitute of Actuaries Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical
More informationPension Annuity. Policy Conditions Document reference: PPAS1(6) This is an important document. Please keep it in a safe place.
Pesio Auity Policy Coditios Documet referece: PPAS1(6) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity. These
More information1 + r. k=1. (1 + r) k = A r 1
Perpetual auity pays a fixed sum periodically forever. Suppose a amout A is paid at the ed of each period, ad suppose the per-period iterest rate is r. The the preset value of the perpetual auity is A
More information1 Random Variables and Key Statistics
Review of Statistics 1 Radom Variables ad Key Statistics Radom Variable: A radom variable is a variable that takes o differet umerical values from a sample space determied by chace (probability distributio,
More informationTIME VALUE OF MONEY 6.1 TIME VALUE OF MONEY
C h a p t e r TIME VALUE O MONEY 6. TIME VALUE O MONEY The idividual s preferece for possessio of give amout of cash ow, rather tha the same amout at some future time, is called Time preferece for moey.
More informationENGINEERING ECONOMICS
ENGINEERING ECONOMICS Ref. Grat, Ireso & Leaveworth, "Priciples of Egieerig Ecoomy'','- Roald Press, 6th ed., New York, 1976. INTRODUCTION Choice Amogst Alteratives 1) Why do it at all? 2) Why do it ow?
More informationAsset Valuation with known cash flows. Annuities and Perpetuities care loan, saving for retirement, mortgage
Asset Valuatio with kow cash flows Auities ad Perpetuities care loa, savig for retiremet, mortgage Simple Perpetuity A perpetuity is a stream of cash flows each of the amout of dollars, that are received
More informationChapter 5: Sequences and Series
Chapter 5: Sequeces ad Series 1. Sequeces 2. Arithmetic ad Geometric Sequeces 3. Summatio Notatio 4. Arithmetic Series 5. Geometric Series 6. Mortgage Paymets LESSON 1 SEQUENCES I Commo Core Algebra I,
More informationAnomaly Correction by Optimal Trading Frequency
Aomaly Correctio by Optimal Tradig Frequecy Yiqiao Yi Columbia Uiversity September 9, 206 Abstract Uder the assumptio that security prices follow radom walk, we look at price versus differet movig averages.
More informationAnnual compounding, revisited
Sectio 1.: No-aual compouded iterest MATH 105: Cotemporary Mathematics Uiversity of Louisville August 2, 2017 Compoudig geeralized 2 / 15 Aual compoudig, revisited The idea behid aual compoudig is that
More informationMafatlal Centre, 10th Floor, Nariman Point, Mumbai CIN: U65991MH1996PTC Tel.: Fax:
Mafatlal Cetre, 10th Floor, Narima Poit, Mumbai - 400 021 CIN: U65991MH1996PTC100444 Tel.: 91-22 66578000 Fax: 91-22 66578181 www.dspblackrock.com Jauary 8, 2018 Dear Uit Holder, Sub: Chage i Fudametal
More informationDr. Maddah ENMG 602 Intro to Financial Eng g 01/18/10. Fixed-Income Securities (2) (Chapter 3, Luenberger)
Dr Maddah ENMG 60 Itro to Fiacial Eg g 0/8/0 Fixed-Icome Securities () (Chapter 3 Lueberger) Other yield measures Curret yield is the ratio of aual coupo paymet to price C CY = For callable bods yield
More informationPPI Investment Advice
Tailored property advice ad solutios PPI Ivestmet Advice www.ppiivestmetadvice.com.au portfoliopropertyivestmets.com.au/propertycoach AFSL umber 276 895 PPI, chagig the property ivestig ladscape! Everythig
More information0.1 Valuation Formula:
0. Valuatio Formula: 0.. Case of Geeral Trees: q = er S S S 3 S q = er S S 4 S 5 S 4 q 3 = er S 3 S 6 S 7 S 6 Therefore, f (3) = e r [q 3 f (7) + ( q 3 ) f (6)] f () = e r [q f (5) + ( q ) f (4)] = f ()
More informationliving well in retirement Adjusting Your Annuity Income Your Payment Flexibilities
livig well i retiremet Adjustig Your Auity Icome Your Paymet Flexibilities what s iside 2 TIAA Traditioal auity Icome 4 TIAA ad CREF Variable Auity Icome 7 Choices for Adjustig Your Auity Icome 7 Auity
More informationSCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME
All Right Reserved No. of Pages - 10 No of Questios - 08 SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME YEAR I SEMESTER I (Group B) END SEMESTER EXAMINATION
More informationFEHB. Health Benefits Coverage for Noncareer Employees
FEHB Health Beefits Coverage for Nocareer Employees Notice 426 September 2005 The Federal Employees Health Beefits (FEHB) Program permits certai ocareer (temporary) employees to obtai health isurace, if
More informationRisk transfer mechanisms - converging insurance, credit and financial markets
Risk trasfer mechaisms - covergig isurace, credit ad fiacial markets Presetatio at OECD/CIRC Techical Expert meetig o Reisurace, Jue 2002. Jes Verer Aderse, OECD 1 Outlie Itroductio Growth of risk trasfer
More informationThe Time Value of Money
Part 2 FOF12e_C03.qxd 8/13/04 3:39 PM Page 39 Valuatio 3 The Time Value of Moey Cotets Objectives The Iterest Rate After studyig Chapter 3, you should be able to: Simple Iterest Compoud Iterest Uderstad
More information(Zip Code) OR. (State)
Uiform Applicatio for Ivestmet Adviser Registratio Part II - Page 1 Name of Ivestmet Adviser: Stephe Craig Schulmerich Address: (Number ad Street) 10260 SW Greeburg Rd. Ste 00 (State) (City) Portlad (Zip
More informationSolutions to Interest Theory Sample Questions
to Iterest Theory Sample Questios Solutio 1 C Chapter 4, Iterest Rate Coversio After 7.5 years, the value of each accout is the same: 7.5 7.5 0.04 1001 100e 1.336 e l(1.336) 7.5 0.0396 7.5 Solutio E Chapter
More informationCHAPTER II: FIXED INCOME SECURITIES AND MARKETS
CHAPTER II: FIXED INCOME SECURITIES AND MARKETS 30 FIXED INCOME PORTFOLIO MANAGEMENT A: TYPES OF FIXED INCOME SECURITIES I terms of dollar volume, the U.S. markets for debt istrumets are larger tha for
More informationREINSURANCE ALLOCATING RISK
6REINSURANCE Reisurace is a risk maagemet tool used by isurers to spread risk ad maage capital. The isurer trasfers some or all of a isurace risk to aother isurer. The isurer trasferrig the risk is called
More informationMS-E2114 Investment Science Exercise 2/2016, Solutions
MS-E24 Ivestmet Sciece Exercise 2/206, Solutios 26.2.205 Perpetual auity pays a xed sum periodically forever. Suppose a amout A is paid at the ed of each period, ad suppose the per-period iterest rate
More informationDr. Maddah ENMG 624 Financial Eng g I 03/22/06. Chapter 6 Mean-Variance Portfolio Theory
Dr Maddah ENMG 64 Fiacial Eg g I 03//06 Chapter 6 Mea-Variace Portfolio Theory Sigle Period Ivestmets Typically, i a ivestmet the iitial outlay of capital is kow but the retur is ucertai A sigle-period
More information1031 Tax-Deferred Exchanges
1031 Tax-Deferred Exchages About the Authors Arold M. Brow Seior Maagig Director, Head of 1031 Tax-Deferred Exchage Services, MB Fiacial Deferred Exchage Corporatio Arold M. Brow is the Seior Maagig Director
More informationMath of Finance Math 111: College Algebra Academic Systems
Math of Fiace Math 111: College Algebra Academic Systems Writte By Bria Hoga Mathematics Istructor Highlie Commuity College Edited ad Revised by Dusty Wilso Mathematics Istructor Highlie Commuity College
More informationCurrent Year Income Assessment Form 2017/18
Curret Year Icome Assessmet Form 2017/18 Persoal details Your Customer Referece Number Your Customer Referece Number Name Name Date of birth Address / / Date of birth / / Address Postcode Postcode If you
More informationQuarterly Update First Quarter 2018
EDWARD JONES ADVISORY SOLUTIONS Quarterly Update First Quarter 2018 www.edwardjoes.com Member SIPC Key Steps to Fiacial Success We Use a Established Process 5 HOW CAN I STAY ON TRACK? 4 HOW DO I GET THERE?
More informationAccumUL Plus. United of Omaha Life Insurance Company A Mutual of Omaha Company. product guide
Uited of Omaha Life Isurace Compay A Mutual of Omaha Compay AccumUL Plus product guide L7864_1211 Product base pla features, provisios ad riders may ot be approved i all states. For producer use oly. Not
More informationToday: Finish Chapter 9 (Sections 9.6 to 9.8 and 9.9 Lesson 3)
Today: Fiish Chapter 9 (Sectios 9.6 to 9.8 ad 9.9 Lesso 3) ANNOUNCEMENTS: Quiz #7 begis after class today, eds Moday at 3pm. Quiz #8 will begi ext Friday ad ed at 10am Moday (day of fial). There will be
More informationRecourse vs. Nonrecourse: Commercial Real Estate Financing Which One is Right for You?
The followig iformatio ad opiios are provided courtesy of Wells Fargo Bak, N.A. Recourse vs. Norecourse: Commercial Real Estate Fiacig Which Oe is Right for You? Prepared by: Bill White, Director of Commercial
More informationCAPITALIZATION (PREVENTION) OF PAYMENT PAYMENTS WITH PERIOD OF DIFFERENT MATURITY FROM THE PERIOD OF PAYMENTS
Iteratioal Joural of Ecoomics, Commerce ad Maagemet Uited Kigdom Vol. VI, Issue 9, September 2018 http://ijecm.co.uk/ ISSN 2348 0386 CAPITALIZATION (PREVENTION) OF PAYMENT PAYMENTS WITH PERIOD OF DIFFERENT
More informationfor a secure Retirement Foundation Gold (ICC11 IDX3)* *Form number and availability may vary by state.
for a secure Retiremet Foudatio Gold (ICC11 IDX3)* *Form umber ad availability may vary by state. Where Will Your Retiremet Dollars Take You? RETIREMENT PROTECTION ASSURING YOUR LIFESTYLE As Americas,
More informationEstimating Proportions with Confidence
Aoucemets: Discussio today is review for midterm, o credit. You may atted more tha oe discussio sectio. Brig sheets of otes ad calculator to midterm. We will provide Scatro form. Homework: (Due Wed Chapter
More informationMGF 1107 Miami Dade College MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Persoal Fiace Name MGF 1107 Miami Dade College MULTIPLE CHOICE. Choose the oe alterative that best completes the stateme or aswers the questio. 1) What umber is 32% of 48? 1) A) 1536 B) 153.6 C)
More informationEVEN NUMBERED EXERCISES IN CHAPTER 4
Joh Riley 7 July EVEN NUMBERED EXERCISES IN CHAPTER 4 SECTION 4 Exercise 4-: Cost Fuctio of a Cobb-Douglas firm What is the cost fuctio of a firm with a Cobb-Douglas productio fuctio? Rather tha miimie
More informationNomura Asia Pacific Fonds
Nomura Asia Pacific Fods INVESTMENT OBJECTIVE The fud's ivestmet objective is to achieve a log-term participatio i the dyamic ecoomic growth of the Asia Pacific regio. The fud ivests primarily i equities.
More informationAY Term 2 Mock Examination
AY 206-7 Term 2 Mock Examiatio Date / Start Time Course Group Istructor 24 March 207 / 2 PM to 3:00 PM QF302 Ivestmet ad Fiacial Data Aalysis G Christopher Tig INSTRUCTIONS TO STUDENTS. This mock examiatio
More informationGuide for. Plan Sponsors. Roth 401(k) get retirement right
Uited of Omaha Life Isurace Compay Compaio Life Isurace Compay mutual of omaha retiremet services Roth 401(k) Guide for Pla Sposors MUGC8764_0210 get retiremet right roth 401(k) expads your optios Drive
More information