10. FixedIncome Securities. Basic Concepts


 Helena Logan
 3 years ago
 Views:
Transcription
1 0. FixedIncome Securities Fixedincome securities (FIS) are bonds that have no default risk and their payments are fully determined in advance. Sometimes corporate bonds that do not necessarily have certain future payments are also called xedincome securities. Nominal bonds: Fixed coupon payments, i.e., xed in nominal terms Indexed bonds: Coupon payments indexed to in ation, i.e., xed in real terms In principle xed income securities are as any other securities, but there are some special features:. FIS markets are developed separately from security markets: Own institutional structure, terminology and (academic) study traditions 2. Markets extremely large 3. FISs have a special place in nancial theory: no cash ow uncertainty, so that their price vary only as discount rates vary (with e.g. stocks, also expected future cash ows (dividends) change as discount rates change). Nominal bonds carry information about nominal discount rates, and indexed bonds about real discount rate. 4. Many other assets can be seen as combinations of FISs and derivative security; e.g. a callable bond is a FIS minus a put option. 8 Basic Concepts Zero coupon or discount bonds make a single payment at a date in the future known as the maturity date. The size of this payment is the face value of the bond. The length of time to the maturity date is the maturity of the bond. Coupon bonds make coupon payments of a given fraction of the face value at equally spaced dates up to and including the maturity date, when the face value is also paid. Note: Coupon bonds can be though as packages of discount bonds, one corresponding to each coupon payment and one to the  nal coupon payment together with the repayment of principal. (STRIPS, Separated Trading of Registered Interest and Principal Securities.) 82
2 Yieldtomaturityon a bond is that discount whichequatesthepresentvalueofthebond's payments to its price. For example the yield to maturity on a threeyear bond with annual interest payment of $00, a principal payment of $ 000, and present price $900 is the rate Y that equates the present value of the three years cash ows on bond with its present price 900 = 00 +Y ( + Y ) 2 ( + Y ) 3 : So that Y =4:3%. Discount Bonds Suppose that P nt is the time t price of a discount bond that makes a single payment of $ at time t + n. Thentheyieldtomaturity is obtained from P nt = ( + Y nt ) n; so that Turning to log or continuously compounded variables, we obtain y nt = n p nt: The term structure of interest rates is the set of yields to maturity at a given time, on bonds of di erent maturities. The yield spread s nt = y nt y t is the di erence between the yield on an nperiod bond andtheyieldonaoneperiodbond,andisa measure of the shape of the term structure. The yield curve is a plot of the term structure, that is the plot of Y nt or y nt against n on some particular date t. +Y nt = P n nt : 83 84
3 HoldingPeriod Returns: The holdingperiod return on a bond is the return over some holding period less than the bond's maturity. Let R n;t+ denote the oneperiod holdingperiod return on an nperiod bond purchased at time t andsoldattimet +. The bond will be an (n )periodbondwhenitissold at sale price P n ;t+, and the holding period return is +R n;t+ = P n ;t+ = P nt In logs r n;t+ = p n ;t+ p nt ( + Y nt ) n ( + Y n ;t+ ) n : = ny nt (n )y n ;t+ = y nt (n )(y n ;t+ y nt ): Wecanalsowrite: p nt = r n;t+ + p n ;t+, i.e., today's price is related to tomorrow's price and return over the next period. Solving forwardweobtain(notethatp 0t =sothat p 0t =logp 0t =0) p nt = or in terms of the yield n X r n i;t++i i=0 n X y nt = r n i;t++i : n i=0 I.e., the average per period logreturn. Forward Rates: Bonds of di erent maturities can be combined to guarantee an interest rate on a xedincome investment to be made in the future; the interest rate on this investment is called a forward rate
4 The forward rate is de ned as the return of the time t + n investment P nt =P n+;t : Example. To guarantee at time t an interest rate on oneperiod investment to be made at time t+n, an investor can proceed as follows: ² Suppose the desired future investment will pay $ at time t + n +. ² Buy one (n + )period bond which costs P n+;t at time t and pays $ at time t + n +. But one wants to transfer the cost of this investment from time t to time t + n. To do this { Sell P n+;t =P nt nperiod bonds to nance the investment (and hence transferring time t of P n+;t to time t+n). This produces the desired cash ow P nt (P n+;t =P nt )=P n+;t at time t, exactly enough to o set the negative time t cash ow from the rst transaction. { Pay at time t + n the cash ow of P n+;t =P nt, which is in fact the cost of investment made at t + n for one period. ( + F nt )= = ( + Y n+;t) n+ P n+;t =P nt ( + Y nt ) n : In logarithms f nt = p nt p n+;t = (n +)y n+;t ny nt = y nt +(n +)(y n+;t y nt ); where y nt =log(+y nt ). We observe: ² f nt is positive whenever discount bond prices fall with maturity. ² f nt is above both the nperiod and (n + )period discount bond yields when the (n +)period yield is above the nperiod yield (yield curve is upward sloping) 87 88
5 In summary, we have the interpretation: The yield to maturity is the average cost of borrowing for n periods, while the forward rate is the marginal cost of extending the time period of the loan. Coupon Bonds Let C denote the coupon rate per period (i.e. per period paid coupon price divided by the principal value of the bond), then the yield to maturity Y cnt is obtained as the discount rate which equates the present value of the bond's payments equal to its price at time t P cnt = C C +C + +Y cnt ( + Y cnt ) 2+ + ( + Y cnt ) n Duration and Immunization For discount bonds maturity is the length of time that a bondholder has invested money. For a coupon bond maturity is an imperfect measure of this length of time because much of the investment is paid back as coupons before the maturity date. Abettermeasureis 0 D cnt = nx P cnt i= ( + Y cnt ) i + n ( + Y cnt ) n A : Called Macaulay's duration ² When P cnt = the bond is said to selling at par, andy cnt = C. ² When maturity n is in nite, the bond is called consol or perpetuity, and Y ct = C=P ct. 89 Macaulay, F. (938). Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yield, and Stock Prices in the United States Since 856. National Bureau of Economic Research, New York 90
6 ² If C =0thenD cnt = n the maturity. ² If C>0thenD cnt <n. ² ForaparbondP cnt =, Y cnt = C and D cnt = ( + Y cnt) n ( + Y cnt ) ² For a consol bond with Y ct = C=P ct, D ct = +Y ct Y ct : Furthermore, we observe that D cnt = dp cnt +Y cnt d(+y cnt ) P cnt = dp cnt =P cnt d(+y cnt )=(+Y cnt ) ; i.e. the (negative) elasticity of a coupon bond's price with respect to its gross yield ( + Y cnt ). 9 Modi ed duration D cnt = dp cnt +Y cnt dy cnt P cnt measures the proportional sensitivity of a bond's price to a small absolute change in its yield. Example. If modi ed duration is 0, an increase of one basis point in the yield (say from 3.00% to 3.0%) will cause a 0 basis point (0.0%) drop in the bond price. Immunization was originally de ned as a process to make business immune to general change in interest rate. Nowadays it is de ned as a technique to eliminate sensitivity to shifts in the term structure by matching duration of the assets to the duration of the liabilities. For example one may want to match zero coupon liabilities, such as pension liabilities, to coupon paying Treasury. The problem here is that the Bond portfolio includes short and long term bonds, whose yield curves are not the same. Consequently, term structure of interest is a key issue in the immunization. 92
7 Convexity = d2 P cnt dy 2 cnt P cnt µ = P C P n i(i+) cnt i= (+Y cnt ) i+2 + n(n+) (+Y cnt ) n+2 ; which indicates, for example, how the modi ed duration changes as yield changes. It canbealsousedinasecondordertaylorapproximation of the price impact of a change in yield: dp cn P cn ¼ dp cn dy cn sycn 2 Pcn dy cn + 2 d2 P cn P cn (dy cn ) 2 = (mod dur)dy cn + 2 (conv)(dy cn) 2 : A Loglinear Model for Coupon Bonds: Duration can be used to nd approximate linear relationships between log coupon bond yields, holding period returns, and forward rates that are analogous to the exact relationships for zerocoupon bonds (see earlier). Using a similar approach as with the stock return, we can write r c;n;t+ ¼ k + ½p c;n ;t+ +( ½)c p cnt ; 93 where and ½ = + exp(c p) k = log ½ ( ½)log(=½ ): For a par selling bond ½ ==( + C) =(+ Y cnt ). Using the approximation and solving forward, we obtain p cnt = n X i=0 ½ i h k +( ½)c r c;n i;t++i i : A similar approximation of the log yield to maturity y cnt produces p cnt ¼ P n i=0 ½i [k +( ½)c y cnt ] = ½n ½ [k +( ½)c y cnt] 94
8 Using these two expression of p cnt gives y cnt ¼ ½n ½ n X i=0 ½ i r c;n i;t++i : Thus there is an approximate equality between the log yield to maturity on coupon bond and a weighted average of the returns onthebondwhenitisheldtomaturity. From the above formula we also see that D cnt ¼ ½n ½ = ( + Y cnt) n ( + Y cnt ) : Thus (an approximate analogy for a zerocoupon bond) r c;n;t+ ¼ D cnt y cnt (D cnt )y c;n ;t+ : Finally a similar analysis for an nperiodahead period forward rate implicit in the couponbearing term structure is f nt ¼ D c;n+y c;n+;t D cn y cnt D c;n+ D cn : Estimating the ZeroCoupon Term Structure Suppose we know the prices of discount bonds P ;P 2 ;:::;P n maturing at each coupon date, that is the coupon term structure. Then the price of a coupon bond is P cn = P C + P 2 C + + P n ( + C): Similarly if a complete coupon term structure that is, the prices of coupon bonds P c ;P c2 ; :::;P cn maturing at each coupon date is available, then the zero coupon terms structure can be found applying iteratively the above coupon bond price: P c = P ( + C), so P = P c =( + C), and generally P n = P cn P n C P C +C 95 96
9 Sometimes, however, the terms structure may be morethancomplete in the sense that at least one coupon bond matures on each coupon date and several coupon bond mature on some coupon dates. The prices are likely di erent in these multiple cases. One possibility is to determine a single price by compromising with a regression model P ci n i = P C i + P 2 C i + + P ni ( + C i )+u i ; i =;:::;I,whereC i isthecouponontheith bond and n i is the maturity of the ith bond. The coe±cients are discount bond prices P j, j =;:::;N,whereN =maxn i is the longest coupon bond maturity. OLS can be applied provided that the term structure is complete and I N. Interpreting the Term Structure of Interest Rates Theories of the term structure. Pure expectation hypothesis: For zero coupon bonds E t [R n;t+ ]=r t, for all maturities n, where r t is the riskfree rate. 2. Expectation hypothesis: E t [R n;t+ ] r t = c a constant for all maturities n. 3. Liquidity preference hypothesis: E t [R n;t+ ] r t = T (n) where T (n) >T (n ) >. 4. Time varying risk: E t [R n;t+ ] r t = T (n; z t ), where T is some function of n and set of variables z t. 5. Etc. In practice the term structure, however, is incomplete and other methods must be applied, e.g. spline
10 Here we consider only to some extend the expectation hypotheses. Expectation Hypotheses Pure expectation hypothesis (PEH): Expected excess returns on longterm over shortterm bonds are zero. Expectation Hypothesis (EH): Expected excess returns are constants over time. The rst form PEH equates the one period expected returns on oneperiod and nperiod bonds. The oneperiod return on a oneperiod bond, + Y t,isknown,so +Y t = E t [ + R n;t+ ] = (+Y nt ) n E t h( + Y n ;t+ ) (n )i : A second form of PEH equates the nperiod expected returns on oneperiod and nperiod bonds: ( + Y nt ) n = E t h ( + Yt ) ( + Y ;t+n ) i : From this implies +F n ;t = ( + Y nt) n ( + Y n ;t ) n = E t[+y ;t+n ]: Also it holds that ( + Y nt ) n =(+Y t )E t h ( + Yn ;t+ ) n i : This is inconsistent with the rst form whenever interest rates are random, because then generally " # E t ( + Y n ;t+ ) n 6= h E t ( + Yn ;t+ ) n i 99 00
11 Implications of the Log PEH First Secondly Finally y t = E t [r n;t+ ]: y nt = n n X i=0 E t [y ;t+i ]: f n ;t = E t [y ;t+n ]; which implies furthermore that f nt = E t [y ;t+n ] = i E t he t+ [y ;t+n ] = E t [f n ;t+ ] i.e., f n;t is a martingale. The expectation hypothesis is more general than the PEH allowing di erences in expected returns on bonds of di erent maturities. These di erences are sometimes called term premia. In PEH term premia are zero and in EH they are constant through time. Yield Spreads and Interest Rate Forecasts The yield spread between nperiod and oneperiod yield is s nt = y nt y t. Because we can write y nt = n nx r n i;t++i i= " nx s nt = n E t (y;t+i y t )+(r n+ i;t+i y ;t+i ) # i= " nx = n E t (n i) y;t+i +(r n+ i;t+i y ;t+i ) # i= 0 02
12 That is the yield spread equals a weighted average expected future interest rate changes and an unweighted average of expected future excess returns on long bonds. If the changes in interest rate ( y ;t+i )arestationary and the excess returns r n+ i;t+i y ;t+i are stationary then the yield spread is cointegrated. According to EH E t [r n+ i;t+i y ;t+i ] are constants. This implies that the yield spread is the optimal forecaster of the change in the longbond yield over the life of the short bond, and the optimal forecaster of changes in short rates over the life of the long bond. Recalling that r n;t+ = y nt (n )(y n ;t+ y nt )andy t = E t [r n;t+ ], we obtain under the EH and after some algebra n s nt = E t [y n ;t+ y nt ] and 2 3 n X s nt = E t 4 ( i=n) y 5 ;t+i : i= 03 The former equation shows that when the yield spread is high, the long rate is expected to rise. A high yield spread gives the long bond a yield advantage that must be o set by an anticipated capital loss. The latter equation shows that when the yield spread is high, short rates are expected to rise. An econometric model for testing the former is µ sn t y n ;t+ y n;t = n + n + ² n;t : n An econometric model for testing the latter claim is where s n;t = ¹ n + n s nt + ² nt s n n;t = X ( i=n) y ;t+i i= is the ex post value of the shortrate changes. The expectation hypothesis implies that = for all n. 04
C(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900$. The yield to maturity will then be the y that solves
Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of longterm fixed income securities are federal government bonds, corporate
More informationFINANCIAL AND INVESTMENT INSTRUMENTS. Lecture 6: Bonds and Debt Instruments: Valuation and Risk Management
AIMS FINANCIAL AND INVESTMENT INSTRUMENTS Lecture 6: Bonds and Debt Instruments: Valuation and Risk Management After this session you should Know how to value a bond Know the difference between the term
More informationChapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixedincome securities. Stocks. Real assets (capital budgeting). Part C Determination
More informationI. Readings and Suggested Practice Problems. II. Risks Associated with DefaultFree Bonds
Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with DefaultFree Bonds III. Duration: Details and Examples IV. Immunization
More informationThe 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 differentterm assets. The term structure under certainty Forward rates Theories
More informationZeroCoupon Bonds (Pure Discount Bonds)
ZeroCoupon Bonds (Pure Discount Bonds) The price of a zerocoupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
More informationGlobal Financial Management
Global Financial Management Bond Valuation Copyright 999 by Alon Brav, Campbell R. Harvey, Stephen Gray and Ernst Maug. All rights reserved. No part of this lecture may be reproduced without the permission
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on longterm bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationFixedIncome Securities, Interest Rates and Term Structure of Interest Rates
I FixedIncome ecurities, Interest ates and Term tructure of Interest ates Dipl. Kaufm. alentin Popov tatistics and Econometrics Department University of aarland ofia, pril 2012 I E I T Dipl. Kaufm. alentin
More informationThe Time Value of Money
The Time Value of Money This handout is an overview of the basic tools and concepts needed for this corporate nance course. Proofs and explanations are given in order to facilitate your understanding and
More informationCHAPTER 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
More informationCHAPTER 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
More informationInvestments Analysis
Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest
More informationChapter. Bond Prices and Yields. McGrawHill/Irwin. Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved.
Chapter Bond Prices and Yields McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Bond Prices and Yields Our goal in this chapter is to understand the relationship
More informationLecture Notes: Basic Concepts in Option Pricing  The Black and Scholes Model
Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing  The Black and Scholes Model Recall that the price of an option is equal to
More informationFixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
More informationChapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
More informationDebt Instruments Set 3
Debt Instruments Set 3 Backus/February 9, 1998 Quantifying Interest Rate Risk 0. Overview Examples Price and Yield Duration Risk Management Convexity ValueatRisk Active Investment Strategies Debt Instruments
More informationBond valuation and bond yields
RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments
More informationAlliance Consulting BOND YIELDS & DURATION ANALYSIS. Bond Yields & Duration Analysis Page 1
BOND YIELDS & DURATION ANALYSIS Bond Yields & Duration Analysis Page 1 COMPUTING BOND YIELDS Sources of returns on bond investments The returns from investment in bonds come from the following: 1. Periodic
More informationCHAPTER 10. Bond Prices and Yields
CHAPTER 10 Bond Prices and Yields Interest rates go up and bond prices go down. But which bonds go up the most and which go up the least? Interest rates go down and bond prices go up. But which bonds go
More informationEcon 330 Exam 1 Name ID Section Number
Econ 330 Exam 1 Name ID Section Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If during the past decade the average rate of monetary growth
More informationInternational Money and Banking: 12. The Term Structure of Interest Rates
International Money and Banking: 12. The Term Structure of Interest Rates Karl Whelan School of Economics, UCD Spring 2015 Karl Whelan (UCD) Term Structure of Interest Rates Spring 2015 1 / 35 Beyond Interbank
More informationCoupon Bonds and Zeroes
Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zerocoupon bonds Bond replication Noarbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semiannual compounding
More informationECO 4368 Instructor: Saltuk Ozerturk. Bonds and Their Valuation
ECO 4368 Instructor: Saltuk Ozerturk Bonds and Their Valuation A bond is a long term contract under which a borrower (the issuer) agrees to make payments of interest and principal on speci c dates, to
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationAnswer Key to Midterm
Econ 121 Money and Banking Instructor: Chao Wei Answer Key to Midterm Provide a brief and concise answer to each question. Clearly label each answer. There are 50 points on the exam. 1. (10 points, 3 points
More informationFNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
More informationLecture 12/13 Bond Pricing and the Term Structure of Interest Rates
1 Lecture 1/13 Bond Pricing and the Term Structure of Interest Rates Alexander K. Koch Department of Economics, Royal Holloway, University of London January 14 and 1, 008 In addition to learning the material
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More informationForward Contracts and Forward Rates
Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16
More informationLesson 1. Net Present Value. Prof. Beatriz de Blas
Lesson 1. Net Present Value Prof. Beatriz de Blas April 2006 1. Net Present Value 1 1. Introduction When deciding to invest or not, a rm or an individual has to decide what to do with the money today.
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Longterm Treasury securities have substantial
More informationn(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3
ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric
More informationPractice Set and Solutions #2
723G26/20121010 Practice Set and Solutions #2 What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These
More informationProblems and Solutions
1 CHAPTER 1 Problems 1.1 Problems on Bonds Exercise 1.1 On 12/04/01, consider a fixedcoupon bond whose features are the following: face value: $1,000 coupon rate: 8% coupon frequency: semiannual maturity:
More informationBonds and Yield to Maturity
Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.
More informationBond Valuation. Capital Budgeting and Corporate Objectives
Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What
More informationDebt Instruments Set 2
Debt Instruments Set 2 Backus/October 29, 1998 Bond Arithmetic 0. Overview Zeros and coupon bonds Spot rates and yields Day count conventions Replication and arbitrage Forward rates Yields and returns
More informationVALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below
VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following riskfree debt instrument, which promises to make the respective
More informationBond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview
Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation
More informationLecture 09: Multiperiod Model Fixed Income, Futures, Swaps
Lecture 09: Multiperiod Model Fixed Income, Futures, Swaps Prof. Markus K. Brunnermeier Slide 091 Overview 1. Bond basics 2. Duration 3. Term structure of the real interest rate 4. Forwards and futures
More informationCHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
More informationChapter 4: Common Stocks. Chapter 5: Forwards and Futures
15.401 Part B Valuation Chapter 3: Fixed Income Securities Chapter 4: Common Stocks Chapter 5: Forwards and Futures Chapter 6: Options Lecture Notes Introduction 15.401 Part B Valuation We have learned
More informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exam FM/CAS Exam 2. Chapter 6. Variable interest rates and portfolio insurance. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam
More informationMargin Calculation Methodology and Derivatives and Repo Valuation Methodology
Margin Calculation Methodology and Derivatives and Repo Valuation Methodology 1 Overview This document presents the valuation formulas for interest rate derivatives and repo transactions implemented in
More informationDetermination of Forward and Futures Prices
Determination of Forward and Futures Prices Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012 Short selling A popular trading (arbitrage) strategy is the shortselling or
More informationMaturity and interestrate risk
Interest rate risk, page 1 Maturity and interestrate risk Suppose you buy one of these three bonds, originally selling at a yield to maturity of 8 percent. Yield to Oneyear 30year 30year maturity 8%
More informationMBA Finance PartTime Present Value
MBA Finance PartTime Present Value Professor Hugues Pirotte Spéder Solvay Business School Université Libre de Bruxelles Fall 2002 1 1 Present Value Objectives for this session : 1. Introduce present value
More informationBond Price Volatility. c 2008 Prof. YuhDauh Lyuu, National Taiwan University Page 71
Bond Price Volatility c 2008 Prof. YuhDauh Lyuu, National Taiwan University Page 71 Well, Beethoven, what is this? Attributed to Prince Anton Esterházy c 2008 Prof. YuhDauh Lyuu, National Taiwan University
More informationMidTerm Exam Practice Set and Solutions.
FIN469 Investments Analysis Professor Michel A. Robe MidTerm Exam Practice Set and Solutions. What to do with this practice set? To help students prepare for the midterm exam, two practice sets with
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationBackground Material for Term Structure Models
Term Structure Models: IEOR E471 Spring 21 c 21 by Martin Haugh Background Material for Term Structure Models Basic Theory of Interest Cashflow Notation: We use (c, c 1,..., c i,..., c n ) to denote the
More informationM.I.T. Spring 1999 Sloan School of Management 15.415. First Half Summary
M.I.T. Spring 1999 Sloan School of Management 15.415 First Half Summary Present Values Basic Idea: We should discount future cash flows. The appropriate discount rate is the opportunity cost of capital.
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More informationChapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull
Chapter 4 Interest Rates 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Treasury Rates Rates on instruments issued by a government in its own currency 3 LIBOR and LIBID LIBOR is the rate of interest
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationChapter Nine Selected Solutions
Chapter Nine Selected Solutions 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the
More informationDeterministic CashFlows
IEOR E476: Financial Engineering: DiscreteTime Models c 21 by Martin Haugh Deterministic CashFlows 1 Basic Theory of Interest Cashflow Notation: We use (c, c 1,..., c i,..., c n ) to denote a series
More informationPractice Questions for Midterm II
Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. 1. d. 0.5. By definition, the beta of the market portfolio is
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
More informationLOS 56.a: Explain steps in the bond valuation process.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationIntroduction. example of a AA curve appears at the end of this presentation.
1 Introduction The High Quality Market (HQM) Corporate Bond Yield Curve for the Pension Protection Act (PPA) uses a methodology developed at Treasury to construct yield curves from extended regressions
More informationDuration Defined General Definition duration DS,r of S with respect to the interest rate r Example 1: Example 2:
Duration Defined Duration is a risk management metric that measures the sensitivity of a financial security s value to changes in interest rates. There are many different and seemingly contradictory definitions
More informationFinancialInstitutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:
FIN 683 Professor Robert Hauswald FinancialInstitutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks  Interest Rate Risks 6. A financial institution has the following market
More informationAdvanced Fixed Income Analytics Lecture 1
Advanced Fixed Income Analytics Lecture 1 Backus & Zin/April 1, 1999 Vasicek: The Fixed Income Benchmark 1. Prospectus 2. Models and their uses 3. Spot rates and their properties 4. Fundamental theorem
More informationInvestment Analysis. Bond Value Bond Yields Bond Pricing Relationships Duration Convexity Bond Options. Bonds part 2. Financial analysis
Bond Value Bond Yields Bond Pricing Relationships Duration Convexity Bond Options Investment Analysis Bonds part 2 Financial analysis  2 Duration Duration = the average maturity of the bond s promised
More informationNotes for Lecture 3 (February 14)
INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because
More informationCHAPTER 10 BOND PRICES AND YIELDS
CHAPTER 10 BOND PRICES AND YIELDS 1. a. Catastrophe bond. Typically issued by an insurance company. They are similar to an insurance policy in that the investor receives coupons and par value, but takes
More informationEcon 121 Money and Banking Fall 2009 Instructor: Chao Wei. Midterm. Answer Key
Econ 121 Money and Banking Fall 2009 Instructor: Chao Wei Midterm Answer Key Provide a BRIEF and CONCISE answer to each question. Clearly label each answer. There are 25 points on the exam. I. Formulas
More informationFinal Exam Practice Set and Solutions
FIN469 Investments Analysis Professor Michel A. Robe Final Exam Practice Set and Solutions What to do with this practice set? To help students prepare for the final exam, three practice sets with solutions
More informationChapter 3. Fixed Income Securities
IE 5441 1 Chapter 3. Fixed Income Securities IE 5441 2 Financial instruments: bills, notes, bonds, annuities, futures contracts, mortgages, options,...; assortments that are not real goods but they carry
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationPractice Set #2 and Solutions.
FIN672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,
More informationBonds, Preferred Stock, and Common Stock
Bonds, Preferred Stock, and Common Stock I. Bonds 1. An investor has a required rate of return of 4% on a 1year discount bond with a $100 face value. What is the most the investor would pay for 2. An
More informationFIN 472 FixedIncome Securities Debt Instruments
FIN 472 FixedIncome Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds
More informationProblems and Solutions
Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixedcoupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual
More informationChapter 4 Interest Rates. Options, Futures, and Other Derivatives 9th Edition, Copyright John C. Hull
Chapter 4 Interest Rates 1 Types of Rates! Treasury rate! LIBOR! Fed funds rate! Repo rate 2 Treasury Rate! Rate on instrument issued by a government in its own currency 3 LIBOR! LIBOR is the rate of interest
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationFIXEDINCOME SECURITIES. Chapter 11. Forwards and Futures
FIXEDINCOME SECURITIES Chapter 11 Forwards and Futures Outline Futures and Forwards Types of Contracts Trading Mechanics Trading Strategies Futures Pricing Uses of Futures Futures and Forwards Forward
More informationInterest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
More informationChapter 3: Commodity Forwards and Futures
Chapter 3: Commodity Forwards and Futures In the previous chapter we study financial forward and futures contracts and we concluded that are all alike. Each commodity forward, however, has some unique
More informationTerm Structure of Interest Rates
Appendix 8B Term Structure of Interest Rates To explain the process of estimating the impact of an unexpected shock in shortterm interest rates on the entire term structure of interest rates, FIs use
More informationPractice Set #1 and Solutions.
Bo Sjö 140503 Practice Set #1 and Solutions. What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationFixed Income Securities
3st lecture IES, UK October 7, 2015 Outline Bond Characteristics 1 Bond Characteristics 2 Bond Characteristics Government bond listing Rate Maturity mo/yr Bid Asked Chg Ask yld 3.000 July 12 108:22 108:2320
More informationCHAPTER 6 ASSETLIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTERESTSENSITIVE AND DURATION GAPS
CHAPTER 6 ASSETLIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTERESTSENSITIVE AND DURATION GAPS Goals of This Chapter: The purpose of this chapter is to explore the
More informationa) The Dividend Growth Model Approach: Recall the constant dividend growth model for the price of a rm s stock:
Cost of Capital Chapter 14 A) The Cost of Capital: Some Preliminaries: The Security market line (SML) and capital asset pricing model (CAPM) describe the relationship between systematic risk and expected
More information11.2 Monetary Policy and the Term Structure of Interest Rates
518 Chapter 11 INFLATION AND MONETARY POLICY Thus, the monetary policy that is consistent with a permanent drop in inflation is a sudden upward jump in the money supply, followed by low growth. And, in
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
ECON 4110: Sample Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Economists define risk as A) the difference between the return on common
More informationOptions: Valuation and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 15 Options: Valuation and (No) Arbitrage I. Readings and Suggested Practice Problems II. Introduction: Objectives and Notation III. No Arbitrage Pricing Bound IV. The Binomial
More informationChapter. Interest Rates. McGrawHill/Irwin. Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved.
Chapter Interest Rates McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Interest Rates Our goal in this chapter is to discuss the many different interest rates that
More informationEC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER
EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER NAME: IOANNA KOULLOUROU REG. NUMBER: 1004216 1 Term Paper Title: Explain what is meant by the term structure of interest rates. Critically evaluate
More information1. The Purdue Life Insurance Company has two assets and two liabilities.
Chapter 9, Section 1 1. The Purdue Life Insurance Company has two assets and two liabilities. The assets are: a. A 5 year par value bond with a maturity value of 100,000. The bond pays annual coupons at
More informationAnswers to EndofChapter Questions
Answers to EndofChapter Questions 1. The bond with a C rating should have a higher risk premium because it has a higher default risk, which reduces its demand and raises its interest rate relative to
More informationUnderstanding Fixed Income
Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding
More informationBonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)
More information