Financial Market Analysis (FMAx) Module 4
|
|
- Oswin Cox
- 5 years ago
- Views:
Transcription
1 Financial Market Analsis (FMAx) Module 4 erm Structure of Interest Rates his training material is the propert of the International Monetar Fund (IMF) and is intended for use in IMF Institute for Capacit Development (ICD) courses. An reuse requires the permission of the ICD.
2 he Relevance to You You might be An investment manager A debt manager An economic analst/forecaster
3 Before We Begin he erm Structure of Interest Rates: Provide useful insight about how the market thinks about future interest rate movements. Allows central bankers to gauge market expectation about inflation, growth and risks Allows ou to price an asset
4 Simplifing Assumption o simplif the discussion, we assume the following: he face value of all bonds, M, is $00 Each period is a ear Coupon paments, c, are made annuall Consider onl clean bond pricing
5 Defining the erm Structure of Interest Rates Question: What is the term structure of interest rate? It is the relationship between the ield-to-maturit of zero-coupon bonds and their respective maturit It is often called the spot curve It can be derived mathematicall
6 Defining the erm Structure of Interest Rates he bond pricing formula for a t-ear zero coupon bond. ø ö ç ç è æ t t t P M ( ) M P t t t M DF P t t
7 Defining the erm Structure of Interest Rates 3 A graphical representation of a term structure of interest rates
8 Defining the Zero Coupon Bond Wh use zero-coupon bond? Consider the bond pricing equation of a coupon bond he YM of a coupon bond defines implicitl in the following equation P t c c ~ ~! t ( ) ( ) t t c M ~ t
9 Common Shapes of the Yield Curve
10 Common Shapes of the Yield Curve Remark On the shapes: he shapes showed here are not the onl possible shapes of a ield curve he shape of a ield curve could be more complicated than those On the interpretations: he interpretation given to each shape is not the onl correct interpretation Competing theories to explain the relationship between the shape of the ield curve and interest rates movements.
11 he Yield Curves for Indonesian Sovereign Bond Example: Zero Coupon Yield derived from Indonesian Sovereign Bond on Jan/ nd (blue), Apr/ st (Red) and Jul/ st (Green) Maturit (in ears) Q Q3 Q Source: Bloomberg
12 he Spot Curves for Brazil Sovereign Bond Example: Zero Coupon Yield derived from Brazil Sovereign Bond on Jan/ nd (blue), Apr/ st (Red) and Jul/ st (Green) Maturit (in ears) Q Q Q3 Source: Bloomberg
13 Bond Pricing with the Yield Curve A stream of cash flow: he Price of Strateg A: P(3)
14 Bond Pricing with the Yield Curve A stream of cash flow: he Price of Strateg B: ( 00 5) ~ 5 5 P0 (3) º P0 () P0 () P (3)
15 Defining the Spot Rate he No-Arbitrage Condition: Given the Law of One Price, the price of alternatives A and B should be identical. P(3) ~ P 0 (3) P0 () P0 () ( 00 5) ( ) ( ) P0 (3) 00
16 Defining the Spot Rate Let us generalize the formula to maturit : ( ) ( ) t t t t M c P t P M c P P å å ) ( ) ( ) ( ~ ) ( 0 0 0
17 Defining the Forward Interest Rate Forward Loan: Agreement toda to borrow/lend on some future date at an interest rate that is determined on toda. Forward Rate (or forward interest rate ): Interest rate on a forward loan. he forward rate is not necessaril equal to spot short rate that will prevail in the future.
18 Defining the Forward Interest Rate Forward rates are tightl related to the spot rates b the no-arbitrage condition. Gross Return: ( ) Gross Return: ( )( f ),
19 Defining the Forward Interest Rate 3 he no-arbitrage condition ensures that ( ) ( )( f ), f ( ) ( ),
20 Defining the Forward Interest Rate 4 We can generalize the idea 0, f ( ) ( ) ( ) i i i i i f, ( ) ( ), ø ö ç ç è æ i i i i i f B definition:
21 Defining the Forward Interest Rate 5 It is important to notice and remember that Forward lending/borrowing agreement ma not exist or ma not be allowed in realit in some countries However, forward interest rates can still be calculated as long as the ield curve exists!! f ( ) æ ö i ç i, i ç ( ) i i è ø
22 he Relationship between Spot and Forward Rates Forward interest rates are tightl related to spot interest rates. he are also tightl related to he discount factors (DF) he prices of the corresponding zero-coupon bonds (P)
23 he Relationship between Spot and Forward Rates Let us recall that ( ) ( ), ø ö ç ç è æ ø ö ç ç è æ ø ö ç ç è æ ø ö ç ç è æ i i i i i i i i i i i P P M M P P DF DF f
24 he Relationship between Spot and Forward Rates 3 Spot rates can also be rewritten as a (geometric) average of forward rates. ( ) ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) [ ] f f f f f f f f f f f f f f,,, 0,,,, 0,,,,,,,!!!
25 he Relationship between Spot and Forward Rates 4 [( f )( f )!( f )( f )] 0, ( ) [ ln( f ) ln( f )! ln( f ) ln( f )] ln Since interest rates are generall of a small magnitude 0,,, he spot interest rate is approximatel equal to the arithmetic average of forward interest rate.,,» 0,,!, [ f f f ],,
26 he Relationship between Spot and Forward Rates 5 his expression has an economic interpretation: he spot interest rate at maturit ear is the simple average -ear borrowing cost over ears. he x-ear forward -ear interest rate f x, is the marginal borrowing cost when the loan is extended b one ear.
27 he Relationship between Spot and Forward Rates 6 For example: A 3-ear zero coupon bond is trading at YM of 3% A -ear zero coupon bond is trading at YM of % ( ) 3 æ 0.03 ö f, ç ç ( 0.0) è ø 5.03% he interest rate for the additional ear is 5.03% (after rounding).
28 he Relationship between Spot and Forward Rates 7 Just as we did with spot rates, we can define a forward ield curve. 7 6 Brazil: he spot curve on Jan// Brazil: -ear forward -ear curve on Jan// Maturit (in ears) Source: Bloomber g Years from now
29 he Relationship between Spot and Forward Rates 8 Because the spot interest rate is the average of forward interest rates: spot curve is upward-sloping Forward curve is above the spot curve spot curve is downward-sloping Forward curve is below the spot curve spot curve is flat Forward curve is equal to spot curve.
30 he Par-Yield Defining the par-ield: Measures the coupon rate (in percentage term) at which a coupon bond would be traded at par. he par-ield is often used as a reference for pricing new issues. It is NO the spot interest rate but is closel related to it. hus, ou cannot use it directl for bond pricing or discount future cash-flow
31 he Par-Yield Given the term-structure of interest rates, the par-ield of maturit, implicitl as * c M M M å ( ) t ( ) t t c ( ) DF å ( ) å t DFt * t t t * c, is defined
32 he Par-Yield 3 Similar to the relationship between the spot curve and the forward curve, the parield he par-ield can be viewed as a kind of average of the spot interest rate. he par-ield curve is flatter than both the spot curve and the forward curve.
33 Bootstrapping Defining bootstrapping: If ou fall into a well and no one is around, ou use our bootstrap to help ourself climb up from a well Use available data on coupon bonds to construct the spot curve. he method relies on the assumption that no-arbitrage condition holds.
34 Bootstrapping Recall that the bond price equation, under the assumption of no-arbitrage å ( ) ( ) t t t M c P ) ( ( ) ) ( ø ö ç ç ç ç è æ å t t t c P M c
35 Bootstrapping 3 Suppose ou are given the following: Maturit Coupon Price
36 Bootstrapping 4 he -ear spot interest rate: æ ç ç ç ç è P( ) c M å t c ( ) t t ö ø he -ear spot interest rate: he -ear spot interest rate is then: % æ ö ç ç ç 4.7 ç 99.8 è ø 4.39%
37 Bootstrapping 5 Suppose we have coupon bonds and the maximum maturit among these bond is ears. P( P( P( ) ) ) " CF CF CF DF DF DF CF CF CF DF DF DF! CF! CF! CF DF DF DF
38 Bootstrapping 6 Stack the equations in matrix form é P( ) CF & CF DF ê ê ê ë $ P( ) #%"%! P ù ú ú ú û é ù é ù ê ú ê ú $ ' $ $ ê ú ê ú ê CF & CF ú ê DF ú #% ë %% "%%%! û #"! ë û CF DF
39 Bootstrapping 7 Pre- (Left-) multipl the inverse of cash-flow matrix to the price vector P é DF ù ê ú % ê ú ê DF ú $#" ë û DF inv é CF & CF ù ê ú ê % ' % ú ê CF & CF ú $! ë!!#!!!" û Inverse of CF, CF - é ê ê ê ë P( ) % P( ) $!#!" P ù ú ú ú û
40 Regression Approach More generall, suppose we have N coupon bonds and the maximum maturit is. é P( ) CF & CF DF ê ê ê ë $ P( ) #%"%! N P ù ú ú ú û é ù é ù ê ú ê ú $ ' $ $ ê ú ê ú ê CF N & CF N ú ê DF ú #% ë %% "%%%! û #"! ë û CF DF
41 Regression Approach If N, then regression approach reduce to the bootstrap approach. If N<, then too man discount factors satisf the sstem. If N>, then unique discount factors with pricing error.
42 Regression Approach 3 We can estimate the vector DF b the method of Ordinar-Least-Square (OLS). he pricing error: e Find the DF such that P N å i e i CF DF æ ö ç P( ) å i i CF tdft è t ø is minimized ( ) ( ) OLS estimated discount factor: DF CF' CF CF' P
43 Parametric Yield Curve Models he resulting estimated ield curve is usuall not smooth. Interpolation is often used to calculate the discount factor/spot rate for maturit that we do not have.
44 Parametric Yield Curve Models Parametric function to model the discount factor or the spot curve (or the forward curve) can give ou the desired smoothness. Pros Give the desired smoothness Alleviate the difficult of not enough number of coupon bonds relative to the maximum maturit Cons At the potential expense of higher pricing error. Ma requires non-linear method to estimate.
45 Parametric Yield Curve Models 3 For example he Polnominal Yield Curve. he spot curve can be modeled as a polnominal equation with an order t t b t b t 3 3 a b
46 Parametric Yield Curve Models 4 t t 0.003t t 8% 6% 4% % 0% 8% 6% 4% % 0% Maturit in ears (t)
47 Parametric Yield Curve Models 5 wo other common models: Nelson-Siegel Svennson i é æ i ö ù t ì ï é æ i ö ù t æ i ö ü ï a b ê expç ú b í ê expç ú expç ý ë è t ø û i ï î ë è t ø û i è t ø ï þ t ( i) é æ i ö ù t ï ì é æ ö ù æ ö ï ü ï ì é æ ö ù æ ê ç ç i t í ê ç ç i i t ú ç ç ý í ê ç ç i a b ú ú ç ç exp b exp exp b 3 exp exp ë è t ø û i ï î ë è t ø û i è t ø ï þ ï î ë è t ø û i è t ö ï ü ý ø ï þ
48 he Pure Expectation Hpothesis he strong form of pure expectation hpothesis Forward rates reflect toda s expectation of what spot rates will be in the future. Investors are ASSUMED to be risk-neutral. Investors care about the return onl. Risk is not a concern.
49 he Pure Expectation Hpothesis Consider the three following strategies: A. Bu a -ear zero-coupon bond on toda. ( ) B. Bu a -ear zero-coupon bond and then roll-over with a one-ear forward -ear zero-coupon bond on toda. ( )( f, ) C. Bu a -ear zero-coupon bond on toda and then roll-over the proceed with another -ear zero-coupon one ear later ( )( E[, ])
50 he Pure Expectation Hpothesis 3 Recall that no-arbitrage condition ensures that ( ) ( )( f, ) Pure expectation hpothesis: Investors will be indifferent between all three strategies if the expected return is the same: ( )( f,) ( )( E[, ]) f E[ ],,
51 he Pure Expectation Hpothesis 4 Moreover, this implies that ( ) (, )( E[, ])» E[ ], Extending the logic to the -ear case:» E[, ]! E[, ]
52 he Pure Expectation Hpothesis 5 Forward rates correspond to toda s expectations of future spot rates [ > > Þ E, ] If i.e., market participants are expecting an increase in the spot rate in the future. An upward-sloping spot curve suggests that the market is expecting rates to rise.
53 he Pure Expectation Hpothesis % Jul-3 Jan-4 Jul-4 Jan-5 Axis itle 0 -r spot rate Expected one-r forward -ear spot
54 erm Premium here must be something else that helps explain. Suppose that E[, ] tp, and ASSUME that E[, ] hen tp, tp > 0 If, then > (even though the market does not expect rates to rise.),
55 erm Premium tp, Question: What is? It is often called the term premium --- he premium that investors require to hold a bond with a particular maturit over another maturit (We usuall consider the term premium of longer-bond over short-term bond!) Alternativel, the no-arbitrage condition suggests that we can define it as tp, f,, E[ ] (he excess of the forward rate over pure expectation of future interest rate.)
56 erm Premium 3 he term-premium of longer-term bond over shorter-term bond is usuall (but not alwas). Positive: Investors are assumed to be risk-averse in order to justif the positive term-premium Increasing: Longer the maturit, higher the price sensitivit.
57 erm Premium 4 he term-premium can then be decomposed into two components. [Price] risk premium (increasing with the maturit; First-order): Higher the duration, more sensitive is the price to a change in interest rates; Convexit premium (decreasing with the maturit Second-order): Higher the convexit, for the same amount of interest rate Drop è larger the price increases Increase è smaller the price decreases he term-premium can be positive or negative depending on which component dominates.
58 Market Segmentation 5 Market Segmentation or Preferred Habitat Hpothesis Bonds of a given maturit are mainl traded b a particular group of investors. Longer-term bond ó Pension fund he suppl and demand conditions of a bond with a given maturit are independent to the suppl and demand conditions of bonds of other maturit. Arbitrage opportunit across maturities is missing. his explanation is less popular nowadas.
59 Module Wrap-Up he erm Structure of Interest Rates Relates the zero coupon ields to different maturities. Zero coupon ields are often not readil available. Need to construct the curve using coupon bonds and their prices. Bootstrap and Regression Parametric Models provide smoother ields
60 Module Wrap-Up If the Pure Expectation Hpothesis holds he ield curve essentiall reflects the market forecast of future interest rate movements. he presence of a term-premium, necessitates a theor to model the termpremium.
ACC 471 Practice Problem Set #2 Fall Suggested Solutions
ACC 471 Practice Problem Set #2 Fall 2002 Suggested Solutions 1. Text Problems: 11-6 a. i. Current ield: 70 960 7 29%. ii. Yield to maturit: solving 960 35 1 1 1 000 1 for gives a ield to maturit of 4%
More informationFinancial Market Analysis (FMAx) Module 3
Financial Market Analysis (FMAx) Module 3 Bond Price Sensitivity This training material is the property of the International Monetary Fund (IMF) and is intended for use in IMF Institute for Capacity Development
More informationFinancial Market Analysis (FMAx) Module 3
Financial Market Analysis (FMAx) Module 3 Bond Price Sensitivity This training material is the property of the International Monetary Fund (IMF) and is intended for use in IMF Institute for Capacity Development
More informationFinancial Market Analysis (FMAx) Module 2
Financial Market Analysis (FMAx) Module 2 Bond Pricing This training material is the property of the International Monetary Fund (IMF) and is intended for use in IMF Institute for Capacity Development
More information1. Parallel and nonparallel shifts in the yield curve. 2. Factors that drive U.S. Treasury security returns.
LEARNING OUTCOMES 1. Parallel and nonparallel shifts in the yield curve. 2. Factors that drive U.S. Treasury security returns. 3. Construct the theoretical spot rate curve. 4. The swap rate curve (LIBOR
More informationS&P/JPX JGB VIX Index
S&P/JPX JGB VIX Index White Paper 15 October 015 Scope of the Document This document explains the design and implementation of the S&P/JPX Japanese Government Bond Volatility Index (JGB VIX). The index
More informationIndian Sovereign Yield Curve using Nelson-Siegel-Svensson Model
Indian Sovereign Yield Curve using Nelson-Siegel-Svensson Model Of the three methods of valuing a Fixed Income Security Current Yield, YTM and the Coupon, the most common method followed is the Yield To
More informationGlobal Financial Management
Global Financial Management Bond Valuation Copyright 24. All Worldwide Rights Reserved. See Credits for permissions. Latest Revision: August 23, 24. Bonds Bonds are securities that establish a creditor
More informationMonetary Economics Fixed Income Securities Term Structure of Interest Rates Gerald P. Dwyer November 2015
Monetary Economics Fixed Income Securities Term Structure of Interest Rates Gerald P. Dwyer November 2015 Readings This Material Read Chapters 21 and 22 Responsible for part of 22.2, but only the material
More informationFINS2624 Summary. 1- Bond Pricing. 2 - The Term Structure of Interest Rates
FINS2624 Summary 1- Bond Pricing Yield to Maturity: The YTM is a hypothetical and constant interest rate which makes the PV of bond payments equal to its price; considered an average rate of return. It
More informationWe consider three zero-coupon bonds (strips) with the following features: Bond Maturity (years) Price Bond Bond Bond
15 3 CHAPTER 3 Problems Exercise 3.1 We consider three zero-coupon bonds (strips) with the following features: Each strip delivers $100 at maturity. Bond Maturity (years) Price Bond 1 1 96.43 Bond 2 2
More informationProblems and Solutions
1 CHAPTER 1 Problems 1.1 Problems on Bonds Exercise 1.1 On 12/04/01, consider a fixed-coupon bond whose features are the following: face value: $1,000 coupon rate: 8% coupon frequency: semiannual maturity:
More informationFoundations of Finance
Lecture 7: Bond Pricing, Forward Rates and the Yield Curve. I. Reading. II. Discount Bond Yields and Prices. III. Fixed-income Prices and No Arbitrage. IV. The Yield Curve. V. Other Bond Pricing Issues.
More informationCHAPTER 14. Bond Characteristics. Bonds are debt. Issuers are borrowers and holders are creditors.
Bond Characteristics 14-2 CHAPTER 14 Bond Prices and Yields Bonds are debt. Issuers are borrowers and holders are creditors. The indenture is the contract between the issuer and the bondholder. The indenture
More information14.02 Principles of Macroeconomics Problem Set 6 Solutions Fall 2004
Part I. True/False/Uncertain Justif our answer with a short argument. 4.0 Principles of Macroeconomics Problem Set 6 Solutions Fall 004. In an econom with technological progress, the saving rate is irrelevant
More information14.02 Principles of Macroeconomics Quiz #3, Answers
14.0 Principles of Macroeconomics Quiz #3, Answers Name: Signature: Date : Read all questions carefull and completel before beginning the exam. There are four sections and ten pages make sure ou do them
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES. Expectations hypothesis: The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is explained
More informationMeasuring Interest Rates. Interest Rates Chapter 4. Continuous Compounding (Page 77) Types of Rates
Interest Rates Chapter 4 Measuring Interest Rates The compounding frequency used for an interest rate is the unit of measurement The difference between quarterly and annual compounding is analogous to
More informationGRAPHS IN ECONOMICS. Appendix. Key Concepts. A Positive Relationship
Appendi GRAPHS IN ECONOMICS Ke Concepts Graphing Data Graphs represent quantit as a distance on a line. On a graph, the horizontal scale line is the -ais, the vertical scale line is the -ais, and the intersection
More informationBond Prices and Yields
Bond Characteristics 14-2 Bond Prices and Yields Bonds are debt. Issuers are borrowers and holders are creditors. The indenture is the contract between the issuer and the bondholder. The indenture gives
More informationFin 5633: Investment Theory and Problems: Chapter#15 Solutions
Fin 5633: Investment Theory and Problems: Chapter#15 Solutions 1. Expectations hypothesis: The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping
More informationLecture Notes 1 Part B: Functions and Graphs of Functions
Lecture Notes 1 Part B: Functions and Graphs of Functions In Part A of Lecture Notes #1 we saw man examples of functions as well as their associated graphs. These functions were the equations that gave
More informationChapter 4 Interest Rate Measurement and Behavior Chapter 5 The Risk and Term Structure of Interest Rates
Chapter 4 Interest Rate Measurement and Behavior Chapter 5 The Risk and Term Structure of Interest Rates Fisher Effect (risk-free rate) Interest rate has 2 components: (1) real rate (2) inflation premium
More informationThe Firm s Short-Run Supply. Decision
The Short-Run The short-run is a period of time in which at least one of the firm s inputs is fixed (as a result of previous decisions). For example, the lease on land ma be for one ear, in which case
More informationSolution to Problem Set 2
M.I.T. Spring 1999 Sloan School of Management 15.15 Solution to Problem Set 1. The correct statements are (c) and (d). We have seen in class how to obtain bond prices and forward rates given the current
More information3/24/2016. Intermediate Microeconomics W3211. Lecture 12: Perfect Competition 2: Cost Minimization. The Story So Far. Today. The Case of One Input
1 Intermediate Microeconomics W3211 Lecture 12: Perfect Competition 2: Cost Minimization Columbia Universit, Spring 2016 Mark Dean: mark.dean@columbia.edu Introduction 2 The Stor So Far. 3 Toda 4 We have
More informationBOND ANALYTICS. Aditya Vyas IDFC Ltd.
BOND ANALYTICS Aditya Vyas IDFC Ltd. Bond Valuation-Basics The basic components of valuing any asset are: An estimate of the future cash flow stream from owning the asset The required rate of return for
More informationFoundations of Finance
Lecture 9 Lecture 9: Theories of the Yield Curve. I. Reading. II. Expectations Hypothesis III. Liquidity Preference Theory. IV. Preferred Habitat Theory. Lecture 9: Bond Portfolio Management. V. Reading.
More informationLesson 6: Extensions and applications of consumer theory. 6.1 The approach of revealed preference
Microeconomics I. Antonio Zabalza. Universit of Valencia 1 Lesson 6: Etensions and applications of consumer theor 6.1 The approach of revealed preference The basic result of consumer theor (discussed in
More informationME II, Prof. Dr. T. Wollmershäuser. Chapter 8 Monetary Policy Transmission: IS-MP-PC-Analysis
ME II, Prof. Dr. T. Wollmershäuser Chapter 8 Monetar Polic Transmission: IS-MP-PC-Analsis Version: 15.7.21 Shortcomings of the IS-LM-Analsis Ultimate goal of the ECB: Price stabilit (formulated in terms
More informationFinancial Market Analysis (FMAx) Module 1
Financial Market Analysis (FMAx) Module 1 Pricing Money Market Instruments This training material is the property of the International Monetary Fund (IMF) and is intended for use in IMF Institute for Capacity
More informationMoney and Banking. Lecture I: Interest Rates. Guoxiong ZHANG, Ph.D. September 11th, Shanghai Jiao Tong University, Antai
Money and Banking Lecture I: Interest Rates Guoxiong ZHANG, Ph.D. Shanghai Jiao Tong University, Antai September 11th, 2018 Interest Rates Are Important Source: http://www.cartoonistgroup.com Concept of
More informationShow sufficient work and clearly mark your answers. Each problem is worth 10 points.
Page 1 of 5 MAP 4170 Name: Test 4 Date: December 8, 2011 Show sufficient work and clearl mark our answers. Each problem is worth 10 points. 1. The modified duration of a perpetuit immediate with level
More informationP1.T4.Valuation Tuckman, Chapter 5. Bionic Turtle FRM Video Tutorials
P1.T4.Valuation Tuckman, Chapter 5 Bionic Turtle FRM Video Tutorials By: David Harper CFA, FRM, CIPM Note: This tutorial is for paid members only. You know who you are. Anybody else is using an illegal
More informationFinancial Market Analysis (FMAx) Module 6
Financial Market Analysis (FMAx) Module 6 Asset Allocation and iversification This training material is the property of the International Monetary Fund (IMF) and is intended for use in IMF Institute for
More informationAppendix A Financial Calculations
Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition By Andrew M. Chisholm 010 John Wiley & Sons, Ltd. Appendix A Financial Calculations TIME VALUE OF MONEY
More informationRepresentation of Preferences
Consumer Preference and The Concept Of Utilit Representation of Preferences Bundle/basket a combination of goods and services that an individual might consume. Eample: Bundle A = (60, 30) contains 60 units
More information3.36pt. Karl Whelan (UCD) Term Structure of Interest Rates Spring / 36
3.36pt Karl Whelan (UCD) Term Structure of Interest Rates Spring 2018 1 / 36 International Money and Banking: 12. The Term Structure of Interest Rates Karl Whelan School of Economics, UCD Spring 2018 Karl
More informationINVESTMENTS. Instructor: Dr. Kumail Rizvi, PhD, CFA, FRM
INVESTMENTS Instructor: Dr. KEY CONCEPTS & SKILLS Understand bond values and why they fluctuate How Bond Prices Vary With Interest Rates Four measures of bond price sensitivity to interest rate Maturity
More informationCHAPTER 5 THE COST OF MONEY (INTEREST RATES)
CHAPTER 5 THE COST OF MONEY (INTEREST RATES) 1 Learning Outcomes LO.1 Describe the cost of money and factors that affect the cost of money. LO.2 Describe how interest rates are determined. LO.3 Describe
More informationBond and Common Share Valuation
Bond and Common Share Valuation Lakehead University Fall 2004 Outline of the Lecture Bonds and Bond Valuation The Determinants of Interest Rates Common Share Valuation 2 Bonds and Bond Valuation A corporation
More informationBond Valuation. FINANCE 100 Corporate Finance
Bond Valuation FINANCE 100 Corporate Finance Prof. Michael R. Roberts 1 Bond Valuation An Overview Introduction to bonds and bond markets» What are they? Some examples Zero coupon bonds» Valuation» Interest
More informationDUKE UNIVERSITY The Fuqua School of Business. Financial Management Spring 1989 TERM STRUCTURE OF INTEREST RATES*
DUKE UNIVERSITY The Fuqua School of Business Business 350 Smith/Whaley Financial Management Spring 989 TERM STRUCTURE OF INTEREST RATES* The yield curve refers to the relation between bonds expected yield
More informationMARKET INPUTS. Joint UNCTAD, IMF and World Bank MTDS Workshop Geneva, October 1-5, 2018
MARKET INPUTS Joint UNCTAD, IMF and World Bank MTDS Workshop Geneva, October 1-5, 2018 MARKET INTEREST RATES The cash flows as well as the cost and risk of a given debt management strategy will depend
More informationInformation, efficiency and the core of an economy: Comments on Wilson s paper
Information, efficiency and the core of an economy: Comments on Wilson s paper Dionysius Glycopantis 1 and Nicholas C. Yannelis 2 1 Department of Economics, City University, Northampton Square, London
More informationCHAPTER 8. Valuing Bonds. Chapter Synopsis
CHAPTER 8 Valuing Bonds Chapter Synopsis 8.1 Bond Cash Flows, Prices, and Yields A bond is a security sold at face value (FV), usually $1,000, to investors by governments and corporations. Bonds generally
More informationCHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS
CHAPTER 15 The Term Structure of Interest Rates McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 15-2 Overview of Term Structure The yield curve is a graph that
More informationDebt. Last modified KW
Debt The debt markets are far more complicated and filled with jargon than the equity markets. Fixed coupon bonds, loans and bills will be our focus in this course. It's important to be aware of all of
More informationZero-Coupon Bonds (Pure Discount Bonds)
Zero-Coupon Bonds (Pure Discount Bonds) By Eq. (1) on p. 23, the price of a zero-coupon bond that pays F dollars in n periods is where r is the interest rate per period. F/(1 + r) n, (9) Can be used to
More informationBOND VALUATION. YTM Of An n-year Zero-Coupon Bond
BOND VALUATION BOND VALUATIONS BOND: A security sold by governments and corporations to raise money from investors today in exchange for promised future payments 1. ZERO COUPON BONDS ZERO COUPON BONDS:
More informationFIN 6160 Investment Theory. Lecture 9-11 Managing Bond Portfolios
FIN 6160 Investment Theory Lecture 9-11 Managing Bond Portfolios Bonds Characteristics Bonds represent long term debt securities that are issued by government agencies or corporations. The issuer of bond
More informationModelling the Zero Coupon Yield Curve:
Modelling the Zero Coupon Yield Curve: A regression based approach February,2010 12 th Global Conference of Actuaries Srijan Sengupta Section 1: Introduction What is the zero coupon yield curve? Its importance
More informationMorningstar Rating Analysis
Morningstar Research January 2017 Morningstar Rating Analysis of European Investment Funds Authors: Nikolaj Holdt Mikkelsen, CFA, CIPM Ali Masarwah Content Morningstar European Rating Analysis of Investment
More informationChapter 2: BASICS OF FIXED INCOME SECURITIES
Chapter 2: BASICS OF FIXED INCOME SECURITIES 2.1 DISCOUNT FACTORS 2.1.1 Discount Factors across Maturities 2.1.2 Discount Factors over Time 2.1 DISCOUNT FACTORS The discount factor between two dates, t
More informationMathematics of Financial Derivatives
Mathematics of Financial Derivatives Lecture 9 Solesne Bourguin bourguin@math.bu.edu Boston University Department of Mathematics and Statistics Table of contents 1. Zero-coupon rates and bond pricing 2.
More informationINV3702 INVESTMENTS: FIXED INCOME ANALYSIS EXAM MEMO MAY/JUNE 2012
INV3702 INVESTMENTS: FIXED INCOME ANALYSIS EXAM MEMO MAY/JUNE 2012 SECTION A: MULTIPLE CHOICE QUESTIONS (30 MARKS) *THERE MAY BE MINOR EDITORIAL DIFFERENCES BETWEEN THE QUESTIONS IN THIS MEMO AND THOSE
More informationIt is a measure to compare bonds (among other things).
It is a measure to compare bonds (among other things). It provides an estimate of the volatility or the sensitivity of the market value of a bond to changes in interest rates. There are two very closely
More informationINTEREST RATE FORWARDS AND FUTURES
INTEREST RATE FORWARDS AND FUTURES FORWARD RATES The forward rate is the future zero rate implied by today s term structure of interest rates BAHATTIN BUYUKSAHIN, CELSO BRUNETTI 1 0 /4/2009 2 IMPLIED FORWARD
More informationSurvey of Math Chapter 21: Savings Models Handout Page 1
Chapter 21: Savings Models Handout Page 1 Growth of Savings: Simple Interest Simple interest pays interest only on the principal, not on any interest which has accumulated. Simple interest is rarely used
More informationMoney and Banking. Lecture I: Interest Rates. Guoxiong ZHANG, Ph.D. September 12th, Shanghai Jiao Tong University, Antai
Money and Banking Lecture I: Interest Rates Guoxiong ZHANG, Ph.D. Shanghai Jiao Tong University, Antai September 12th, 2017 Interest Rates Are Important Source: http://www.cartoonistgroup.com Concept of
More informationChapter 7: Interest Rates and Bond Valuation, Part II
Chapter 7: Interest Rates and Bond Valuation, Part II Faculty of Business Administration Lakehead University Spring 2003 May 15, 2003 Outline 7A-C Review Questions 7.2 More on Bond Features 7.3 Bond Ratings
More informationThe Fixed Income Valuation Course. Sanjay K. Nawalkha Gloria M. Soto Natalia A. Beliaeva
Interest Rate Risk Modeling The Fixed Income Valuation Course Sanjay K. Nawalkha Gloria M. Soto Natalia A. Beliaeva Interest t Rate Risk Modeling : The Fixed Income Valuation Course. Sanjay K. Nawalkha,
More informationCHAPTER 15. The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS
CHAPTER 15 The Term Structure of Interest Rates INVESTMENTS BODIE, KANE, MARCUS McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. INVESTMENTS BODIE, KANE, MARCUS
More informationLecture 20: Bond Portfolio Management. I. Reading. A. BKM, Chapter 16, Sections 16.1 and 16.2.
Lecture 20: Bond Portfolio Management. I. Reading. A. BKM, Chapter 16, Sections 16.1 and 16.2. II. Risks associated with Fixed Income Investments. A. Reinvestment Risk. 1. If an individual has a particular
More informationDerivatives Options on Bonds and Interest Rates. Professor André Farber Solvay Business School Université Libre de Bruxelles
Derivatives Options on Bonds and Interest Rates Professor André Farber Solvay Business School Université Libre de Bruxelles Caps Floors Swaption Options on IR futures Options on Government bond futures
More informationInformation in Financial Market Indicators: An Overview
Information in Financial Market Indicators: An Overview By Gerard O Reilly 1 ABSTRACT Asset prices can provide central banks with valuable information regarding market expectations of macroeconomic variables.
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 informationAggregate Demand. Reading. Mankiw, Macroeconomics: Chapter 9.3 and 11.2,.3 and Appendix. Dudley Cooke. Trinity College Dublin
Aggregate Demand Dudle Cooke Trinit College Dublin Dudle Cooke (Trinit College Dublin) Aggregate Demand 1/37 Reading Mankiw, Macroeconomics: Chapter 9.3 and 11.2,.3 and Appendix. Dudle Cooke (Trinit College
More information8.3 Coupon Bonds, Current yield, and Yield to Maturity
8.3 Coupon Bonds, Current yield, and Yield to Maturity 8.3.a Coupon Bonds Coupon bond: It makes periodic payments of interest. Coupon payments:periodic payments of interest are called coupons. Coupon rate:
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps 1 Outline PART ONE Chapter 1: interest rate forward contracts and their pricing and mechanics 2 Outline PART TWO Chapter 2: basic and customized swaps and their pricing
More informationProperties of Demand Functions. Chapter Six. Own-Price Changes Fixed p 2 and y. Own-Price Changes. Demand
Properties of Demand Functions Chapter Six Demand Comparative statics analsis of ordinar demand functions -- the stud of how ordinar demands (,p 2,) and (,p 2,) change as prices, p 2 and income change.
More informationQuestion 1: Productivity, Output and Employment (30 Marks)
ECON 222 Macroeconomic Theory I Fall Term 2010 Assignment 2 Due: Drop Box 2nd Floor Dunning Hall by noon October 15th 2010 No late submissions will be accepted No group submissions will be accepted No
More informationGLM III - The Matrix Reloaded
GLM III - The Matrix Reloaded Duncan Anderson, Serhat Guven 12 March 2013 2012 Towers Watson. All rights reserved. Agenda "Quadrant Saddles" The Tweedie Distribution "Emergent Interactions" Dispersion
More informationModule 3: Factor Models
Module 3: Factor Models (BUSFIN 4221 - Investments) Andrei S. Gonçalves 1 1 Finance Department The Ohio State University Fall 2016 1 Module 1 - The Demand for Capital 2 Module 1 - The Supply of Capital
More informationLecture 9. Basics on Swaps
Lecture 9 Basics on Swaps Agenda: 1. Introduction to Swaps ~ Definition: ~ Basic functions ~ Comparative advantage: 2. Swap quotes and LIBOR zero rate ~ Interest rate swap is combination of two bonds:
More informationOutline Types Measures Spot rate Bond pricing Bootstrap Forward rates FRA Duration Convexity Term structure. Interest Rates.
Haipeng Xing Department of Applied Mathematics and Statistics Outline 1 Types of interest rates 2 Measuring interest rates 3 The n-year spot rate 4 ond pricing 5 Determining treasury zero rates the bootstrap
More informationINTEREST RATES Overview Real vs. Nominal Rate Equilibrium Rates Interest Rate Risk Reinvestment Risk Structure of the Yield Curve Monetary Policy
INTEREST RATES Overview Real vs. Nominal Rate Equilibrium Rates Interest Rate Risk Reinvestment Risk Structure of the Yield Curve Monetary Policy Some of the following material comes from a variety of
More informationTHE NEW EURO AREA YIELD CURVES
THE NEW EURO AREA YIELD CURVES Yield describe the relationship between the residual maturity of fi nancial instruments and their associated interest rates. This article describes the various ways of presenting
More informationMFE8812 Bond Portfolio Management
MFE8812 Bond Portfolio Management William C. H. Leon Nanyang Business School January 16, 2018 1 / 63 William C. H. Leon MFE8812 Bond Portfolio Management 1 Overview Value of Cash Flows Value of a Bond
More informationChapter 4. Consumer Choice. A Consumer s Budget Constraint. Consumer Choice
Chapter 4 Consumer Choice Consumer Choice In Chapter 3, we described consumer preferences Preferences alone do not determine choices We must also specifi constraints In this chapter, we describe how consumer
More informationSECTION A: MULTIPLE CHOICE QUESTIONS. 1. All else equal, which of the following would most likely increase the yield to maturity on a debt security?
SECTION A: MULTIPLE CHOICE QUESTIONS 2 (40 MARKS) 1. All else equal, which of the following would most likely increase the yield to maturity on a debt security? 1. Put option. 2. Conversion option. 3.
More informationMathematics of Financial Derivatives. Zero-coupon rates and bond pricing. Lecture 9. Zero-coupons. Notes. Notes
Mathematics of Financial Derivatives Lecture 9 Solesne Bourguin bourguin@math.bu.edu Boston University Department of Mathematics and Statistics Zero-coupon rates and bond pricing Zero-coupons Definition:
More information5 Profit maximization, Supply
Microeconomics I - Lecture #5, March 17, 2009 5 Profit maximization, Suppl We alread described the technological possibilities now we analze how the firm chooses the amount to produce so as to maximize
More informationLecture on Duration and Interest Rate Risk 1 (Learning objectives at the end)
Bo Sjö 03--07 (updated formulas 0a and 0b) Lecture on Duration and Interest Rate Risk (Learning objectives at the end) Introduction In bond trading, bond portfolio management (debt management) movements
More informationInterest Rate Markets
Interest Rate Markets 5. Chapter 5 5. Types of Rates Treasury rates LIBOR rates Repo rates 5.3 Zero Rates A zero rate (or spot rate) for maturity T is the rate of interest earned on an investment with
More informationCOST OF CAPITAL IN INTERNATIONAL MKTS
COST OF CAPITAL IN INTERNATIONAL MKTS Capital Structure and Cost of Capital Cost of Capital - Country Risk affects discount rates - Different countries will have different risk free rates (k f ). - High
More informationChapter 10 - Term Structure of Interest Rates
10-1 Chapter 10 - Term Structure of Interest Rates Section 10.2 - Yield Curves In our analysis of bond coupon payments, for example, we assumed a constant interest rate, i, when assessing the present value
More informationHedging with Futures Contracts
sau24557_app24.qxd 1/6/03 12:38 PM Page 1 Chapter 24 Managing Risk with Derivative Securities 1 Appendix 24A: Hedging with Futures Contracts Macrohedging with Futures The number of futures contracts that
More information1. The real risk-free rate is the increment to purchasing power that the lender earns in order to induce him or her to forego current consumption.
Chapter 02 Determinants of Interest Rates True / False Questions 1. The real risk-free rate is the increment to purchasing power that the lender earns in order to induce him or her to forego current consumption.
More informationTerm Structure of Interest Rates. For 9.220, Term 1, 2002/03 02_Lecture7.ppt
Term Structure of Interest Rates For 9.220, Term 1, 2002/03 02_Lecture7.ppt Outline 1. Introduction 2. Term Structure Definitions 3. Pure Expectations Theory 4. Liquidity Premium Theory 5. Interpreting
More informationBond Analysis & Valuation Solutions
Bond Analysis & Valuation s Category of Problems 1. Bond Price...2 2. YTM Calculation 14 3. Duration & Convexity of Bond 30 4. Immunization 58 5. Forward Rates & Spot Rates Calculation... 66 6. Clean Price
More informationSurvey of Math: Chapter 21: Consumer Finance Savings (Lecture 1) Page 1
Survey of Math: Chapter 21: Consumer Finance Savings (Lecture 1) Page 1 The mathematical concepts we use to describe finance are also used to describe how populations of organisms vary over time, how disease
More informationDuality & The Dual Simplex Method & Sensitivity Analysis for Linear Programming. Metodos Cuantitativos M. En C. Eduardo Bustos Farias 1
Dualit & The Dual Simple Method & Sensitivit Analsis for Linear Programming Metodos Cuantitativos M. En C. Eduardo Bustos Farias Dualit EverLP problem has a twin problem associated with it. One problem
More informationEconomics 345. We know that a money demand function can be described as:
conomics 345 The Arithmetic of Monetar Growth, Inflation and the xchange Rate in the Monetar Approach We know that a mone demand function can be described as: αr ( M / ) =. e where M is the nominal quantit
More informationSome Formulas neglected in Anderson, Sweeny, and Williams, with a Digression on Statistics and Finance
Some Formulas neglected in Anderson, Sween, and Williams, with a Digression on Statistics and Finance Transformations of a Single Random variable: If ou have a case where a new random variable is defined
More informationLecture 03 Consumer Preference Theory
Lecture 03 Consumer reference Theor 1. Consumer preferences will tell us how an individual would rank (i.e. compare the desirabilit of) an two consumption bundles (or baskets), assuming the bundles were
More informationPortfolio Management Philip Morris has issued bonds that pay coupons annually with the following characteristics:
Portfolio Management 010-011 1. a. Critically discuss the mean-variance approach of portfolio theory b. According to Markowitz portfolio theory, can we find a single risky optimal portfolio which is suitable
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationAlan Brazil. Goldman, Sachs & Co.
Alan Brazil Goldman, Sachs & Co. Assumptions: Coupon paid every 6 months, $100 of principal paid at maturity, government guaranteed 1 Debt is a claim on a fixed amount of cashflows in the future A mortgage
More informationReading. Valuation of Securities: Bonds
Valuation of Securities: Bonds Econ 422: Investment, Capital & Finance University of Washington Last updated: April 11, 2010 Reading BMA, Chapter 3 http://finance.yahoo.com/bonds http://cxa.marketwatch.com/finra/marketd
More information