Practice Set and Solutions #2

Size: px
Start display at page:

Download "Practice Set and Solutions #2"

Transcription

1 723G26/ 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 sets contain worked-out problems in corporate finance and investments, with a bias toward quantitative problems. These sets are not graded, and there is no need to hand-in the solutions. Students are strongly encouraged to solve them, discuss the solutions with other course participants, and discuss any problems with their teacher. Some questions in the final exam might resemble the problems given here. Question 1 The current one-year Treasury bill rate ( 1 r 1 ) is 5.2 percent, and the implicit forward one-year rate 1 f 2 12 months from now is 5.8 percent. According to the unbiased expectations theory, what should be the current rate ( 1 r 2 ) for a two-year Treasury security? Question 2 The Wall Street Journal reported interest rates of 6 percent, 6.35 percent, 6.65 percent, and 6.75 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6? Question 3 You note the following yield curve in The Wall Street Journal. According to the unbiased expectations hypothesis, what is the implicit one-year forward rate for the period beginning two years from today, 2f 1? Maturity Yield One day 2% One year 5.5% Two years 6.5 Three years 9 Question 4 1

2 a) If both buyers (the public) and sellers of bonds (business) thinks that inflation will go up how will that change the demand for bonds, interest rates and the slope of the yield curve. b) If investors (demand for bonds) think that bad times are coming how will that change the demand for bonds, interest rates and slope the yield curve? Question 5 Based on economists = forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: Question 6 1R 1 = 5.65% E( 2 r 1 ) = 6.75% L 2 = 0.05% E( 3 r 1 ) = 6.85% L 3 = 0.10% E( 4 r 1 ) = 7.15% L 4 = 0.12% Using the liquidity premium hypothesis and plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. A pension fund is attempting to balance one of the bond portfolios under its management. The fund has identified three bonds which have five-year maturities and which trade at a yield to maturity (YTM) of 9 percent, face value is $1,000. The bonds differ only in that the coupons are 7 percent, 9 percent, and 11 percent. a. What is the duration for each bond? b. What is the relationship between duration and the amount of coupon interest that is paid? Plot the relationship. Question 7 An investor can invest in a 5 year bond with annual coupon payments of 3%. The bond is trading at an YTM of 4%. There also a zero coupon bond with a yield of 1.9%. Both bonds have a face value of a) What is the value of these bonds today? b) If the investor have 10m to invest and wants to create a portfolio with a duration of 3 year how should the investor allocate the portfolio? 2

3 Solutions Solution 1 (1.052)(1.058) = (1 + 1 r 2 ) 2 = ; (1 + 1 r 2 ) = r 2 =.0550 or 5.50 percent Solution 2 [1 + E( i r 1 )] = (1 + 1 R i ) i (1 + 1 R i-1 ) i-1 [1 + E( 4 r 1 )] = (1.0635) 4 (1.06) 3 = E( 4 r 1 ) = 7.41 percent for period 4 [1 + E( 5 r 1 )] = (1.0665) 5 (1.0635) 4 = E( 5 r 1 ) = 7.86 percent for period 5 [1 + E( 6 r 1 )] = (1.0675) 6 (1.0665) 5 = E( 6 r 1 ) = 7.25 percent for period 6 Solution 3 The implicit forward rates are f 2 = [(1 + 1 r 2 ) 2 /(1 + 1 r 1 )] 1 f 2 = [(1.065) 2 /(1.055)] - 1 = 7.51% Solution 4 a) If inflation is going up existing bonds, with given nominal values and coupons, do not offer a yield that compensates for inflation (r = real rate + expected inflation). Thus, demand is lowered and prices of bonds fall until they offer the required yield. In addition, if prices are expected to go up it makes sense to consume today (incl. buying capital goods) before prices increase. For business today s bonds have a low real yield, why it is profitable to increase the supply of bonds and invest more. They will increase the supply of long term bonds and drive prices down. The outcome is a shift up in the yield curve, as the yield adjusts to higher inflation expectations. We can make a case for a steeper slope, in particular if expected inflation is associated with a boom in the economy. b) Coming bad times means that you have to save more for the bad times going. Cut down on current consumption and buy bonds that mature when the bad times are coming. Say that you expect bad times 18 months from now, then you buy bonds with a maturity, which in turn drives up the price of these bonds and brings down the yield. You could see the yield curve becoming humped shaped with lower mid term bonds selling at higher prices than long-term bonds. Solution 5 3

4 1r 1 = 5.65% 1r 2 = [( )( )] ½ - 1= 6.22% 1r 3 = [( )( )( )] 1/3-1 = 6.47% 1r 4 = [( )( )( )( )] 1/4-1 = 6.67% and the current yield curve will be upward sloping as shown: YTM 6.67% 6.47% 6.22% 5.65% Term to Maturity (in years) Solution 6 Five-year Bond: Par value = $1,000, Maturity = 5 years, R = 9%, Coupon rate = 7% t CF PV of CF PV of CF x t 1 $70 $64.22 $ $70 $58.92 $ $70 $54.05 $ $70 $49.59 $ $1,070 $ $3, $ $4, Duration = $4,019.71/$ = R = 9% Coupon rate = 9% t CF PV of CF PV of CF x t 1 $90 $82.57 $ $90 $75.75 $ $90 $69.50 $ $90 $63.76 $ $1,090 $ $3, $1, $4, Duration = $4,239.72/$1, = R = 9% Coupon rate = 11% 4

5 t CF PV of CF PV of CF x t 1 $110 $ $ $110 $92.58 $ $110 $84.94 $ $110 $77.93 $ $1,110 $ $3, $1, $4, Duration = $4,459.73/$1, = b. What is the relationship between duration and the amount of coupon interest that is paid? Plot the relationship. Years Duration and Coupon Rates % 9% 11% Coupon Rates Duration decreases as the amount of coupon interest increases. Duration Change in Coupon Duration % % % Solution 7 a) The solution is given by the standard formulas for bond valuation (calculate the present value of the cash flows, using YTM as the discount rate. The duration of the five year bond is 4.71 years. The duration of the one-year zero coupon bond is 1 year. A portfolio with the duration 3 years is created by mixing the 5 and one year bonds such that the combined portfolio has a duration of 3 years. Le the weight in the portfolio of the one year bond be w 1 and the weight of the five year bond is w 2 = (1-w 1 ). The solution is given by the weighted duration of the two bonds being equal to 3 (years), 3 = 1 x w x (1-w 1 ) The solution is 3 = w 1 *1 + (1-w 1 )* = w w

6 -1.71 = (1-4.71) w 1 w 1 = -1.71/-3.71) = 0.46 and w 1 = 0.46 and w 2 = (1- w 1 ) = In money terms the investor should allocate 0.46 x 10m = 4.6m in the one year bond, and the 5.4m in the 5 year bond. 6

Practice Set and Solutions #2

Practice Set and Solutions #2 2013-11-07 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 sets contain

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

More information

Answers to End-of-Chapter Questions

Answers to End-of-Chapter Questions Answers to End-of-Chapter 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 information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

More information

Answer Key to Midterm

Answer 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 information

Practice Set #1 and Solutions.

Practice Set #1 and Solutions. Bo Sjö 14-05-03 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 information

Term Structure of Interest Rates

Term Structure of Interest Rates Appendix 8B Term Structure of Interest Rates To explain the process of estimating the impact of an unexpected shock in short-term interest rates on the entire term structure of interest rates, FIs use

More information

Investment Analysis (FIN 670) Fall Homework 3

Investment Analysis (FIN 670) Fall Homework 3 Investment Analysis (FIN 670) Fall 2009 Homework 3 Instructions: please read carefully You should show your work how to get the answer for each calculation question to get full credit You should make 2

More information

Practice Set #2 and Solutions.

Practice Set #2 and Solutions. FIN-672 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 information

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;

More information

Econ 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 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 information

Bond valuation and bond yields

Bond 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 information

Midterm Exam 1. 1. (20 points) Determine whether each of the statements below is True or False:

Midterm Exam 1. 1. (20 points) Determine whether each of the statements below is True or False: Econ 353 Money, Banking, and Financial Institutions Spring 2006 Midterm Exam 1 Name The duration of the exam is 1 hour 20 minutes. The exam consists of 11 problems and it is worth 100 points. Please write

More information

Chapter 6 Interest Rates and Bond Valuation

Chapter 6 Interest Rates and Bond Valuation Chapter 6 Interest Rates and Bond Valuation Solutions to Problems P6-1. P6-2. LG 1: Interest Rate Fundamentals: The Real Rate of Return Basic Real rate of return = 5.5% 2.0% = 3.5% LG 1: Real Rate of Interest

More information

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions. Bond Pricing - 1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is

More information

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

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 long-term fixed income securities are federal government bonds, corporate

More information

Chapter Nine Selected Solutions

Chapter 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 information

DURATION AND CONVEXITY

DURATION AND CONVEXITY CHAPTER 5 DURATION AND CONVEXITY KEY CONCEPTS Duration Modified duration Convexity DURATION Bonds, as discussed in previous chapters of this book, are subject to the following major risks: Risk of default

More information

2. What is your best estimate of what the price would be if the riskless interest rate was 9% (compounded semi-annually)? (1.04)

2. What is your best estimate of what the price would be if the riskless interest rate was 9% (compounded semi-annually)? (1.04) Lecture 4 1 Bond valuation Exercise 1. A Treasury bond has a coupon rate of 9%, a face value of $1000 and matures 10 years from today. For a treasury bond the interest on the bond is paid in semi-annual

More information

Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage

Bonds 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

ANSWERS TO END-OF-CHAPTER PROBLEMS WITHOUT ASTERISKS

ANSWERS TO END-OF-CHAPTER PROBLEMS WITHOUT ASTERISKS Part III Answers to End-of-Chapter Problems 97 CHAPTER 1 ANSWERS TO END-OF-CHAPTER PROBLEMS WITHOUT ASTERISKS Why Study Money, Banking, and Financial Markets? 7. The basic activity of banks is to accept

More information

EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS TERM PAPER

EC247 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 information

Introduction to Bond Valuation. Types of Bonds

Introduction to Bond Valuation. Types of Bonds Introduction to Bond Valuation (Text reference: Chapter 5 (Sections 5.1-5.3, Appendix)) Topics types of bonds valuation of bonds yield to maturity term structure of interest rates more about forward rates

More information

Review for Exam 1. Instructions: Please read carefully

Review for Exam 1. Instructions: Please read carefully Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation

More information

The Term Structure of Interest Rates CHAPTER 13

The Term Structure of Interest Rates CHAPTER 13 The Term Structure of Interest Rates CHAPTER 13 Chapter Summary Objective: To explore the pattern of interest rates for different-term assets. The term structure under certainty Forward rates Theories

More information

Maturity and interest-rate risk

Maturity and interest-rate risk Interest rate risk, page 1 Maturity and interest-rate risk Suppose you buy one of these three bonds, originally selling at a yield to maturity of 8 percent. Yield to One-year 30-year 30-year maturity 8%

More information

Chapter Two. Determinants of Interest Rates. McGraw-Hill /Irwin. Copyright 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter Two. Determinants of Interest Rates. McGraw-Hill /Irwin. Copyright 2001 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Two Determinants of Interest Rates Interest Rate Fundamentals Nominal interest rates - the interest rate actually observed in financial markets directly affect the value (price) of most securities

More information

CHAPTER 14: BOND PRICES AND YIELDS

CHAPTER 14: BOND PRICES AND YIELDS CHAPTER 14: BOND PRICES AND YIELDS PROBLEM SETS 1. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should

More information

Overview of Lecture 5 (part of Lecture 4 in Reader book)

Overview of Lecture 5 (part of Lecture 4 in Reader book) Overview of Lecture 5 (part of Lecture 4 in Reader book) Bond price listings and Yield to Maturity Treasury Bills Treasury Notes and Bonds Inflation, Real and Nominal Interest Rates M. Spiegel and R. Stanton,

More information

The Term Structure of Interest Rates, Spot Rates, and Yield to Maturity

The Term Structure of Interest Rates, Spot Rates, and Yield to Maturity Chapter 5 How to Value Bonds and Stocks 5A-1 Appendix 5A The Term Structure of Interest Rates, Spot Rates, and Yield to Maturity In the main body of this chapter, we have assumed that the interest rate

More information

Exam 1 Morning Session

Exam 1 Morning Session 91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark

More information

Chapter 6. The Risk and Term Structure of Interest Rates. 6.1 Risk Structure of Interest Rates

Chapter 6. The Risk and Term Structure of Interest Rates. 6.1 Risk Structure of Interest Rates Chapter 6 The Risk and Term Structure of Interest Rates 6.1 Risk Structure of Interest Rates 1) The risk structure of interest rates is A) the structure of how interest rates move over time. B) the relationship

More information

GESTÃO FINANCEIRA II PROBLEM SET 2 - SOLUTIONS

GESTÃO FINANCEIRA II PROBLEM SET 2 - SOLUTIONS GESTÃO FINANCEIRA II PROBLEM SET - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 010-011 Yield to Maturity Chapter 8 Valuing Bonds 8-3. The following

More information

Examination II. Fixed income valuation and analysis. Economics

Examination II. Fixed income valuation and analysis. Economics Examination II Fixed income valuation and analysis Economics Questions Foundation examination March 2008 FIRST PART: Multiple Choice Questions (48 points) Hereafter you must answer all 12 multiple choice

More information

Chapter 3 Fixed Income Securities

Chapter 3 Fixed Income Securities Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-income securities. Stocks. Real assets (capital budgeting). Part C Determination

More information

I. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds

I. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with Default-Free Bonds III. Duration: Details and Examples IV. Immunization

More information

Bonds and Yield to Maturity

Bonds 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 information

Investments Analysis

Investments 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 information

Mid-Term Exam Practice Set and Solutions.

Mid-Term Exam Practice Set and Solutions. FIN-469 Investments Analysis Professor Michel A. Robe Mid-Term Exam Practice Set and Solutions. What to do with this practice set? To help students prepare for the mid-term exam, two practice sets with

More information

Yield Measures, Spot Rates & Forward Rates

Yield Measures, Spot Rates & Forward Rates Fixed Income Yield Measures, Spot Rates & Forward Rates Reading - 57 www.proschoolonline.com/ 1 Sources of Return Coupon interest payment: Periodic coupon interest is paid on the par value of the bond

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE 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 information

高顿网校 财经讲堂 2013 年 CFA 一级考试难点解析. 全球财经证书培训领导品牌 Fixed Income (1) Embedded Options. Fixed Income (1) Example: Embedded Options

高顿网校 财经讲堂 2013 年 CFA 一级考试难点解析. 全球财经证书培训领导品牌  Fixed Income (1) Embedded Options. Fixed Income (1) Example: Embedded Options 高顿网校 财经讲堂 2013 年 CFA 一级考试难点解析 高顿教育旗下品牌 : 高顿网校 Fixed Income (1) Embedded Options Option Type Benefits the Yield Price Call Issuer/Borrower Higher Lower Prepayment Issuer/Borrower Higher Lower Put Buyer

More information

Review for Exam 2. Instructions: Please read carefully

Review for Exam 2. Instructions: Please read carefully Review for Exam 2 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation

More information

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 9th Edition, Copyright John C. Hull

Chapter 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 information

FIN 472 Fixed-Income Securities Debt Instruments

FIN 472 Fixed-Income Securities Debt Instruments FIN 472 Fixed-Income 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 information

Figure 10.1 Listing of Treasury Issues

Figure 10.1 Listing of Treasury Issues CHAPER 10 Bond Prices and Yields 10.1 BOND CHARACERISICS Bond Characteristics reasury Notes and Bonds Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture

More information

Econ 330 Exam 1 Name ID Section Number

Econ 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 information

BUSINESS FINANCE (FIN 312) Spring 2009

BUSINESS FINANCE (FIN 312) Spring 2009 BUSINESS FINANCE (FIN 31) Spring 009 Assignment Instructions: please read carefully You can either do the assignment by yourself or work in a group of no more than two. You should show your work how to

More information

FNCE 301, Financial Management H Guy Williams, 2006

FNCE 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 information

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises.

1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 1. Solutions to PS 1: 1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 7. The bill has a maturity of one-half year, and an annualized

More information

FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

More information

Yield to Maturity Outline and Suggested Reading

Yield to Maturity Outline and Suggested Reading Yield to Maturity Outline Outline and Suggested Reading Yield to maturity on bonds Coupon effects Par rates Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading

More information

7. Bonds and Interest rates

7. Bonds and Interest rates 7. Bonds and Interest rates 1 2 Yields and rates I m thinking of buying a bond that has a face value of $1000, pays semiannual coupons of $40 and has 7 years to maturity. The market price is $943. Fixed

More information

Global Financial Management

Global 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 information

Yield Curve September 2004

Yield Curve September 2004 Yield Curve Basics The yield curve, a graph that depicts the relationship between bond yields and maturities, is an important tool in fixed-income investing. Investors use the yield curve as a reference

More information

Chapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull

Chapter 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 information

VALUATION OF FIXED INCOME SECURITIES. Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting

VALUATION OF FIXED INCOME SECURITIES. Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting VALUATION OF FIXED INCOME SECURITIES Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting OUTLINE Introduction Valuation Principles Day Count Conventions Duration Covexity Exercises

More information

Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk

Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk Bond Valuation 1 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow

More information

Solutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,

Solutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets, FIN 472 Professor Robert Hauswald Fixed-Income Securities Kogod School of Business, AU Solutions 2 1. For the benchmark maturity sectors in the United States Treasury bill markets, Bloomberg reported the

More information

FINANCIAL AND INVESTMENT INSTRUMENTS. Lecture 6: Bonds and Debt Instruments: Valuation and Risk Management

FINANCIAL 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 information

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

More information

Best Credit Data Bond Analytics Calculation Methodology

Best Credit Data Bond Analytics Calculation Methodology Best Credit Data Bond Analytics Calculation Methodology Created by: Pierre Robert CEO and Co-Founder Best Credit Data, Inc. 50 Milk Street, 17 th Floor Boston, MA 02109 Contact Information: pierre@bestcreditanalysis.com

More information

Chapter 5: Valuing Bonds

Chapter 5: Valuing Bonds FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A long-term debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations

More information

Answers to Review Questions

Answers to Review Questions Answers to Review Questions 1. The real rate of interest is the rate that creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual

More information

Chapter 4 Valuing Bonds

Chapter 4 Valuing Bonds Chapter 4 Valuing Bonds MULTIPLE CHOICE 1. A 15 year, 8%, $1000 face value bond is currently trading at $958. The yield to maturity of this bond must be a. less than 8%. b. equal to 8%. c. greater than

More information

Estimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu.

Estimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu. Estimating Risk free Rates Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 Adamodar@stern.nyu.edu Estimating Risk free Rates Models of risk and return in finance start

More information

2. Determine the appropriate discount rate based on the risk of the security

2. Determine the appropriate discount rate based on the risk of the security Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

More information

Chapter 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. 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 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity

More information

CHAPTER 14: BOND PRICES AND YIELDS

CHAPTER 14: BOND PRICES AND YIELDS CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3-month T-bill: ( 100,000 97,645 )4 1 = 1.02412 4 1 =.10 or 10% b. Effective annual interest rate on coupon bond paying 5% semiannually:

More information

Duration and convexity

Duration and convexity Duration and convexity Prepared by Pamela Peterson Drake, Ph.D., CFA Contents 1. Overview... 1 A. Calculating the yield on a bond... 4 B. The yield curve... 6 C. Option-like features... 8 D. Bond ratings...

More information

Alliance Consulting BOND YIELDS & DURATION ANALYSIS. Bond Yields & Duration Analysis Page 1

Alliance 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 information

Notes for Lecture 3 (February 14)

Notes 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 information

LOS 56.a: Explain steps in the bond valuation process.

LOS 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 information

Money and Banking Prof. Yamin Ahmad ECON 354 Spring 2006

Money and Banking Prof. Yamin Ahmad ECON 354 Spring 2006 Money and Banking Prof. Yamin Ahmad ECON 354 Spring 2006 Final Exam Name Id # Instructions: There are 30 questions on this exam. Please circle the correct solution on the exam paper and fill in the relevant

More information

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond 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 long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

More information

1. Present Value. 2. Bonds. 3. Stocks

1. Present Value. 2. Bonds. 3. Stocks Stocks and Bonds 1. Present Value 2. Bonds 3. Stocks 1 Present Value = today s value of income at a future date Income at one future date value today of X dollars in one year V t = X t+1 (1 + i t ) where

More information

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.)

Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.) Chapter 6 Interest Rates And Bond Valuation Learning Goals 1. Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. 2. Review the legal aspects of bond financing

More information

CHAPTER 7 INTEREST RATES AND BOND VALUATION

CHAPTER 7 INTEREST RATES AND BOND VALUATION CHAPTER 7 INTEREST RATES AND BOND VALUATION Answers to Concepts Review and Critical Thinking Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury

More information

Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

More information

Interest Rates and Commercial Real Estate By Robert Hand

Interest Rates and Commercial Real Estate By Robert Hand Interest Rates and Commercial Real Estate By Robert Hand When you hear on TV that the Fed moved rates lower today, the anchorperson is attempting to share news that will help you, but actually the news

More information

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices 196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its

More information

CHAPTER 10 BOND PRICES AND YIELDS

CHAPTER 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 information

Bond Pricing Fundamentals

Bond Pricing Fundamentals Bond Pricing Fundamentals Valuation What determines the price of a bond? Contract features: coupon, face value (FV), maturity Risk-free interest rates in the economy (US treasury yield curve) Credit risk

More information

Practice Problems for FE 486B Thursday, February 2, 2012. a) Which choice should you make if the interest rate is 3 percent? If it is 6 percent?

Practice Problems for FE 486B Thursday, February 2, 2012. a) Which choice should you make if the interest rate is 3 percent? If it is 6 percent? Practice Problems for FE 486B Thursday, February 2, 2012 1) Suppose you win the lottery. You have a choice between receiving $100,000 a year for twenty years or an immediate payment of $1,200,000. a) Which

More information

Exam 1 Sample Questions

Exam 1 Sample Questions Exam 1 Sample Questions 1. Asset allocation refers to. A. the allocation of the investment portfolio across broad asset classes B. the analysis of the value of securities C. the choice of specific assets

More information

Principles of Managerial Finance. Lawrence J. Gitman Chad J. Zutter

Principles of Managerial Finance. Lawrence J. Gitman Chad J. Zutter Global edition Principles of Managerial Finance Fourteenth edition Lawrence J. Gitman Chad J. Zutter This page is intentionally left blank. 278 Part 3 Valuation of Securities Figure 6.2 Impact of Inflation

More information

Forward guidance: Estimating the path of fixed income returns

Forward guidance: Estimating the path of fixed income returns FOR INSTITUTIONAL AND PROFESSIONAL INVESTORS ONLY NOT FOR RETAIL USE OR PUBLIC DISTRIBUTION Forward guidance: Estimating the path of fixed income returns IN BRIEF Over the past year, investors have become

More information

Bond Valuation. Chapter 7. Example (coupon rate = r d ) Bonds, Bond Valuation, and Interest Rates. Valuing the cash flows

Bond Valuation. Chapter 7. Example (coupon rate = r d ) Bonds, Bond Valuation, and Interest Rates. Valuing the cash flows Bond Valuation Chapter 7 Bonds, Bond Valuation, and Interest Rates Valuing the cash flows (1) coupon payment (interest payment) = (coupon rate * principal) usually paid every 6 months (2) maturity value

More information

Yield Curve. Term Structure. Observed Yield Curves

Yield Curve. Term Structure. Observed Yield Curves Yield Curve The term structure refers to the relationship between short-term and long-term interest rates. The yield curve plots the yield to maturity against the term to maturity (figure 1). One plots

More information

Lecture Notes on MONEY, BANKING, AND FINANCIAL MARKETS. Peter N. Ireland Department of Economics Boston College.

Lecture Notes on MONEY, BANKING, AND FINANCIAL MARKETS. Peter N. Ireland Department of Economics Boston College. Lecture Notes on MONEY, BANKING, AND FINANCIAL MARKETS Peter N. Ireland Department of Economics Boston College irelandp@bc.edu http://www2.bc.edu/~irelandp/ec261.html Chapter 5: The Behavior of Interest

More information

ECONOMICS 422 MIDTERM EXAM 1 R. W. Parks Autumn (30) Pandora lives in a two period Fisherian world. Her utility function for 2

ECONOMICS 422 MIDTERM EXAM 1 R. W. Parks Autumn (30) Pandora lives in a two period Fisherian world. Her utility function for 2 NAME: ECONOMICS 422 MIDTERM EXAM 1 R. W. Parks Autumn 1994 Answer all questions on the examination sheets. Weights are given in parentheses. In general you should try to show your work. If you only present

More information

VALUING FLOATING RATE BONDS (FRBS)

VALUING FLOATING RATE BONDS (FRBS) VALUING FLOATING RATE BONDS (FRBS) A. V. Rajwade * Valuing Floating Rate Bonds (FRBs) 1. The principal features of floating rate bonds can be summarised simply: these are bonds day T-bill, refixed every

More information

Investment and Portfolio Management. Lecture 8 Bond Prices and Yields. Bond Characteristics

Investment and Portfolio Management. Lecture 8 Bond Prices and Yields. Bond Characteristics Investment and Portfolio Management Ms. Pham Le Thu Nga Lecture 8 Bond Prices and Yields Chapter 14 14-2 Bond Characteristics Face or par value (normally bullet maturity) Coupon rate (normally fixed) Zero

More information

AFM 271 Practice Problem Set #1 Spring 2005

AFM 271 Practice Problem Set #1 Spring 2005 AFM 271 Practice Problem Set #1 Spring 2005 1. Text problems: Chapter 1 1, 3, 4 Chapter 2 5 Chapter 3 2, 6, 7 Chapter 4 2, 6, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 38, 40, 46, 48 Chapter 5 2, 4,

More information

Fixed Income Securities

Fixed 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 12 108:22 108:23-20

More information

Interest Rates and Bond Valuation

Interest Rates and Bond Valuation and Bond Valuation 1 Bonds Debt Instrument Bondholders are lending the corporation money for some stated period of time. Liquid Asset Corporate Bonds can be traded in the secondary market. Price at which

More information

Examination II. Fixed income valuation and analysis. Economics

Examination II. Fixed income valuation and analysis. Economics Examination II Fixed income valuation and analysis Economics Answers Foundation examination March 009 FIRST PART: Multiple Choice Questions a) 8 b) c) 9 d) d) 0 d) 4 b) b) 5 a) c) 6 b) c) 7 c) S MCQ March09

More information

Introduction to Bonds

Introduction to Bonds Bonds are a debt instrument, where the bond holder pays the issuer an initial sum of money known as the purchase price. In turn, the issuer pays the holder coupon payments (annuity), and a final sum (face

More information