VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below"

Transcription

1 VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following risk-free debt instrument, which promises to make the respective payments when the appropriate annual rates are as shown in the last column. Year Cash Payment Appropriate Annual Rate 1 $15, % 2 17, , , For each of the following, calculate the price per $1,000 of par value assuming semiannual coupon payments. Coupon Bond Years to Rate Required Maturity Yield A 8% 9 7% B C D Consider a bond selling at par ($100) with a coupon rate of 6% and 10 years to maturity. a. What is the price of this bond if the required yield is 15%? b. What is the price of this bond if the required yield increases from 15% to 16%, and by what percentage did the price of this bond change? c. What is the price of this bond if the required yield is 5%? d. What is the price of this bond if the required yield increases from 5% to 6%, and by what percentage did the price of this bond change? e. From your answers to parts (b) and (d) what can you say about the relative price volatility of a bond in high compared to low interest rate environments? 5. Suppose you purchased a debt obligation 3 years ago at its par value of $100,000.The market price of this debt obligation today is $90,000. What are some of the reasons why the price of this debt obligation could have declined since you purchased it 3 years ago? 9. A portfolio manager is considering buying two bonds. Bond A matures in 3 years and has a coupon rate of 10% payable semiannually. Bond B, of the same credit quality, matures in 10 years and has a coupon rate of 12% payable semiannually. Both bonds are priced at par. 1

2 a. Suppose the portfolio manager plans to hold the bond that is purchased for 3 years. Which would be the best bond for the portfolio manager to purchase? b. Suppose the portfolio manager plans to hold the bond that is purchased for 6 years instead of 3 years. In this case, which would be the best bond for the portfolio manager to purchase? c. Suppose that the portfolio manager is managing the assets of a life insurance company that issued a 5-year guaranteed investment contract (GIC). The interest rate that the life insurance company agreed to pay is 9% on a semiannual basis. Which of the two bonds should the portfolio manager purchase to assure that the GIC payments will be satisfied and that a profit will be generated by the life insurance company? 10. What is meant by reinvestment risk when purchasing a bond? 11. Can you tell from the following information which of the three bonds will have the greatest price volatility, assuming each is trading to offer the same yield to maturity? Coupon Bond Rate Maturity X 8% 9 years Y Z Calculate the requested measures for bonds A and B (assume each bond pays interest semiannually): A B Coupon 8% 9% Yield to maturity 8% 8% Maturity (in 2 5 years) Par Price a. Calculate the duration for the two bonds by changing the yield up and down 25 basis points. b. Calculate the duration for the two bonds by changing the yield up and down by 10 basis points. c. Compare your answers to parts (a) and (b). d. Calculate the Macaulay duration for the two bonds. e. Calculate the modified duration for the two bonds. f. Compare the modified duration for the two bonds computed in parts (e) and (a). 14. Which of the following bonds will have the larger price change for a 50 basis point change in yield? Bond Duration Price 2

3 E 7 50 F What is the difference between modified duration and effective duration? 16. What is assumed about how the yield curve changes when using duration? 17. An investor is discussing the duration of a highly complex bond with his broker. The broker tells the investor that the duration of this bond is negative 5. The investor is confused about the negative value and tells the broker that the figure must be in error because the duration is always positive because it is some type of weighted average of time of the cash flows. Comment. 18. As a portfolio manager, you present a report to a client. The report indicates the duration of each security in the portfolio. One of the securities has a maturity of 15 years but duration of 25. The client believes that the report contains an error because she believes that the duration cannot be greater than the security's maturity. What would be your response to this client? 19. A strategy called immunization is used by institutional investors to protect a portfolio against an adverse change in interest rates. Basically this strategy seeks to offset interest rate risk and reinvestment risk. Why do these two risks offset each other to a certain extent when interest rates change? 3

4 VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS ANSWERS TO QUESTIONS 1. In terms of the notation used in the chapter: a 1 = $15,000 r 1 =.080 a 2 = $17,000 r 2 =.085 a 3 = $20,000 r 3 =.090 a 4 = $21,000 r 4 =.095 P 0 = 15, 000 (1.080) 17, (1.080)(1.085) 20, (1.080)(1.085)(1.090) 21, (1.080)(1.085)(1.090)(1.095) = $13, $14, $15, $15, = $59, The price of bond A is $1,065.95; the price of bond B is $1,000, price of bond C is $ and price of bond D (zero coupon) is $ The original bond yield is 6 percent. a. If required yield is 15%, the price of bond will be b. When yield increases to 16%, price of bond will decrease to , and percentage decrease is c. If the required yield is 5%, the price of bond will be d. If required yield increases from 5% to 6%, we are back to the original data, and the selling price will be 100. The decrease in price is ( ) = -7.17%. e. The percentage change observed in prices of bonds in (b) and (d) suggest that relative price volatility is more when initial yield is low (part d) and less when initial level is high (part b). 5. The price of this debt obligation can change over time for any one of the following reasons: (1) a rise in the level of interest rates in the economy over the past three years; (2) an increase in the required yield due to a change in the yield spread between non-treasury and Treasury securities; (3) a decline in the perceived credit quality of the debtor. 9. a. It must be stressed that there is no way to determine which bond will provide the best return. Since these bonds are priced at par, the yield to maturity for bonds A and B is 10% and 12%, respectively. However, yield to maturity tells us absolutely nothing about the dollars that will be generated from holding each bond. The number of dollars that will be received from investing in Bond A depends on the reinvestment rate over the three years. Thus for this bond, there is reinvestment risk. For Bond B, the dollars that will be realized depend on the yield for 7-year bonds three years from now (because Bond B will be a 7-year bond at that time). The portfolio manager is 4

5 exposed to both reinvestment risk and interest rate (or price) risk. b. If the holding period is six years rather than three years, the answer is the same as in (a); it is not possible to determine a priori which bond will provide the best return. The dollars received from investing in Bond A will not only depend on the reinvestment rates over the first three years, but also reinvestment rates from years three to six. c. Once again, it is not possible to lock in a profit or spread with either bond because of reinvestment risk for both bonds and interest rate (or price risk) for Bond B. As an aside, this fundamental principle has been overlooked by many financial institutions who believe that a "yield" indicates the return that will be realized. 10. The concept of yield to maturity assumes that the investor will realize the yield to maturity that is calculated at the time of purchase only if (1) all the coupon payments can be reinvested at the yield to maturity, and (2) the bond is held to maturity. With respect to the first assumption, the risk that an investor faces is that future interest rates at which the coupon can be reinvested will be less than the yield to maturity at the time the bond is purchased. This risk is reinvestment risk. 11. From the properties of price volatility, it is not possible to say which has the greatest price volatility. An unambiguous answer requires that both the coupon rate be lower and the maturity be greater than the other bonds. The purpose of this question is to demonstrate to students the need to quantify price volatility, i.e., the factors that affect price volatility are insufficient to indicate relative price volatility. 12. Note that a 25 bp increase in yield translates into a.125% increase in semiannual yield when calculating prices. Thus, in this case, an increase in 25 bp gives a semiannual yield of 4.125% and a decrease leads to a yield of 3.875%; a 10% bp increase gives a yield of 4.05% and a decrease leads to a yield of 3.95%. To estimate duration using Equation 18.10, however, dy must NOT be adjusted. In the text examples, the values in Table 18-1 are found using semiannual rates, where dy is applied to the annual equivalent -- a 50 basis point increase in rates, from 9%, would give a semiannual yield of 4.75%. Part a For Bond A in part a of the question, the duration is found using Bond A N = 4, I = 8/2 = 4, FV = 100, PMT = 4, cpt PV = 100 N = 4, I = 8.25/2 =4.125, FV = 100, PMT = 4, cpt PV = N = 4, I = 7.75/2 =, FV = 100, PMT = 4, cpt PV = Equation 18.10, where V + is , V - is , dy is , and V 0 is

6 Duration Part b Bond A N = 4, I = 8/2 = 4, FV = 100, PMT = 4, cpt PV = 100 N = 4, I = 8.1/2 =4.05, FV = 100, PMT = 4, cpt PV = N = 4, I = 7.9/2 =3.95, FV = 100, PMT = 4, cpt PV = Equation 18.10, where V + is 99.5, V - is , dy is , and V 0 is 100. Duration Bond A Bond B a. Duration with 25 bp change b. D with 10 bp change c. There was a much larger change in duration for the bond which was trading above par, as should be expected. d. Macaulay duration for Bond A is found using the following equation D (1) $ 40 (1.04 ) (2 ) $ 40 (1.04 ) 2 $ 1, 000 (3 ) $ 40 (1.04 ) 3 ( 4 ) $ 1, 040 (1.04 ) semiannual periods This amount would be annual periods. The Macaulay duration for Bond B is on a semiannual basis, or annual periods. e. The modified duration for Bond A is modified duration = Macaulay duration 1 + yield For Bond B, the modified duration is

7 f. Modified duration appears to track closely with the numbers produced in part a of the question. 14. Bond E will have 3.5 percentage change in price, while bond F will have a 2.5 percentage change in its price. However, the dollar amount of price change for bond F is larger than bond E. 15. Modified duration doesn't take into account changes in the bond value due to embedded options. Effective duration is flexible enough to allow analysts to reflect options and their exercise in the value of the bond. 16. When using any measure of duration, there is an implicit assumption that the yield curve shifts in parallel. 17. Duration describes how the value of a security changes when rates change, or what our best guess of that change will be. Measures such as the Macaulay duration are required to be positive because of the way that they are derived, but duration itself can take any value. One example of securities which have a negative duration is interest-only securities derived from mortgage portfolios. The value of these securities falls when rates fall due to the fact that homeowners will prepay their mortgages and the income of the portfolio will fall, lowering the expected cash flows from the pool of mortgages over time. 18. When the client believes that there is an error in your report, he is referring to the concept of Macaulay duration as some measure of the weighted average life of a bond. Thus he is right that a bond with a maturity of 15 years cannot have a Macaulay duration of 25. The duration of the bond, however, can take on any value. In this case, it means that the bond in question will be more sensitive to changes in rates than bonds with a 15- year term. 19. It is possible to create a portfolio of debt securities where the loss in one component of the return (for example, reinvestment loss) is offset by a gain in the other (for example, price gain). Particularly, if a portfolio is constructed such that its duration is equal to the investment horizon, it may be possible to offset interest rate risk (price risk) and reinvestment risk. A rise in market interest rates will lead to a loss in the market value of the portfolio, but a gain on account of higher returns earned on reinvested coupons. A fall in market interest rates will lead to a gain the market value of the portfolio, but a loss on account of lower returns earned on reinvested coupons. Thus the portfolio is "immunized" against changes in interest rates. 7

Practice Questions for Midterm II

Practice 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 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

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

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

American Options and Callable Bonds

American 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 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. Bond Prices and Yields. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter. Bond Prices and Yields. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Bond Prices and Yields McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Bond Prices and Yields Our goal in this chapter is to understand the relationship

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

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This assignment will focus on using the TI - 83 to calculate the price of a Zero

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

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

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

CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS

CHAPTER 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 information

Asset Valuation Debt Investments: Analysis and Valuation

Asset Valuation Debt Investments: Analysis and Valuation Asset Valuation Debt Investments: Analysis and Valuation Joel M. Shulman, Ph.D, CFA Study Session # 15 Level I CFA CANDIDATE READINGS: Fixed Income Analysis for the Chartered Financial Analyst Program:

More information

Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31-Jan-08 interest rates as of: 29-Feb-08 Run: 2-Apr-08 20:07 Book

Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31-Jan-08 interest rates as of: 29-Feb-08 Run: 2-Apr-08 20:07 Book Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31Jan08 interest rates as of: 29Feb08 Run: 2Apr08 20:07 Book Book Present Modified Effective Projected change in net present

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

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 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

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

Understanding duration and convexity of fixed income securities. Vinod Kothari

Understanding duration and convexity of fixed income securities. Vinod Kothari Understanding duration and convexity of fixed income securities Vinod Kothari Notation y : yield p: price of the bond T: total maturity of the bond t: any given time during T C t : D m : Cashflow from

More information

You 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?

You 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 information

TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this

More information

Click Here to Buy the Tutorial

Click Here to Buy the Tutorial FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following

More information

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

A) 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 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

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

CHAPTER 16: MANAGING BOND PORTFOLIOS

CHAPTER 16: MANAGING BOND PORTFOLIOS CHAPTER 16: MANAGING BOND PORTFOLIOS PROBLEM SETS 1. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their prices and their

More information

Bond Valuation. What is a bond?

Bond Valuation. What is a bond? Lecture: III 1 What is a bond? Bond Valuation When a corporation wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities called bonds. A bond

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 25 multiple choice questions and 5 work problems covering chapter 1, 2, 3, 4, 14, 16. Questions in the multiple choice section will

More information

Finance Homework Julian Vu May 28, 2008

Finance Homework Julian Vu May 28, 2008 Finance Homework Julian Vu May 28, 2008 Assignment: p. 28-29 Problems 1-1 and 1-2 p. 145-147 Questions 4-2, 4-3, and 4-4, and Problems 4-1, 4-2, 4-3, and 4-13 P1-1 A Treasury Bond that matures in 10 years

More information

Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS 9-1 a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as

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

ANSWERS TO STUDY QUESTIONS

ANSWERS TO STUDY QUESTIONS ANSWERS TO STUDY QUESTIONS Chapter 17 17.1. The details are described in section 17.1.1. 17.3. Because of its declining payment pattern, a CAM would be most useful in an economy with persistent deflation

More information

Financial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:

Financial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure: FIN 683 Professor Robert Hauswald Financial-Institutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks - Interest Rate Risks 6. A financial institution has the following market

More information

Weekly Relative Value

Weekly Relative Value Back to Basics Identifying Value in Fixed Income Markets As managers of fixed income portfolios, one of our key responsibilities is to identify cheap sectors and securities for purchase while avoiding

More information

CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 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. Long-term Treasury securities have substantial

More information

CHAPTER 10. Bond Prices and Yields

CHAPTER 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 information

issue brief Duration Basics January 2007 Duration is a term used by fixed-income investors, California Debt and Investment Advisory Commission

issue brief Duration Basics January 2007 Duration is a term used by fixed-income investors, California Debt and Investment Advisory Commission issue brief California Debt and Investment Advisory Commission # 06-10 January 2007 Duration Basics Introduction Duration is a term used by fixed-income investors, financial advisors, and investment advisors.

More information

Zero-Coupon Bonds (Pure Discount Bonds)

Zero-Coupon Bonds (Pure Discount Bonds) Zero-Coupon Bonds (Pure Discount Bonds) The price of a zero-coupon 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 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

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

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

Finance 350: Problem Set 6 Alternative Solutions

Finance 350: Problem Set 6 Alternative Solutions Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual 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 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

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

Bond 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. 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 information

Callable Bonds - Structure

Callable Bonds - Structure 1.1 Callable bonds A callable bond is a fixed rate bond where the issuer has the right but not the obligation to repay the face value of the security at a pre-agreed value prior to the final original maturity

More information

Maturity targeted Bond Funds Lock in Anticipated Yield to Maturity

Maturity targeted Bond Funds Lock in Anticipated Yield to Maturity Winter 11 Maturity targeted Bond Funds Lock in Anticipated Yield to Maturity How fund dinvestors can benefit fitfrom the permanence and definition of portfolios of bonds, held to their maturity. Matthew

More information

Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

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

Math of Finance. Texas Association of Counties January 2014

Math of Finance. Texas Association of Counties January 2014 Math of Finance Texas Association of Counties January 2014 Money Market Securities Sample Treasury Bill Quote*: N Bid Ask Ask Yld 126 4.86 4.85 5.00 *(Yields do not reflect current market conditions) Bank

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 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

FINC 3630: Advanced Business Finance Additional Practice Problems

FINC 3630: Advanced Business Finance Additional Practice Problems FINC 3630: Advanced Business Finance Additional Practice Problems Accounting For Financial Management 1. Calculate free cash flow for Home Depot for the fiscal year-ended February 1, 2015 (the 2014 fiscal

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

Bond Valuation. Capital Budgeting and Corporate Objectives

Bond 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 marketsĀ» What

More information

American Funds Insurance Series. U.S. Government/ AAA-Rated Securities Fund. Summary prospectus Class 3 shares May 1, 2016

American Funds Insurance Series. U.S. Government/ AAA-Rated Securities Fund. Summary prospectus Class 3 shares May 1, 2016 American Funds Insurance Series U.S. Government/ AAA-Rated Securities Fund Summary prospectus Class 3 shares May 1, 2016 Before you invest, you may want to review the fund s prospectus and statement of

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

Interest Rates and Bond Valuation

Interest Rates and Bond Valuation Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean

More information

ANALYSIS OF FIXED INCOME SECURITIES

ANALYSIS OF FIXED INCOME SECURITIES ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its

More information

MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO

MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO CALIFORNIA DEBT & INVESTMENT ADVISORY COMMISSION MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO SEPTEMBER 2008 CDIAC #08-11 INTRODUCTION California statute requires the governing body of local

More information

Understanding Fixed Income

Understanding 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 information

CHAPTER 5. Interest Rates. Chapter Synopsis

CHAPTER 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 information

3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction. Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

More information

Managing the Investment Portfolio

Managing the Investment Portfolio Managing the Investment Portfolio GSBC Executive Development Institute April 26, 2015 Portfolio Purpose & Objectives Tale of Two Balance Sheets o Components of Core Balance Sheet Originated loans Retail

More information

The cost of capital. A reading prepared by Pamela Peterson Drake. 1. Introduction

The cost of capital. A reading prepared by Pamela Peterson Drake. 1. Introduction The cost of capital A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction... 1 2. Determining the proportions of each source of capital that will be raised... 3 3. Estimating the marginal

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

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates

Analysis 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 information

Financial-Institutions Management. Solutions 6

Financial-Institutions Management. Solutions 6 Solutions 6 Chapter 25: Loan Sales 2. A bank has made a three-year $10 million loan that pays annual interest of 8 percent. The principal is due at the end of the third year. a. The bank is willing to

More information

Fixed Income Arbitrage

Fixed Income Arbitrage Risk & Return Fixed Income Arbitrage: Nickels in Front of a Steamroller by Jefferson Duarte Francis A. Longstaff Fan Yu Fixed Income Arbitrage Broad set of market-neutral strategies intended to exploit

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

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

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

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued 6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

Credit Derivatives. Southeastern Actuaries Conference. Fall Meeting. November 18, 2005. Credit Derivatives. What are they? How are they priced?

Credit Derivatives. Southeastern Actuaries Conference. Fall Meeting. November 18, 2005. Credit Derivatives. What are they? How are they priced? 1 Credit Derivatives Southeastern Actuaries Conference Fall Meeting November 18, 2005 Credit Derivatives What are they? How are they priced? Applications in risk management Potential uses 2 2 Credit Derivatives

More information

Chapter 22 Credit Risk

Chapter 22 Credit Risk Chapter 22 Credit Risk May 22, 2009 20.28. Suppose a 3-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields

More information

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i)

Basic Financial Tools: A Review. 3 n 1 n. PV FV 1 FV 2 FV 3 FV n 1 FV n 1 (1 i) Chapter 28 Basic Financial Tools: A Review The building blocks of finance include the time value of money, risk and its relationship with rates of return, and stock and bond valuation models. These topics

More information

BUSINESS FINANCE (FIN 312) Spring 2008

BUSINESS FINANCE (FIN 312) Spring 2008 BUSINESS FINANCE (FIN 312) Spring 2008 Assignment 3 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

More information

CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are

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

Mortgage-Backed Securities. Mortgage Loans Pass-throughs and Prepayments CMOs Analysis of MBS Pricing and Convexity

Mortgage-Backed Securities. Mortgage Loans Pass-throughs and Prepayments CMOs Analysis of MBS Pricing and Convexity Mortgage-Backed Securities/1 Asset-Backed Securities Mortgage-Backed Securities Prof. Ian Giddy Stern School of Business New York University Mortgages and MBS Mortgage Loans Pass-throughs and Prepayments

More information

Chapter 6 Valuing Bonds. (1) coupon payment - interest payment (coupon rate * principal) - usually paid every 6 months.

Chapter 6 Valuing Bonds. (1) coupon payment - interest payment (coupon rate * principal) - usually paid every 6 months. Chapter 6 Valuing Bonds Bond Valuation - value the cash flows (1) coupon payment - interest payment (coupon rate * principal) - usually paid every 6 months. (2) maturity value = principal or par value

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

Prepared by: Dalia A. Marafi Version 2.0

Prepared by: Dalia A. Marafi Version 2.0 Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version

More information

C H A P T E R Investing in Bonds 441

C H A P T E R Investing in Bonds 441 Investing in Bonds C H A P T E R 16 Tom scratched his head for a moment. This was something entirely new to him. His broker was recommending a car and junk? And who were all these people that his broker

More information

What Does a Mutual Fund s Term Tell Investors? by Geng Deng, Craig McCann and Edward O Neal 1

What Does a Mutual Fund s Term Tell Investors? by Geng Deng, Craig McCann and Edward O Neal 1 Introduction What Does a Mutual Fund s Term Tell Investors? by Geng Deng, Craig McCann and Edward O Neal 1 In a previous article, we highlighted a flaw in the average credit quality statistic frequently

More information

Chapter 4 Bonds and Their Valuation ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Bonds and Their Valuation ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 4 Bonds and Their Valuation ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as government

More information

1. The Purdue Life Insurance Company has two assets and two liabilities.

1. 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 information

CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS

CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS Goals of This Chapter: The purpose of this chapter is to explore the

More information

SAMPLE MID-TERM QUESTIONS

SAMPLE MID-TERM QUESTIONS SAMPLE MID-TERM QUESTIONS William L. Silber HOW TO PREPARE FOR THE MID- TERM: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below,

More information

Mathematics. Rosella Castellano. Rome, University of Tor Vergata

Mathematics. 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 information

Chapter 6 The Tradeoff Between Risk and Return

Chapter 6 The Tradeoff Between Risk and Return Chapter 6 The Tradeoff Between Risk and Return MULTIPLE CHOICE 1. Which of the following is an example of systematic risk? a. IBM posts lower than expected earnings. b. Intel announces record earnings.

More information

Module 5: Interest concepts of future and present value

Module 5: Interest concepts of future and present value Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

More information

Trading the Yield Curve. Copyright 1999-2006 Investment Analytics

Trading the Yield Curve. Copyright 1999-2006 Investment Analytics Trading the Yield Curve Copyright 1999-2006 Investment Analytics 1 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading

More information

Exercise 1 for Time Value of Money

Exercise 1 for Time Value of Money Exercise 1 for Time Value of Money MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing

More information

Final Exam Practice Set and Solutions

Final Exam Practice Set and Solutions FIN-469 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 information

- Short term notes (bonds) Maturities of 1-4 years - Medium-term notes/bonds Maturities of 5-10 years - Long-term bonds Maturities of 10-30 years

- Short term notes (bonds) Maturities of 1-4 years - Medium-term notes/bonds Maturities of 5-10 years - Long-term bonds Maturities of 10-30 years Contents 1. What Is A Bond? 2. Who Issues Bonds? Government Bonds Corporate Bonds 3. Basic Terms of Bonds Maturity Types of Coupon (Fixed, Floating, Zero Coupon) Redemption Seniority Price Yield The Relation

More information

Chapter Review and Self-Test Problems. Answers to Chapter Review and Self-Test Problems

Chapter Review and Self-Test Problems. Answers to Chapter Review and Self-Test Problems 236 PART THREE Valuation of Future Cash Flows Chapter Review and Self-Test Problems 7.1 Bond Values A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually,

More information