Problems and Solutions


 Helen Garrett
 1 years ago
 Views:
Transcription
1 Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixedcoupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual maturity: 0/06/04 What are the future cash flows delivered by this bond? Solution.. The coupon cash flow is equal to $40 8% $,000 Coupon = = $40 It is delivered on the following future dates: 0/06/0, /06/0, 0/06/03, /06/03 and 0/06/04. The redemption value is equal to the face value $,000 and is delivered on maturity date 0/06/04. Exercise. Consider the same bond as in the previous exercise. We are still on /04/0.. Compute the accrued interest taking into account the Actual/Actual daycount basis.. Same question if we are now on 09/06/0. Solution.. The last coupon has been delivered on /06/0. There are 8 days between /06/0 and /04/0, and 8 days between the last coupon date /06/0 and the next coupon date 0/06/0. Hence, the accrued interest is equal to $6.88 Accrued Interest = 8 $40 = $ The last coupon has been delivered on 0/06/0. There are 3 days between 0/06/0 and 09/06/0, and 84 days between the last coupon date 0/06/0 and the next coupon date /06/0. Hence, the accrued interest is equal to $6.739 Accrued Interest = 3 $40 = $
2 Problems and Solutions Exercise.3 Solution.3 Exercise.4 Solution.4 An investor has a cash of $0,000,000 at disposal. He wants to invest in a bond with $,000 nominal value and whose dirty price is equal to 07.47%.. What is the number of bonds he will buy?. Same question if the nominal value and the dirty price of the bond are respectively $00 and 98.43%.. The number of bonds he will buy is given by the following formula Cash Number of bonds bought = Nominal Value of the bond dirty price Here, the number of bonds is equal to 9,306. n is equal to 0,6 n = 0,000,000, % = 9, n = 0,000, % = 0,7.3 On 0//99, consider a fixedcoupon bond whose features are the following: face value: Eur 00 coupon rate: 0% coupon frequency: annual maturity: 04//08 Compute the accrued interest taking into account the four different daycount bases: Actual/Actual, Actual/36, Actual/360 and 30/360. The last coupon has been delivered on 04//99. There are 93 days between 04//99 and 0//99, and 366 days between the last coupon date 04//99 and the next coupon date 04//00. The accrued interest with the Actual/Actual daycount basis is equal to Eur % Eur 00 = Eur The accrued interest with the Actual/36 daycount basis is equal to Eur % Eur 00 = Eur The accrued interest with the Actual/360 daycount basis is equal to Eur % Eur 00 = Eur There are days between 04//99 and 04/30/99, months between May and September, and days between 09/30/99 and 0//99, so that there
3 Problems and Solutions 3 are 90 days between 04//99 and 0//99 on the 30/360 daycount basis = 90 Exercise. inally, the accrued interest with the 30/360 daycount basis is equal to Eur % Eur 00 = Eur Some bonds have irregular first coupons. A long first coupon is paid on the second anniversary date of the bond and starts accruing on the issue date. So, the first coupon value is greater than the normal coupon rate. A long first coupon with regular value is paid on the second anniversary date of the bond and starts accruing on the first anniversary date. So, the first coupon value is equal to the normal coupon rate. A short first coupon is paid on the first anniversary date of the bond and starts accruing on the issue date. The first coupon value is smaller than the normal coupon rate. A short first coupon with regular value is paid on the first anniversary date of the bond and has a value equal to the normal coupon rate. Consider the four following bonds with nominal value equal to million euros and annual coupon frequency: ond : issue date 0//96, coupon %, maturity date 0//0, long first coupon, redemption value 00%; ond : issue date 0//96, coupon %, maturity date 0//0, long first coupon with regular value, redemption value 99%; ond 3: issue date //9, coupon 3%, maturity date 3 years and months, short first coupon, redemption value 00%; ond 4: issue date 08//9, coupon 4.%, maturity date 08//00, short first coupon with regular value, redemption value 00%. Compute the future cash flows of each of these bonds. Solution. ond pays 00,000 euros on 0//98, 0,000 euros on 0//99, 0//00, 0//0 and,00,000 euros on 0//0. ond pays 0,000 euros on 0//98, 0//99, 0//00, 0//0 and,040,000 euros on 0//0. ond 3 pays,000 euros on 0//96, 30,000 euros on 0//97, 0//98 and,030,000 euros on 0//99. ond 4 pays 4,000 euros on 08//96, 08//97, 08//98, 08//99 and,04,000 euros on 08//00. Exercise.8 Solution.8 An investor wants to buy a bullet bond of the automotive sector. He has two choices: either invest in a US corporate bond denominated in euros or in a rench corporate bond with same maturity and coupon. Are the two bonds comparable? The answer is no. irst, the coupon and yield frequency of the US corporate bond is semiannual, while it is annual for the rench corporate bond. To compare the yields
4 4 Problems and Solutions on the two instruments, you have to convert either the semiannual yield of the US bond into an equivalently annual yield or the annual yield of the rench bond into an equivalently semiannual yield. Second, the two bonds do not necessarily have the same rating, that is, the same credit risk. Third, they do not necessarily have the same liquidity. Exercise.3 Treasury bills are quoted using the yield on a discount basis or on a moneymarket basis.. The yield on a discount basis denoted by y d is computed as y d = P n where is the face value, P the price, the yearbasis 36 or 360 and n is the number of calendar days remaining to maturity. Prove in this case that the price of the Tbill is obtained using the equation P = n y d. The yield on a moneymarket basis denoted by y m is computed as y m = y d n y d Prove in this case that the price of the Tbill is obtained using the equation 3. Show that P = + n y m y d = y m + n y m Solution.3. rom the equation we find and finally, we obtain. rom the equation y d = P n y d P = n = P n y d y m = y d n y d
5 Problems and Solutions we find Then, we have inally, we obtain 3. rom the equation y m = n y m P n P = P P n n = = P P P = + n y m n P P = P we find Then, we have y m = y d n y d y m n y d y d = 0 y d n y m = y m inally, we obtain y d = y m + n y m Exercise. What is the price P of the certificate of deposit issued by bank X on 06/06/00, with maturity 08//00, face value $0,000,000, an interest rate at issuance of % falling at maturity and a yield of 4.% as of 07/3/00? Solution. Recall that the price P of such a product is given by + c n c P = + ym n m where is the face value, c the interest rate at issuance, n c is the number of days between issue and maturity, is the yearbasis 360 or 36, y m is the yield on a moneymarket basis and n m is the number of days between settlement and maturity. Then, the price P of the certificate of deposit issued by bank X is equal to + % P = $0,000,000 = $0,079, % 360 Indeed, there are 80 calendar days between 06/06/00 and 08//00, and calendar days between 07/3/00 and 08//00
6 6 Problems and Solutions Exercise.6 Solution.6 On 0/03/00, an investor buys $ million US Till with maturity date 06/7/00 and discount yield.76% on the settlement date.. What is the price of the Till?. What is the equivalent moneymarket yield?. The settlement date of the transaction is 0/04/00 trading date plus working day. There are 74 calendar days between the settlement date and the maturity date. The price P of the Till is equal to 00.76% 74 = The equivalent moneymarket yield is equal to.77%.76% % =.77% CHAPTER Problems Exercise. Suppose the year continuously compounded interest rate is %. What is the effective annual interest rate? Solution. The effective annual interest rate is R = e 0. = 0.7 =.7%. Exercise. Solution. If you deposit $,00 in a bank account that earns 8% annually on a continuously compounded basis, what will be the account balance in 7.4 years? The account balance in 7.4 years will be $,00.e 8% 7.4 = $4,4.98 Exercise.3 Solution.3 Exercise.7 If an investment has a cumulative 63.4% rate of return over 3.78 years, what is the annual continuously compounded rate of return? The annual continuously compounded rate of return R is such that We find R c = ln.634/3.78 = 3%..634 = e 3.78Rc. What is the price of a year bond with a nominal value of $00, a yield to maturity of 7% with annual compounding frequency, a 0% coupon rate and an annual coupon frequency?. Same question for a yield to maturity of 8%, 9% and 0%. Conclude.
7 Problems and Solutions 7 Solution.7. The price P of a bond is given by the formula n N c P = + y i + N + y n which simplifies into P = N c y i= [ ] + y n + N + y n where N, c, y and n are respectively the nominal value, the coupon rate, the yield to maturity and the number of years to maturity of the bond. Here, we obtain for P P = 0 7% [ ] + 7% % P is then equal to.30% of the nominal value or $.30. Note that we can also use the Excel function Price to obtain P.. Prices of the bond for different yields to maturity YTM are given in the following table YTM % Price $ ond prices decrease as rates increase. Exercise.0 Solution.0. What is the yield to maturity of a year bond with a nominal value of $00, a 0% coupon rate, an annual coupon frequency and a price of 97.86?. Same question for a price of 00 and The yield to maturity y of this bond is the solution to the following equation [ ] + P = N c y + y n N + y n where N, c, P and n are respectively the nominal value, the coupon rate, the price and the number of years to maturity of the bond. Here, y is solution to = 0 y [ ] + y y Using, for example, Newton s three points method or the Solver function in Excel, we obtain 0.74%. Note that we can also use the Excel function Yield to obtain y.. Yields to maturity YTM of the bond for different prices are given in the following table
8 8 Problems and Solutions Price YTM % Exercise.3 Solution.3 Consider the following bond: annual coupon %, maturity years, annual compounding frequency.. What is its relative price change if its required yield increases from 0% to %?. What is its relative price change if its required yield increases from % to 6%? 3. What conclusion can you draw from these examples? Explain why.. The initial price P is equal to P = + 0% + + 0% + + 0% % % = After the yield change, the price becomes P = + % + + % + + % % % = 77.8 Hence, the bond price has decreased by P P = 3.97% P. The initial price P is equal to P = + % + + % + + % % % = 00 After the yield change, the price becomes P = + 6% + + 6% + + 6% % % = Hence, the bond price has decreased by P P = 4.% P 3. In low interestrate environments, the relative price volatility of a bond is higher than in high interestrate environments for the same yield change here, in our example +%. This is due to the convexity relationship between the price of a bond and its yield.
9 Problems and Solutions 9 Exercise.4 Solution.4 We consider the following zerocoupon curve: Maturity years ZeroCoupon Rate % What is the price of a year bond with a $00 face value, which delivers a % annual coupon rate?. What is the yield to maturity of this bond? 3. We suppose that the zerocoupon curve increases instantaneously and uniformly by 0.%. What is the new price and the new yield to maturity of the bond? What is the impact of this rate increase for the bondholder? 4. We suppose now that the zerocoupon curve remains stable over time. You hold the bond until maturity. What is the annual return rate of your investment? Why is this rate different from the yield to maturity?. The price P of the bond is equal to the sum of its discounted cash flows and given by the following formula P = + 4% % % % % = $ The yield to maturity R of this bond verifies the following equation = + R i R Using the Excel function Yield, we obtain % for R. 3. The new price P of the bond is given by the following formula: P = i= + 4.% + + % + +.% % % = $ The new yield to maturity R of this bond verifies the following equation = + R i R i= Using the Excel function yield, we obtain.468% for R. The impact of this rate increase is an absolute capital loss of $.37 for the bondholder. Absolute Loss = = $.37
10 0 Problems and Solutions and a relative capital loss of.34% Relative Loss = =.34% 4. efore maturity, the bondholder receives intermediate coupons that he reinvests in the market: after one year, he receives $ that he reinvests for 4 years at the 4year zerocoupon rate to obtain on the maturity date of the bond + 4.9% 4 = $6.044 after two years, he receives $ that he reinvests for 3 years at the 3year zerocoupon rate to obtain on the maturity date of the bond + 4.7% 3 = $.7469 after three years, he receives $ that he reinvests for years at the year zerocoupon rate to obtain on the maturity date of the bond + 4.% = $.460 after four years, he receives $ that he reinvests for year at the year zerocoupon rate to obtain on the maturity date of the bond + 4% = $. after five years, he receives the final cash flow equal to $0. The bondholder finally obtains $7.464 five years later = $7.464 which corresponds to a 4.944% annual return rate / = 4.944% This return rate is different from the yield to maturity of this bond % because the curve is not flat at a % level. With a flat curve at a % level, we obtain $7.608 five years later = $7.608 which corresponds exactly to a % annual return rate / = % Exercise. Let us consider the two following rench Treasury bonds whose characteristics are the following:
11 Problems and Solutions Name Maturity Coupon Price years Rate % ond 6 00 ond Your investment horizon is 6 years. Which of the two bonds will you select? Solution. Exercise.8 It depends on the level of the reinvestment rate, at which you can reinvest the coupons of ond, as well as on the yield to maturity of ond at horizon. If you suppose, for example, that the reinvestment rate is equal to the yield to maturity of ond at horizon, then the total return of ond will decrease as the reinvestment rate increases, as opposed to ond. Indeed, while the unique source of return for ond is its reinvested coupons, it lies for ond in its price appreciation. ond and ond will yield nearly the same annualized return.% for a reinvestment rate of 6.36%. We consider three bonds with the following features ond Maturity years Annual Coupon Price ond ond ond ind the year, year and 3year zerocoupon rates from the table above.. We consider another bond with the following features ond Maturity Annual Coupon Price ond 4 3 years Use the zerocoupon curve to price this bond. 3. ind an arbitrage strategy. Solution.8. The year zerocoupon rate denoted by R0,, verifies 0 + R0, = 06.6 We find the expression R0, = = 3.8% The year zerocoupon rate denoted by R0,, verifies % R0, = 06.0 We find the expression / 08 R0, = = 4.738% %
12 Problems and Solutions The 3year zerocoupon rate denoted by R0, 3, verifies % % R0, 3 3 = 06.4 We find the expression /3 08 R0, 3 = % =.78% %. The price P of ond 4 using the zerocoupon curve is given by the following formula: 9 P = + 3.8% % % 3 = This bond is underpriced by the market compared to its theoretical value. There is an arbitrage if the market price of this bond reverts to the theoretical value. We have to simply buy the bond at a $09.0 price and hope that it is mispriced by the market and will soon revert to around $ Exercise.0 We consider two bonds with the following features ond Maturity years Coupon Rate % Price YTM % ond 0 0,3..39 ond YTM stands for yield to maturity. These two bonds have a $,000 face value, and an annual coupon frequency.. An investor buys these two bonds and holds them until maturity. Compute the annual return rate over the period, supposing that the yield curve becomes instantaneously flat at a.4% level and remains stable at this level during 0 years.. What is the rate level such that these two bonds provide the same annual return rate? In this case, what is the annual return rate of the two bonds? Solution.0. We consider that the investor reinvests its intermediate cash flows at a unique.4% rate. or ond, the investor obtains the following sum at the maturity of the bond % i +,00 =,8. i= which corresponds exactly to a.3703% annual return rate.,8. /0 =.3703%,3.
13 Problems and Solutions 3 or ond, the investor obtains the following sum at the maturity of the bond % i +,00 =, i= which corresponds exactly to a.489% annual return rate., /0 =.489% We have to find the value R, such that 00 9 i= + R i +,00,3. = 0 9 i= + R i +, Using the Excel solver, we finally obtain % for R. The annual return rate of the two bonds is equal to.664% 00 9i= i /0 +,00 =.664%,3. Exercise.4 Assume that the following bond yields, compounded semiannually: 6month Treasury Strip:.00%; year Treasury Strip:.%; 8month Treasury Strip:.7%.. What is the 6month forward rate in six months?. What is the year forward rate in six months? 3. What is the price of a semiannual 0% coupon Treasury bond that matures in exactly 8 months? Solution R 0, = + R 0, =.0 + 0, 0., 0. 0, 0., 0. =.003% + R 0,. 3 = + R 0, =.0 + 0, 0., ,0., + 0, 0., 0, 0., = 6.60% 3. The cash flows are coupons of % in six months and a year, and coupon plus principal payment of 0% in 8 months. We can discount using the spot rates
14 4 Problems and Solutions that we are given: 0 P = = Exercise.6 Solution.6 Consider a coupon bond with n = 0 semesters i.e., 0 years to maturity, an annual coupon rate c = 6.% coupons are paid semiannually, and nominal value N = $,000. Suppose that the semiannually compounded yield to maturity YTM of this bond is y =.%.. Compute the current price of the bond using the annuity formula.. Compute the annually compounded YTM and the current yield of the bond. Compare them with y. 3. If the yield to maturity on the bond does not change over the next semester, what is the Holding Period Return HPR obtained from buying the bond now and selling it one semester from now, just after coupon payment? At what price will the bond sell one semester from now just after coupon payment?. or the current price of the bond, we use the formula P 0 = N c + y so that P 0 =,000 6.%.% + y / n N + y / n,000 =, The annually compounded yield to maturity YTM denoted by y and the current yield denoted by y c are obtained using the following formulas: y = + y = = y c = cn 0.06,000 = = P 0,076.4 Therefore, they are both larger than y. 3. irst, we compute P, the price of the bond one semester from now: P = N c N + y =,000 6.%.% =, y / n y / n +, The Holding Period Return from buying the bond now and selling it one semester from now is then: HPR = P P 0 + cn,073.0, = =.7% P 0,076.4
Problems and Solutions
1 CHAPTER 1 Problems 1.1 Problems on Bonds Exercise 1.1 On 12/04/01, consider a fixedcoupon bond whose features are the following: face value: $1,000 coupon rate: 8% coupon frequency: semiannual maturity:
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationFINANCE 1. DESS Gestion des Risques/Ingéniérie Mathématique Université d EVRY VAL D ESSONNE EXERCICES CORRIGES. Philippe PRIAULET
FINANCE 1 DESS Gestion des Risques/Ingéniérie Mathématique Université d EVRY VAL D ESSONNE EXERCICES CORRIGES Philippe PRIAULET 1 Exercise 1 On 12/04/01 consider a fixed coupon bond whose features are
More informationCHAPTER 7: FIXEDINCOME SECURITIES: PRICING AND TRADING
CHAPTER 7: FIXEDINCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The presentvalue calculation is used to estimate how much an investor should pay for a bond;
More informationBond Pricing Fundamentals
Bond Pricing Fundamentals Valuation What determines the price of a bond? Contract features: coupon, face value (FV), maturity Riskfree interest rates in the economy (US treasury yield curve) Credit risk
More informationNATIONAL STOCK EXCHANGE OF INDIA LIMITED
NATIONAL STOCK EXCHANGE OF INDIA LIMITED Capital Market FAQ on Corporate Bond Date : September 29, 2011 1. What are securities? Securities are financial instruments that represent a creditor relationship
More informationChapter 8 Interest Rates and Bond Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 8 Interest Rates and Bond Valuation Oct. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Know the important
More informationOverview 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 informationACI THE FINANCIAL MARKETS ASSOCIATION
ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARDFORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on longterm bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationIntroduction to Fixed Income (IFI) Course Syllabus
Introduction to Fixed Income (IFI) Course Syllabus 1. Fixed income markets 1.1 Understand the function of fixed income markets 1.2 Know the main fixed income market products: Loans Bonds Money market instruments
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationSolutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,
FIN 472 Professor Robert Hauswald FixedIncome 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 informationIntroduction 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 informationMoney Market and Debt Instruments
Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz
More informationChapter 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 informationChapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter  The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationI. Readings and Suggested Practice Problems. II. Risks Associated with DefaultFree Bonds
Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with DefaultFree Bonds III. Duration: Details and Examples IV. Immunization
More informationInterest Rate and Credit Risk Derivatives
Interest Rate and Credit Risk Derivatives Interest Rate and Credit Risk Derivatives Peter Ritchken Kenneth Walter Haber Professor of Finance Weatherhead School of Management Case Western Reserve University
More informationMath 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 informationLOS 56.a: Explain steps in the bond valuation process.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction
More informationNotes for Lecture 3 (February 14)
INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because
More informationChapter. Bond Prices and Yields. McGrawHill/Irwin. Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved.
Chapter Bond Prices and Yields McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Bond Prices and Yields Our goal in this chapter is to understand the relationship
More informationSS15 FixedIncome: Basic Concepts SS15 FixedIncome: Analysis of Risk
SS15 FixedIncome: Basic Concepts SS15 FixedIncome: Analysis of Risk SS 15 R52 FI Securities: Defining Elements R53 FI Markets: Issuance, Trading, and Funding R54 Introduction to FI Valuation SS 16 R55
More informationBond Return Calculation Methodology
Bond Return Calculation Methodology Morningstar Methodology Paper June 30, 2013 2013 Morningstar, Inc. All rights reserved. The information in this document is the property of Morningstar, Inc. Reproduction
More informationANALYSIS 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 informationVALUATION 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 informationExercise 6 Find the annual interest rate if the amount after 6 years is 3 times bigger than the initial investment (3 cases).
Exercise 1 At what rate of simple interest will $500 accumulate to $615 in 2.5 years? In how many years will $500 accumulate to $630 at 7.8% simple interest? (9,2%,3 1 3 years) Exercise 2 It is known that
More information2. What is your best estimate of what the price would be if the riskless interest rate was 9% (compounded semiannually)? (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 semiannual
More informationBonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)
More informationFinancial Mathematics for Actuaries. Chapter 6 Bonds and Bond Pricing
Financial Mathematics for Actuaries Chapter 6 Bonds and Bond Pricing 1 Learning Objectives 1. Types, features and risks of bond investments 2. Formulas for pricing a bond 3. Construction of bond amortization
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationYIELD CURVE GENERATION
1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A
More informationGlobal Financial Management
Global Financial Management Bond Valuation Copyright 999 by Alon Brav, Campbell R. Harvey, Stephen Gray and Ernst Maug. All rights reserved. No part of this lecture may be reproduced without the permission
More informationIn this chapter we will learn about. Treasury Notes and Bonds, Treasury Inflation Protected Securities,
2 Treasury Securities In this chapter we will learn about Treasury Bills, Treasury Notes and Bonds, Strips, Treasury Inflation Protected Securities, and a few other products including Eurodollar deposits.
More informationFixed Income Knowledge Series 2. Characteristics and Pricing of Government Bonds
Fixed Income Knowledge Series 2 Characteristics and Pricing of Government Bonds Government bonds are fixed income securities issued by the Government of India (GOI). The total outstanding bonds issued
More informationCHAPTER 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. Longterm Treasury
More informationHEC Paris MBA Program. Financial Markets Prof. Laurent E. Calvet Fall 2010 MIDTERM EXAM. 90 minutes Open book
HEC Paris MBA Program Name:... Financial Markets Prof. Laurent E. Calvet Fall 2010 MIDTERM EXAM 90 minutes Open book The exam will be graded out of 100 points. Points for each question are shown in brackets.
More informationFinance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation
Finance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation Lecture 5: Interest Rates and Bond Valuation Know the important bond features and bond types Understand bond values and why
More informationFNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
More informationInterest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
More informationChapter 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 informationCHAPTER 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 informationNote: There are fewer problems in the actual Midterm Exam!
HEC Paris Practice Midterm Exam Questions Version with Solutions Financial Markets BS Fall 200 Note: There are fewer problems in the actual Midterm Exam! Problem. Is the following statement True, False
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More informationChapter 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 information2. 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 informationAlliance Consulting BOND YIELDS & DURATION ANALYSIS. Bond Yields & Duration Analysis Page 1
BOND YIELDS & DURATION ANALYSIS Bond Yields & Duration Analysis Page 1 COMPUTING BOND YIELDS Sources of returns on bond investments The returns from investment in bonds come from the following: 1. Periodic
More informationAFM 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 informationReview 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 informationCHAPTER 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 informationPractice Set #2 and Solutions.
FIN672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,
More informationSpot rates, forward rates and plot of the term structure of interest rate.
A N A L Y T I C A L F I N A N C E I I BILLS, NOTES AND BONDS MARKETS: Spot rates, forward rates and plot of the term structure of interest rate FOTSING ARMAND HAMADOU H TAKOETA FRED 1 INTRODUCTION: 3 11
More informationBond Market Overview and Bond Pricing
Bond Market Overview and Bond Pricing. Overview of Bond Market 2. Basics of Bond Pricing 3. Complications 4. Pricing Floater and Inverse Floater 5. Pricing Quotes and Accrued Interest What is A Bond? Bond:
More informationBonds calculations. Description. Cash flows. Zero coupons. Yield. Yield to call. Price and yield relationship. Yield curve pricing
4 Bonds calculations Description Cash flows Zero coupons Yield Yield to call Price and yield relationship Yield curve pricing Other yield measures Yield measures Exercise Summary File: MFME2_04.xls 43
More informationZeroCoupon Bonds (Pure Discount Bonds)
ZeroCoupon Bonds (Pure Discount Bonds) The price of a zerocoupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
More informationBest Credit Data Bond Analytics Calculation Methodology
Best Credit Data Bond Analytics Calculation Methodology Created by: Pierre Robert CEO and CoFounder Best Credit Data, Inc. 50 Milk Street, 17 th Floor Boston, MA 02109 Contact Information: pierre@bestcreditanalysis.com
More informationDuration 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. Optionlike features... 8 D. Bond ratings...
More information1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
More informationCHAPTER 16: MANAGING BOND PORTFOLIOS
CHAPTER 16: MANAGING BOND PORTFOLIOS PROBLEM SETS 1. While it is true that shortterm rates are more volatile than longterm rates, the longer duration of the longerterm bonds makes their prices and their
More informationChapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull
Chapter 4 Interest Rates 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Treasury Rates Rates on instruments issued by a government in its own currency 3 LIBOR and LIBID LIBOR is the rate of interest
More informationFINANCIAL MATHEMATICS MONEY MARKET
FINANCIAL MATHEMATICS MONEY MARKET 1. Methods of Interest Calculation, Yield Curve and Quotation... 2 1.1 Methods to Calculate Interest... 2 1.2 The Yield Curve... 6 1.3 Interpolation... 8 1.4 Quotation...
More informationFINANCIAL AND INVESTMENT INSTRUMENTS. Lecture 6: Bonds and Debt Instruments: Valuation and Risk Management
AIMS FINANCIAL AND INVESTMENT INSTRUMENTS Lecture 6: Bonds and Debt Instruments: Valuation and Risk Management After this session you should Know how to value a bond Know the difference between the term
More informationCHAPTER 14: BOND PRICES AND YIELDS
CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3month Tbill: ( 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 informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationChapter 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 informationChapter 3. Fixed Income Securities
IE 5441 1 Chapter 3. Fixed Income Securities IE 5441 2 Financial instruments: bills, notes, bonds, annuities, futures contracts, mortgages, options,...; assortments that are not real goods but they carry
More informationExcel Financial Functions
Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money
More informationYield 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 informationInvestments Analysis
Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest
More informationBOND ANALYSIS AND VALUATION
BOND ANALYSIS AND VALUATION CEFA 003/004 LECTURE NOTES Mats Hansson Svenska handelshögskolan Institutionen för finansiell ekonomi och ekonomisk statistik TU1.UT TUFIXED TU.UT TUBOND TU3.UT TUDAY i Contents
More informationFixedincome Securities Lecture 3: Yield curves. Connecting various yield curves: intuition
Philip H. Dybvig Washington University in Saint Louis The term structure of interest rates Fixedincome Securities Lecture 3: Yield curves Relations among yield curves: intuition Conventions and complications
More informationExamination 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 informationAsset 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 informationTrading the Yield Curve. Copyright 19992006 Investment Analytics
Trading the Yield Curve Copyright 19992006 Investment Analytics 1 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading
More information7. 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 informationUS TREASURY SECURITIES  Issued by the U.S. Treasury Department and guaranteed by the full faith and credit of the United States Government.
Member NASD/SIPC Bond Basics TYPES OF ISSUERS There are essentially five entities that issue bonds: US TREASURY SECURITIES  Issued by the U.S. Treasury Department and guaranteed by the full faith and
More informationUnderstanding 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 informationDebt Instruments Set 2
Debt Instruments Set 2 Backus/October 29, 1998 Bond Arithmetic 0. Overview Zeros and coupon bonds Spot rates and yields Day count conventions Replication and arbitrage Forward rates Yields and returns
More informationInvestment 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 14 142 Bond Characteristics Face or par value (normally bullet maturity) Coupon rate (normally fixed) Zero
More informationBond valuation and bond yields
RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments
More informationCalculation Convention for Inflation Linked Bond
Calculation Convention for Inflation Linked Bond Bond Pricing and Product Development The Thai Bond Market Association (ThaiBMA) Introduction In May 0, Thai bond market will probably have a new type of
More informationCONSUMER PRICE INDEX (CPI) INDEXED GOVERNMENT BONDS
REPUBLIC OF TURKEY PRIME MINISTRY UNDERSECRETARIAT OF TREASURY CONSUMER PRICE INDEX (CPI) INDEXED GOVERNMENT BONDS INVESTORS GUIDE DECEMBER 2009 TABLE OF CONTENTS I. GENERAL ISSUES... 1 II. TERMS OF THE
More informationPractice Set #1 and Solutions.
Bo Sjö 140503 Practice Set #1 and Solutions. What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets
More informationFIN 472 FixedIncome Securities Debt Instruments
FIN 472 FixedIncome Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds
More informationExam 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 informationCHAPTER 10 BOND PRICES AND YIELDS
CHAPTER 10 BOND PRICES AND YIELDS 1. a. Catastrophe bond. Typically issued by an insurance company. They are similar to an insurance policy in that the investor receives coupons and par value, but takes
More informationLecture 11 FixedIncome Securities: An Overview
1 Lecture 11 FixedIncome Securities: An Overview Alexander K. Koch Department of Economics, Royal Holloway, University of London January 11, 2008 In addition to learning the material covered in the reading
More informationFINANCIAL MATHEMATICS FIXED INCOME
FINANCIAL MATHEMATICS FIXED INCOME 1. Converting from Money Market Basis to Bond Basis and vice versa 2 2. Calculating the Effective Interest Rate (Nonannual Payments)... 4 3. Conversion of Annual into
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationSolutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at
More informationChapter Review Problems
Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute
More informationRelative value analysis: calculating bond spreads Moorad Choudhry January 2006
Relative value analysis: calculating bond spreads Moorad Choudhry January 2006 Relative value analysis: bond spreads Moorad Choudhry Investors measure the perceived market value, or relative value, of
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationCHAPTER 4. Definition 4.1 Bond A bond is an interestbearing certificate of public (government) or private (corporate) indebtedness.
CHAPTER 4 BOND VALUATION Gentlemen prefer bonds. Andrew Mellon, 18551937 It is often necessary for corporations and governments to raise funds to cover planned expenditures. Corporations have two main
More informationVALUE 11.125%. $100,000 2003 (=MATURITY
NOTES H IX. How to Read Financial Bond Pages Understanding of the previously discussed interest rate measures will permit you to make sense out of the tables found in the financial sections of newspapers
More informationMBA Finance PartTime Present Value
MBA Finance PartTime Present Value Professor Hugues Pirotte Spéder Solvay Business School Université Libre de Bruxelles Fall 2002 1 1 Present Value Objectives for this session : 1. Introduce present value
More information