# Bond Return Calculation Methodology

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Bond Return Calculation Methodology Morningstar Methodology Paper June 30, Morningstar, Inc. All rights reserved. The information in this document is the property of Morningstar, Inc. Reproduction or transcription by any means, in whole or in part, without the prior written consent of Morningstar, Inc., is prohibited.

2 Content Introduction 3 Coupon Payment and Accrued Interest 5 Coupon Dates 5 Coupon Payment Amount and Accrued Interest 6 Actual/Actual Day-Count Convention 7 Actual/365 Day-Count Convention 8 Actual/360 Day-Count Convention 9 30/360 Day-Count Convention 10 Bond Total Return 12 Daily Total Return 12 Daily Total Return Index 13 Morningstar Bond Return Calculation Methodology June 30,

3 Introduction A bond is a debt instrument. The borrowing entity promises to pay a specified sum of money at specific future dates. The promised payment consists of two components: interest and principal. For example, the borrower, or issuer, has an obligation to pay interest at a fixed rate twice a year and repay the principal upon the date of maturity. The principal, the amount that the borrower must repay to the lender, is also called the face value or par value. For a bond, the interest payment is called a coupon. The coupon rate is the interest rate expressed in percentage of principal. Since bond issuers do not distribute coupon payments on a daily basis, a bond buyer must pay the seller for the amount of interest earned by the latter since the previous coupon date; this is called accrued interest. Upon transaction, the buyer pays the seller the agreed-upon price, aka the "clean" price, for the bond plus accrued interest. The clean price plus accrued interest is called the "dirty" price. Bonds do not transact every day, so market price is not always observable. Therefore, for the purpose of calculating the daily returns of bonds, Morningstar uses the evaluated price, which is the theoretical fair price of a bond obtained from third-party providers. This methodology document addresses the return calculation of fixed-rate and zero-coupon bonds. Fixed-rate bonds pay periodic coupons that are constant over the bond's life. Zerocoupon bonds do not pay periodic interest and are issued at a discount to par value. The methodology does not currently address other types of bonds such as floating-rate notes, bonds that need principal factors such as mortgage-backed, commercial mortgage-backed, and asset-backed bonds, Treasury Inflation-Protected Securities, and so on. Morningstar Bond Return Calculation Methodology June 30,

4 Introduction (continued) In order to calculate a bond's return, the following information about the bond is required or could be used as a substitute for required information: Coupon payment frequency: expressed as the number of coupon payments in a year, 1=annually, 2=semiannually, 4=quarterly, 12=monthly, and so on. EOM: end-of-month. This indicates whether all coupon payment dates fall on the last day of the month. For example, if the first coupon for a semiannual bond is June 30, the next coupon is paid on Dec. 31 if the bond is EOM and Dec. 30 if it is not. Coupon rate: annual coupon rate of the bond, expressed as a percentage of par value. Day-count convention: the bond's day-count convention for coupon payments and accrued interest calculation. Please refer to the Day-Count Convention sections of this document for details. First coupon date: date of the first coupon payment for the bond. Maturity date: date the bond issuer must return the principal. Clean price: price of the bond without accrued interest. For the purpose of calculating daily return of bonds, Morningstar uses the evaluated price, which is the theoretical fair price of a bond obtained from third-party providers. Morningstar does not calculate a return stream for a bond under the following conditions: Coupon payment frequency, coupon rate, or day-count convention is not available, and the bond is not a zero-coupon bond. The first coupon date and the maturity date are both unavailable, as we would be unable to determine when coupon payments ought to occur. Morningstar stops further updates to a stream of returns under the following conditions: The bond is missing more than five consecutive days of clean price. If the clean price recommences at a future date, the return series for this bond restarts from that day onward. Default, issuer files for bankruptcy protection, delisting, or indefinite suspension. If the issuer emerges from default or bankruptcy at a future date, the return series for this bond restarts from that day forward. Morningstar Bond Return Calculation Methodology June 30,

5 Coupon Payment and Accrued Interest Coupon, the interest payment of a bond, is a significant source of a bond's return. This section describes the calculation of the coupon payment and its related measure, accrued interest. The section is not applicable to a zero-coupon bond as there is no period coupon payment. Coupon Dates The following information is needed to determine the dates on which coupons are paid: first coupon date, coupon payment frequency, and whether the coupon payment dates fall on the last day of the month. The first coupon date indicates when the first coupon payment occurs, and subsequent coupon payments are made on the same day of the month in regular intervals based on the coupon payment frequency. Because each month may have a different number of days, when the first coupon date falls on the month-end of a smaller month, it is important to know whether coupon payment dates always fall on the last day of the month for the bond in question. For example, if the first coupon for a semiannual bond is June 30, the next coupon is paid on Dec. 31 for an end-of-month, or EOM, bond, and it is on Dec. 30 for a bond that is not EOM. Similarly, if the first coupon for a quarterly EOM bond is Feb. 28, the subsequent coupon payments are on May 31, August 31, Nov. 30, and Feb. 29 for a leap year. Morningstar does not make adjustments when coupon dates fall on weekends or national holidays, or for any other reason that may make the timing of the receipt of coupon payments differ from the entitlement date of the coupon. When the first coupon date is not available, Morningstar uses the maturity date and works backward using the coupon payment frequency to generate a series of coupon payment dates. As stated in the Introduction, in the case that both the first coupon date and the maturity date are unavailable for a bond that is not a zero-coupon bond, Morningstar does not calculate a return stream. Morningstar Bond Return Calculation Methodology June 30,

6 Coupon Payment and Accrued Interest (continued) Coupon Payment Amount and Accrued Interest At each coupon payment date, one would intuitively expect the coupon payments to be the annual coupon rate divided by the number of periodic coupons in the year, but this is not always the case. Similarly, it is not always true that adding all coupon payments for the year results in the annual coupon rate. This is because there are different day-count conventions, each with a unique way of handling the fact that the number of days between coupon payments varies, and so does the number of days in a year depending on whether it is a leap year. Accrued interest is also an important part of a bond's return. Since bond issuers do not distribute coupon payments on a daily basis, a bond buyer must pay the seller for the amount of interest earned by the latter since the previous coupon date; this is accrued interest. On a daily basis, the market value of a bond, also known as the dirty price, is the clean price plus accrued interest. While the clean price is obtained directly from third-party providers as the evaluated or theoretical price of the bond, accrued interest and coupon payment must be calculated. The following formula is applicable to both coupon payment and accrued interest calculation since accrued interest is essentially prorated coupon payment: [1] Interest t = Coupon Rate Day-Count Factor t, where Interest t = Coupon payment or accrued interest on valuation day t, expressed as percentage of par value Coupon Rate = Annual coupon rate of a bond, expressed as a percentage of par value Day-Count Factor t = Day-count factor on valuation day t Note: Accrued interest is zero on a coupon date. Morningstar Bond Return Calculation Methodology June 30,

7 Coupon Payment and Accrued Interest (continued) The day-count factor is an essential step in the calculation of coupon payment and accrued interest for a bond. It is based on the bond's day-count convention and coupon payment frequency. The day-count convention determines the effective number of days between two dates in question, regardless of how many actual calendar days set them apart. In the case of coupon payment calculation, it is the effective number of days between the date of the coupon payment that is being calculated and the date of the previous coupon payment. For accrued interest calculation, it is the effective number of days between the previous coupon date and the valuation date. There is no central authority defining day-count conventions, and variations exist within the same general convention. The following sections address in detail Morningstar's methodology for the most commonly used day-count conventions: 1. Actual/actual 2. Actual/ Actual/ /360 Actual/Actual Day-Count Convention The actual/actual day-count convention counts the actual number of days in the interest valuation period as well as the actual number of days of the year in question, taking into account that there are 366 days in a leap year. Under this method, all coupon payments are always for the same amount regardless of the length in the coupon period, and each coupon payment is prorated equally among the days in the coupon period for the purpose of daily accrual calculation. For example, for a bond that pays a 4% coupon rate semiannually, one coupon period may have 181 days and the next coupon period 184 days, but the bondholder is paid the same amount on each coupon date, which is 2% in this example. The coupon payment for the first coupon period is equally prorated among its 181 days for daily accrual, and the coupon payment for the second coupon period is equally prorated among its 184 days. Morningstar Bond Return Calculation Methodology June 30,

8 Coupon Payment and Accrued Interest (continued) For the actual/actual day-count convention, the day-count factor on a given coupon or valuation date is [2] Day-Count Factor t = ( 1 / Freq ) ( Num Prev,t / Num Prev,Next ), where Freq = Coupon payment frequency, expressed as number of coupon payments per year Num Prev,t = Number of days between the previous coupon date and the valuation date Num Prev,Next = Number of days between the previous coupon date and the next coupon date Notes: The coupon payment frequency is expressed as the number of coupon payments in a year: 1=annually, 2=semiannually, 4=quarterly, 12=monthly, and so on. When calculating the day-count factor for a coupon payment on a given coupon date, the previous coupon date refers to the date of the preceding coupon, while both the valuation date and the next coupon date are the coupon date in question. For example, when calculating the day-count factor for the semiannual coupon payment on Aug. 15, 2010, the previous coupon date is May 15, 2010, and both the valuation date and the next coupon date are Aug. 15, Intrinsically, this reduces the formula to 1 over coupon frequency, which is why the coupon payments are always the same throughout the bond's life. Actual/365 Day-Count Convention The actual/365 day-count convention counts the actual number of days in the interest valuation period but assumes there are always 365 days in a year, regardless of leap year. Under this method, coupon payments vary from coupon period to coupon period due to the differing length of each period. Furthermore, the sum of coupon amounts exceeds the annual coupon rate in a leap year for having gained an extra day of interest. Morningstar Bond Return Calculation Methodology June 30,

9 Coupon Payment and Accrued Interest (continued) For the actual/365 day-count convention, the day-count factor on a given coupon or valuation date is [3] Day-Count Factor t = Num Prev,t / 365. Note: Similar to the actual/actual day-count convention, when calculating the day-count factor for a coupon payment on a given coupon date, the previous coupon date refers to the date of the preceding coupon, while the valuation date is the coupon date in question. For example, when calculating the day-count factor for the semiannual coupon payment on Aug. 15, 2010, the previous coupon date is May 15, 2010, and the valuation date is Aug. 15, Actual/360 Day-Count Convention The Actual/360 day-count convention counts the actual number of days in the interest valuation period but assumes there are always 360 days in a year, regardless of leap year. Under this method, coupon payments vary from coupon period to coupon period due to the differing length of each period. Furthermore, the sum of coupon amounts always exceeds the annual coupon rate for having gained five or six additional days of interest. For the actual/360 day-count convention, the day-count factor on a given coupon or valuation date is [4] Day-Count Factor t = Num Prev,t / 360. Note: Similar to the actual/365 day-count convention, when calculating the day-count factor for a coupon payment on a given coupon date, the previous coupon date refers to the date of the preceding coupon, while the valuation date is the coupon date in question. Morningstar Bond Return Calculation Methodology June 30,

10 Coupon Payment and Accrued Interest (continued) 30/360 Day-Count Convention The 30/360 day-count convention assumes there are 30 days in a month and 360 days in a year, regardless of leap year. The spirit of this method is for all coupon payments to be the same amount regardless of the length in the coupon period, while holding the daily accrual rate constant. Since the method assumes there are 30 days in a month and the daily accrual rate is constant, the daily accrual is zero for seven days each year. Those seven days are either the 31st or the first calendar day of a month that follows a 31-day month, depending on whether the bond is EOM. Similarly, in a regular year, three days' worth of accrual is assigned to Feb. 28 or March 1, depending on whether the bond is EOM that pays a coupon in February. In a leap year, this is reduced to two days' worth of accrual. For the 30/360 day-count convention, the day-count factor on a given coupon or valuation date is [5] Day-Count Factor t = [(360 ( Y t Y Prev ) + 30 ( M t M Prev ) + ( D t D Prev )]/360, where Y t = Year number that the valuation day t falls in, expressed as a number, such as 2010 for Aug. 15, 2010 Y Prev = Year number that the previous coupon date falls in, expressed as a number M t = Month number that the valuation day t falls in, expressed as a number, such as 8 for Aug. 15, 2010 M Prev = Month number that the previous coupon date falls in, expressed as a number D t = Day number of the valuation day t (exceptions below), expressed in number, such as 15 for Aug. 15, 2010 D Prev = Day number of the previous coupon date (exceptions below), expressed as a number Note: Similar to the actual/360 day-count convention, when calculating the day-count factor for a coupon payment on a given coupon date, the previous coupon date refers to the date of the preceding coupon, while the valuation date is the coupon date in question. Morningstar Bond Return Calculation Methodology June 30,

11 Morningstar Bond Return Calculation Methodology June 30,

12 Coupon Payment and Accrued Interest (continued) Exceptions: The day number of the previous coupon day, D Prev, is changed to 30 when the previous coupon occurs on the 31st of the month. The day number of the previous coupon day, D Prev, is changed to 30 when both of the following conditions occur: the previous coupon falls on the last day of February, and the bond is EOM. The day number of the valuation day, D t, is changed to 30 when both of the following conditions occur: the valuation day is the 31st of the month, and D Prev = 30 after applying the exceptions outlined in the previous two bullet points. The day number of the valuation day, D t, is changed to 30 when all of the following conditions occur: the valuation day falls on the last day of February, the bond is EOM, and the end of February is one of the periodic coupon dates for this bond. Morningstar Bond Return Calculation Methodology June 30,

13 Bond Total Return Daily Total Return The daily total return of a bond takes into consideration both capital appreciation and income. It is the combination of the change in market value of the bond and coupon payment received on the valuation date, assuming that the latter occurs at the end of the day. The market value of a bond, also known as the dirty price, is the clean price plus accrued interest. The clean price is obtained directly from third-party providers as the evaluated or theoretical price of the bond, and the accrued interest and coupon payment are calculated based on formula [1] above. The formula for the daily total return of a bond is as follows: [6] TR t-1,t = ( P t + AI t + Coupon t ) / ( P t-1 + AI t-1 ) - 1, where TR t-1,t = Total return on day t, which is earned from the end of the previous day to the end of the valuation day P t = Clean price on the valuation day t AI t = Accrued interest on the valuation day t P t-1 = Clean price on the day prior to the valuation day AI t-1 = Accrued interest on the day prior to the valuation day Coupon t = Coupon payment on the valuation day t Notes: Coupon and accrued interest for a zero-coupon bond are zero. Accrued interest is zero on a coupon date. Missing clean price: when the clean price of a bond is missing, the clean price from the most recent past is carried over for up to five days. For example, if a bond is missing prices from Oct. 27 to Oct. 31, the clean price from Oct. 26 is carried over to fill the missing clean price on these five days. Only the clean price is carried over; the dirty price could be different on each of these five days as coupon payments and accrued interest continue being calculated on a daily basis. If the clean price is also missing on Nov. 1, this exceeds the five-day carryover limit and the return stream is stopped as of Oct. 31. If the clean price recommences at a future day, the return series for this bond restarts from that day onward, and historical return prior to the Morningstar Bond Return Calculation Methodology June 30,

14 Bond Total Return (continued) recommencement is erased because the interruption is too large to be considered continuous. Daily Total Return Index To efficiently calculate the return between any two days, it is often helpful to think in terms of index level, in other words, growth in wealth such as growth of \$100. Morningstar calls this data stream the daily total return index. The formula for it is as follows: [7] DRI t = DRI t-1 (1+TR t-1,t ), where DRI t = Daily total return index on the valuation day t DRI t-1 = Daily return index on the day prior to the valuation day This concept assumes that total return compounds over time. When compounding, coupon payments are assumed to be reinvested on the coupon payment date at the day's price (the dirty price is the same as the clean price as there is no accrued interest). An alternative view on the concept of compounding is to assume that the coupon is not reinvested but instead returned directly to the investor so that this cash flow exits the portfolio and does not produce a cash drag. In the absence of a cash drag, the portfolio is growing at the total return. Therefore, compounding makes sense no matter whether one believes that coupon payments ought to be reinvested or withdrawn. Morningstar Bond Return Calculation Methodology June 30,

### 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

### 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

### Problems and Solutions

Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: \$,000 coupon rate: 8% coupon frequency: semiannual

### FAQ. 1. What is a Bond & Sukuk?

FAQ 1. What is a Bond & Sukuk? Bonds or Sukuk are fixed income security or debt security issued by companies or governments (the issuer) to raise funds to meet their financing needs. A bond that is issued

### NATIONAL 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

### SS15 Fixed-Income: Basic Concepts SS15 Fixed-Income: Analysis of Risk

SS15 Fixed-Income: Basic Concepts SS15 Fixed-Income: 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

### CANADIAN CONVENTIONS IN FIXED INCOME MARKETS

INVESTMENT INDUSTRY ASSOCIATION OF CANADA CANADIAN CONVENTIONS IN FIXED INCOME MARKETS A REFERENCE DOCUMENT OF FIXED INCOME SECURITIES FORMULAS AND PRACTICES Release: 1.0 www.iiac.ca FORWARD This document

### Interest 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

### Bond 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

### Notes for Lecture 3 (February 14)

INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because

### Introduction to Bonds

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

### Chapter 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

### The AFR and the Value of Debt

Gift and Estate Tax Valuation Insights The AFR and the Value of Debt Robert P. Schweihs When a promissory note that was established at the prevailing applicable federal rate (AFR) is recapitalized at the

### CANADIAN CONVENTIONS IN FIXED INCOME MARKETS

INVESTMENT INDUSTRY ASSOCIATION OF CANADA CANADIAN CONVENTIONS IN FIXED INCOME MARKETS A REFERENCE DOCUMENT OF FIXED INCOME SECURITIES FORMULAS AND PRACTICES Release: 1.1 www.iiac.ca FORWARD This document

### Index. 1. Financial Markets: Overview. 2. The Bond Market. 3. Risks Associated with Fixed Income Investments. 4. Bond Characteristics and Valuation

Index 1. Financial Markets: Overview 2. The Bond Market 3. Risks Associated with Fixed Income Investments 4. Bond Characteristics and Valuation 5. Macro Environment Chapter 24 Bond Characteristics and

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

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

### CHAPTER15. Long-Term Liabilities. Acct202 15-1

CHAPTER15 Long-Term Liabilities Acct202 15-1 15-2 PreviewofCHAPTER15 Bond Basics Bonds are a form of interest-bearing notes payable. Three advantages over common stock: 1. Stockholder control is not affected.

### Bond Pricing Fundamentals

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

### Calculation 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

### 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

### 1 Pricing of Financial Instruments

ESTM 60202: Financial Mathematics ESTEEM Fall 2009 Alex Himonas 01 Lecture Notes 1 September 30, 2009 1 Pricing of Financial Instruments These lecture notes will introduce and explain the use of financial

### Investors Chronicle Roadshow 2011. Trading Bonds on the London Stock Exchange

Investors Chronicle Roadshow 2011 Trading Bonds on the London Stock Exchange Agenda How do bonds work? Risks associated with bonds Order book for Retail Bonds London Stock Exchange Website Tools 2 How

### Financial 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

### US 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

### Compound Interest Chapter 8

8-2 Compound Interest Chapter 8 8-3 Learning Objectives After completing this chapter, you will be able to: > Calculate maturity value, future value, and present value in compound interest applications,

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

### Maturity and interest-rate risk

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

### CONSUMER 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

### Bonds 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

### 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.

### Wealth Management Education Series. Cultivate an Understanding of Bonds

Wealth Management Education Series Cultivate an Understanding of Bonds Wealth Management Education Series Cultivate an Understanding of Bonds Managing your wealth well is like tending a beautiful formal

### CHAPTER 7 INTEREST RATES AND BOND VALUATION

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

### Fixed Income Securities

3st lecture IES, UK October 7, 2015 Outline Bond Characteristics 1 Bond Characteristics 2 Bond Characteristics Government bond listing Rate Maturity mo/yr Bid Asked Chg Ask yld 3.000 July 12 108:22 108:23-20

### Investment Analysis (FIN 670) Fall Homework 3

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

### Yield Measures, Spot Rates & Forward Rates

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

### Maturity The date where the issuer must return the principal or the face value to the investor.

PRODUCT INFORMATION SHEET - BONDS 1. WHAT ARE BONDS? A bond is a debt instrument issued by a borrowing entity (issuer) to investors (lenders) in return for lending their money to the issuer. The issuer

### Tax rules for bond investors

Tax rules for bond investors Understand the treatment of different bonds Paying taxes is an inevitable part of investing for most bondholders, and understanding the tax rules, and procedures can be difficult

### 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

### FIXED/ADJUSTABLE RATE NOTE (One-Year Treasury Index Rate Caps Fixed Rate Conversion Option)

FIXED/ADJUSTABLE RATE NOTE (One-Year Treasury Index Rate Caps Fixed Rate Conversion Option) THIS NOTE PROVIDES FOR A CHANGE IN MY FIXED INTEREST RATE TO AN ADJUSTABLE INTEREST RATE. THIS NOTE LIMITS THE

### 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

### Bond 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:

### Exit Strategies for Fixed Rate Financing. Comparing Yield Maintenance and Defeasance Alternatives. by Regan Campbell and Jehane Walsh

Defeasance Vs. Yield Maintenance Exit Strategies for Fixed Rate Financing Comparing Yield Maintenance and Defeasance Alternatives by Regan Campbell and Jehane Walsh When looking to refinance or sell a

### In 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.

### Introduction to Bond Math Presentation to CDIAC

October 2, 2008 Peter Taylor, Managing Director, Public Finance Department Matthew Koch, Vice President, Public Finance Department Introduction to Bond Math Presentation to CDIAC Agenda Agenda I. What

### CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING

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

### RMA Committee on Securities Lending

RMA Committee on Securities Lending Statement of Best Practice Valuation of Accrued Interest and Collateral held against loans of Fixed Income securities borrowed under an MSLA Goal of this paper The U.S.

### Fixed 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

### 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

### 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

### FIN 472 Fixed-Income Securities Forward Rates

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

### SEF Rule 802 Credit Derivatives Product Descriptions

SEF Rule 802 Credit Derivatives Product Descriptions Products Rule 802 (1) Credit Derivatives Indices (2) Credit Derivatives Tranches (3) [Reserved] (4) IOS Index Credit Default Swaps (5) iboxx Total Return

### Excel 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

### CHAPTER 10 Reporting and Analyzing Liabilities. Accounting for Notes Payable Obligations in the form of written notes are recorded as notes payable.

CHAPTER 10 Reporting and Analyzing Liabilities Accounting for Notes Payable Obligations in the form of written notes are recorded as notes payable. Notes payable usually require the borrower to pay interest

### - 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

### Money 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

### 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

### 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 markets» What

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

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

### WHEREAS, the Board of Directors desires to modify and amend the Investment Guidelines effective immediately;

A RESOLUTION OF THE ENERGY IMPROVEMENT CORPORATION ( EIC or the Corporation ) WITH RESPECT TO THE REVIEW AND APPROVAL OF THE CORPORATION'S INVESTMENT GUIDELINES AND INVESTMENT REPORT WHEREAS, the Corporation

### 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

### 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

### SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

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

Chapter 4 Interest Rates 1 Types of Rates! Treasury rate! LIBOR! Fed funds rate! Repo rate 2 Treasury Rate! Rate on instrument issued by a government in its own currency 3 LIBOR! LIBOR is the rate of interest

### Simple Interest. and Simple Discount

CHAPTER 1 Simple Interest and Simple Discount Learning Objectives Money is invested or borrowed in thousands of transactions every day. When an investment is cashed in or when borrowed money is repaid,

### Lesson 6 Save and Invest: Bonds Lending Your Money

Lesson 6 Save and Invest: Bonds Lending Your Money Lesson Description This lesson introduces bonds as an investment option. Using a series of classroom visuals, students will identify the three main parts

### ECO 4368 Instructor: Saltuk Ozerturk. Bonds and Their Valuation

ECO 4368 Instructor: Saltuk Ozerturk Bonds and Their Valuation A bond is a long term contract under which a borrower (the issuer) agrees to make payments of interest and principal on speci c dates, to

### Section 5.2 Compound Interest

Section 5.2 Compound Interest With annual simple interest, you earn interest each year on your original investment. With annual compound interest, however, you earn interest both on your original investment

### Basic Concept of Time Value of Money

Basic Concept of Time Value of Money CHAPTER 1 1.1 INTRODUCTION Money has time value. A rupee today is more valuable than a year hence. It is on this concept the time value of money is based. The recognition

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

### Stable Value Funds and Investment Contracts An Overview

Stable Value Funds and Investment Contracts An Overview February 2006 Topix Primer Series www.aicpa.org/ebpaqc EBPAQC@aicpa.org Introduction Many defined contribution plans today offer a low-risk investment

### Recommended. Conventions for the Norwegian Certificate and Bond Markets. May 2001 www.finansanalytiker.no

Recommended Conventions for the Norwegian Certificate and Bond Markets May 2001 www.finansanalytiker.no 2 Preface Recently, the Norwegian Society of Financial Analysts (NFF) has become increasingly aware

### Chapter 8: Promissory Notes, Treasury Bills, & Demand Loans

HOSP 1107 (Business Math) Learning Centre Chapter 8: Promissory Notes, Treasury Bills, & Demand Loans Issued by Face Value Term Interest Rate Promissory Note Treasury Bill/T-bill Demand Loan Banks, companies,

### Exercise 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

### Saving and Investing

Presentation Slides \$ Lesson Twelve Saving and Investing 04/09 pay yourself first (a little can add up) example 1: Save this each week At % Interest In 10 years you ll have \$7.00 5% \$4,720 \$14.00 5% \$9,400

### 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:

### EECBG PROGRAM NOTICE EFFECTIVE DATE: July 27, 2010

EECBG PROGRAM NOTICE 10 018 EFFECTIVE DATE: July 27, 2010 SUBJECT: GUIDANCE FOR ENERGY EFFICIENCY AND CONSERVATION BLOCK GRANT GRANTEES ON QUALIFIED ENERGY CONSERVATION BONDS AND NEW CLEAN RENEWABLE ENERGY

### 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

### FinQuiz Notes 2 0 1 5

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### 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

### Chapter 4 Discounted Cash Flow Valuation

University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute

### Interest 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

### U.S. Treasury Securities

U.S. Treasury Securities U.S. Treasury Securities 4.6 Nonmarketable To help finance its operations, the U.S. government from time to time borrows money by selling investors a variety of debt securities

### Accounting Cheat Sheet

DIAGRAM OF TACCOUNTS Assets = Balance Sheet as of 12/31/20 Liabilit ies + = + Equity METHODS & ORGS Accrual basis Follows the matching principle and recognizes transactions as they occur (GAAP Method)

### Stock and Bond Valuation: Annuities and Perpetuities

Stock and Bond Valuation: Annuities and Perpetuities Lecture 3, slides 3.1 Brais Alvarez Pereira LdM, BUS 332 F: Principles of Finance, Spring 2016 February 23, 2016 Important Shortcut Formulas Present

### 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

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

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

Chapter 4 Interest Rates 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Treasury Rates Rates on instruments issued by a government in its own currency 3 LIBOR and LIBID LIBOR is the rate of interest

### Cash Flow Equivalence

Cash Flow Equivalence Introduction This document is intended to demonstrate the level of cash flow equivalence between an Eris credit futures contract and a cleared or un-cleared OTC swap contract referencing

### Waiting to Extend: A Forward-Looking Approach to Fixed Income Investing

Waiting to Extend: A Forward-Looking Approach to Fixed Income Investing Market Commentary May 2016 Investors sometimes want to invest with a money manager who will shorten portfolio duration in advance

### 7. Bonds and Interest rates

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

### 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

### An Investor s Guide to the US Treasury Market

an INVESTOR S GUIDE TO THE US TreASURY MARKET february 2014 An Investor s Guide to the US Treasury Market summary in brief Many investors concerned with principal preservation turn to US Treasury securities

### Answers to Concepts in Review

Answers to Concepts in Review 1. Bonds are appealing to investors because they provide a generous amount of current income and they can often generate large capital gains. These two sources of income together

### 3. Time value of money

1 Simple interest 2 3. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

### 7: Compounding Frequency

7.1 Compounding Frequency Nominal and Effective Interest 1 7: Compounding Frequency The factors developed in the preceding chapters all use the interest rate per compounding period as a parameter. This

### 1.2 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

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

### Coupon Bonds and Zeroes

Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding

### Navigating Rising Rates with Active, Multi-Sector Fixed Income Management

Navigating Rising Rates with Active, Multi-Sector Fixed Income Management 2 With bond yields near 60-year lows and expected to rise, U.S. core bond investors are increasingly questioning how to mitigate