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LM01 Alternative Investment Features, Methods, and Structures

LM01 Categories, Characteristics, and Compensation Structures of Alternative Investments

LM01 Corporate Structures and Ownership

LM01 Derivative Instrument and Derivative Market Features

LM01 Ethics and Trust in the Investment Profession

LM01 Fixed-Income Instrument Features

LM01 Fixed-Income Securities: Defining Elements

LM01 Introduction to Financial Statement Analysis

LM01 Market Organization & Structure

LM01 Market Organization and Structure

LM01 Organizational Forms, Corporate Issuer Features, and Ownership

LM01 Portfolio Management Overview

LM01 Portfolio Management: An Overview

LM01 Rates and Returns

LM01 The Firm & Market Structures

LM01 Time Value of Money

LM01 Topics in Demand and Supply Analysis

LM02 Alternative Investment Performance and Returns

LM02 Analyzing Income Statements

LM02 Code of Ethics and Standards of Professional Conduct

LM02 Code of Ethics and Standards of Professional Conduct Profession

LM02 Financial Reporting Standards

LM02 Fixed Income Markets - Issuance Trading and Funding

LM02 Fixed-Income Cash Flows and Types

LM02 Forward Commitment and Contingent Claim Features and Instruments

LM02 Introduction to Corporate Governance and Other ESG Considerations

LM02 Investors and Other Stakeholders

LM02 Organizing, Visualizing, and Describing Data

LM02 Performance Calculation and Appraisal of Alternative Investments

LM02 Portfolio Risk & Return: Part I

LM02 Portfolio Risk and Return Part I

LM02 Security Market Indexes

LM02 The Firm and Market Structures

LM02 Time Value of Money in Finance

LM02 Understanding Business Cycles

LM03 Aggregate Output, Prices and Economic Growth

LM03 Analyzing Balance Sheets

LM03 Business Models & Risks

LM03 Corporate Governance: Conflicts, Mechanisms, Risks, and Benefits

LM03 Derivative Benefits, Risks, and Issuer and Investor Uses

LM03 Fiscal Policy

LM03 Fixed-Income Issuance and Trading

LM03 Guidance for Standards I-VII

LM03 Guidance for Standards I–VII

LM03 Introduction to Fixed Income Valuation

LM03 Investments in Private Capital: Equity and Debt

LM03 Market Efficiency

LM03 Portfolio Risk & Return: Part II

LM03 Portfolio Risk and Return Part II

LM03 Private Capital, Real Estate, Infrastructure, Natural Resources, and Hedge Funds

LM03 Probability Concepts

LM03 Statistical Measures of Asset Returns

LM03 Understanding Income Statements

LM04 An Introduction to Asset-Backed Securities

LM04 Analyzing Statements of Cash Flows I

LM04 Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

LM04 Basics of Portfolio Planning & Construction

LM04 Basics of Portfolio Planning and Construction

LM04 Capital Investments

LM04 Common Probability Distributions

LM04 Fixed-Income Markets for Corporate Issuers

LM04 Introduction to the Global Investment Performance Standards (GIPS)

LM04 Monetary Policy

LM04 Overview of Equity Securities

LM04 Probability Trees and Conditional Expectations

LM04 Real Estate and Infrastructure

LM04 Understanding Balance Sheets

LM04 Understanding Business Cycles

LM04 Working Capital and Liquidity.

LM05 Analyzing Statements of Cash Flows II

LM05 Capital Investments and Capital Allocation

LM05 Company Analysis: Past and Present

LM05 Fixed-Income Markets for Government Issuers

LM05 Introduction to Geopolitics

LM05 Introduction to Industry and Company Analysis

LM05 Monetary and Fiscal Policy

LM05 Natural Resources

LM05 Portfolio Mathematics

LM05 Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

LM05 Pricing and Valuation of Forward Contracts.

LM05 Sampling and Estimation

LM05 The Behavioral Biases of Individuals

LM05 Understanding Cash Flow Statements

LM05 Understanding Fixed-Income Risk and Return

LM05 Working Capital & Liquidity

LM06 Analysis of Inventories

LM06 Capital Structure

LM06 Cost of Capital-Foundational Topics

LM06 Equity Valuation: Concepts and Basic Tools

LM06 Financial Analysis Techniques

LM06 Fixed-Income Bond Valuation: Prices and Yields

LM06 Fundamentals of Credit Analysis

LM06 Hedge Funds

LM06 Hypothesis Testing

LM06 Industry and Competitive Analysis

LM06 International Trade

LM06 Introduction to Geopolitics

LM06 Introduction to Risk Management

LM06 Pricing and Valuation of Futures Contracts

LM06 Simulation Methods

LM07 Analysis of Long-Term Assets

LM07 Business Models

LM07 Capital Flows and the FX Market

LM07 Capital Structure

LM07 Company Analysis: Forecasting

LM07 Estimation and Inference

LM07 International Trade and Capital Flows

LM07 Introduction to Digital Assets

LM07 Introduction to Linear Regression

LM07 Inventories

LM07 Pricing and Valuation of Interest Rate and Other Swaps

LM07 Pricing and Valuation of Interest Rates and Other Swaps

LM07 Technical Analysis

LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds.

LM08 Currency Exchange Rates

LM08 Equity Valuation: Concepts and Basic Tools

LM08 Exchange Rate Calculations

LM08 Fintech in Investment Management

LM08 Hypothesis Testing

LM08 Long Lived Assets

LM08 Measures of Leverage

LM08 Pricing and Valuation of Options

LM08 Topics in Long-Term Liabilities and Equity

LM08 Yield and Yield Spread Measures for Floating-Rate Instruments

LM09 Analysis of Income Taxes

LM09 Income Taxes

LM09 Option Replication Using Put-Call Parity

LM09 Option Replication Using Put–Call Parity

LM09 Parametric and Non-Parametric Tests of Independence

LM09 The Term Structure of Interest Rates: Spot, Par, and Forward Curves

LM10 Financial Reporting Quality

LM10 Interest Rate Risk and Return

LM10 Non-current (Long-Term) Liabilities

LM10 Simple Linear Regression

LM10 Valuing a Derivative Using a One-Period Binomial Model

LM11 Financial Analysis Techniques

LM11 Financial Reporting Quality

LM11 Introduction to Big Data Techniques

LM11 Yield-Based Bond Duration Measures and Properties

LM12 Applications of Financial Statement Analysis

LM12 Introduction to Financial Statement Modeling

LM12 Yield-Based Bond Convexity and Portfolio Properties

LM13 Curve-Based and Empirical Fixed-Income Risk Measures

LM14 Credit Risk

LM15 Credit Analysis for Government Issuers

LM16 Credit Analysis for Corporate Issuers

LM17 Fixed-Income Securitization

LM18 Asset-Backed Security (ABS) Instrument and Market Features

LM19 Mortgage-Backed Security (MBS) Instrument and Market Features

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IFT Notes for Level I CFA^® Program

LM03 Introduction to Fixed Income Valuation

Part 1

1. Introduction

In this reading, we will see how to value different types of fixed-income securities such as fixed-rate bonds, floating-rate bonds, and money market securities. This reading will cover:

How to price a bond.
How bond prices and yields are calculated.
The term structure of interest rates.
Yield spreads over benchmark interest rates.

2. Bond Prices and the Time Value of Money

2.1. Bond Pricing with a Market Discount Rate

A bond’s price is the present value of all future cash flows at the market discount rate. The discount rate is the rate of return required by investors given the risk of investment in the bond. It is also known as the required yield, or required rate of return.

PV of bond = $\frac{PMT}{{\left(1+r\right)}^1}+\frac{PMT}{{\left(1+r\right)}^2}+\dots +\frac{PMT+FV}{{\left(1+r\right)}^N}$

where:
PMT = coupon payment per period
FV= par value of the bond paid at maturity
r = market discount rate
N = number of periods until maturity

Example

The coupon rate on a bond is 4% and the payment is made once a year. The time to maturity is five years and the market discount rate is 6%. What is the bond price per 100 of par value?

Solution:

Start by drawing a timeline for the cash flows. The par value of the bond or principal is $100. A coupon payment of $4 is made every year. At maturity (at the end of five years), a payment of $104 (principal of $100 + coupon of $4) is made.

We are required to calculate the present value of bond at time t = 0. For that, we discount all the future cash flows at the market discount rate of 6%.

End of year	Type of cash flow	Amount	Present value
1	Coupon	4	3.77
2	Coupon	4	3.55
3	Coupon	4	3.36
4	Coupon	4	3.17
5	Coupon + principal	104	77.71
			91.56

Using the formula,

PV = $\frac{4}{1.06}+\frac{4}{{1.06}^2}+\frac{4}{{1.06}^3}+\frac{4}{{1.06}^4}+\frac{104}{{1.06}^5}$ = 91.575

Note: The table and formula above were just for your understanding.

On the exam, solve this quickly using a financial calculator:

N = 5; I/Y = 6; FV = 100; PMT = 4; PV = ? PV = -91.575

Notice the present value of the bond (91.575) is lower than the par value of the bond (100).

Premium, Par and Discount Bonds

Example

Assume we have another bond with a coupon rate of 8%, paid annually. If the market discount rate is again 6%, what is the price of the bond?

Solution:

Note that the coupon rate here is higher than the market rate. Calculate PV using these input values: N = 5; I/Y = 6; PMT = 8; FV = 100; CPT PV

PV = -108.425. In this case, the present value of the bond is higher than its par value. Such a bond is called a premium bond. Since the coupon rate (8%) is higher than the required return of 6%, investors pay more than the par value for the bond.

What if the coupon rate is 6%?

N = 5; I/Y = 6; PMT = 6; FV = 100; CPT PV

PV = -100. The present value is equal to the par value of the bond.

What if the coupon rate is 2%?

N = 5; I/Y = 6; PMT = 2; FV = 100; CPT PV

PV = -83.151. This type of bond, which sells at a price below its par value, is called a discount bond. Investors require a return of 6% but it pays a coupon of only 2%, so investors pay less.

Par, premium or discount	Relationship between coupon rate & market discount rate
Par bond	Coupon rate = market discount rate
Discount bond	Coupon rate < market discount rate
Premium bond	Coupon rate > market discount rate

2.2. Yield to maturity

The yield to maturity (YTM) is the internal rate of return on the cash flows – the uniform interest rate that will make the sum of the present values of future cash flows equal to the price of the bond. It is the implied market discount rate. In simpler terms, it is a bond’s internal rate of return – the rate of return on a bond including interest payments and capital gain if the bond is held until maturity. Yield to maturity is based on three important assumptions:

The investor holds the bond to maturity.
The issuer does not default on payments and pays coupon and principal as they come due.
The investor is able to reinvest all proceeds (coupons) at the YTM. (This is an unrealistic assumption as the interest rates may increase or decrease after the bond is purchased. So the coupon may be reinvested at a higher or lower rate.)

Example

A $100 face value bond with a coupon rate of 10% has a maturity of 4 years. The price of the bond is $80. What is its yield to maturity?

Solution:

Based on YTM’s definition, we come up with the equation below:

$80 = \frac{10}{{\left(1+r\right)}^1}+\frac{10}{{\left(1+r\right)}^2}+\frac{10}{{\left(1+r\right)}^3}+\frac{110}{{\left(1+r\right)}^4}$

This equation can be solved using trial and error but it is much easier to use a financial calculator: N = 4; PMT = 10; FV = 100; PV= -80; CPT I/Y = 17.34%. The bond is trading at a discount. So the coupon rate (10%) must be lower than market rate (17.34%).

Example

Calculate the yields-to-maturity for the following bonds: