4.1 Bond Pricing, Price–Yield Relationships & Accrued Interest

Canadian Securities Course CSC

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1 Introduction & Exam Overview

About the CSC Exams

2 Chapter 1: The Canadian Investment Marketplace

1.1 The Canadian Securities Industry & the Investment Dealer's Role 1.2 Financial Intermediaries: Banks, Trusts, Credit Unions, Insurers & Pension Funds 1.3 Financial Market Trends 1.4 Investment Capital, Financial Instruments & Financial Markets 1.5 Canadian Exchanges, ATSs, Dark Pools & the Order Protection Rule 1.6 Canadian Securities Regulators, the CSA & CIRO 1.7 Investor Protection: OSFI, CIPF and CDIC 1.8 Ethics, Standards of Conduct & the Client Focused Reforms 1.9 Conflicts of Interest, Complaint Handling & Remediation

3 Chapter 2: The Economy

2.1 Economics Foundations & Measuring Economic Growth 2.2 The Business Cycle & Economic Indicators 2.3 Inflation & Interest Rates 2.4 The Labour Market & Unemployment 2.5 The Bank of Canada & the Inflation-Control Target 2.6 Implementing Monetary Policy: The Operating Band, Market Operations & Transmission 2.7 Fiscal Policy, Deficits & the Challenges of Government Policy 2.8 International Finance & Trade: The Balance of Payments and the Canadian Dollar

4 Chapter 3: Features and Types of Fixed-Income Securities

3.1 The Fixed-Income Marketplace, Bond Terminology & Security 3.2 Protective Covenants, Retirement Provisions & Extendible/Retractable Features 3.3 Government of Canada Securities: T-Bills, Marketable Bonds & RRBs 3.4 Provincial & Municipal Debt and Strip Bonds 3.5 Corporate Bonds, Credit Spreads & Bond Ratings 3.6 Money Market Instruments, Floating-Rate Notes & International Bonds 3.7 Other Fixed-Income Securities & Reading Bond Quotes

5 Chapter 4: Pricing and Trading of Fixed-Income Securities

4.1 Bond Pricing, Price–Yield Relationships & Accrued Interest 4.2 Yield Calculations & Return Measures 4.3 The Term Structure of Interest Rates & Yield Curve Theories 4.4 Fundamental Bond Pricing Properties: Volatility Rules, Duration & Convexity 4.5 Bond Market Trading & Bond Indexes

6 Chapter 5: Common and Preferred Shares

5.1 Common Shares: Ownership Rights, Voting & Restricted Shares 5.2 Dividends, DRIPs, Stock Splits & Consolidations 5.3 Preferred Shares: Features, Cumulative Dividends & Taxation 5.4 Preferred Share Variations: Convertible, Callable, Retractable, Floating & Rate-Reset 5.5 Fundamental Equity Metrics & Ratios 5.6 Stock Indexes & Averages

7 Chapter 6: Equity Transactions

6.1 Order Types, Execution & Market Mechanics 6.2 Margin Trading: Long Accounts & Borrowing 6.3 Short Selling & Short-Margin Requirements 6.4 Trading & Settlement Procedures: T+1, CDS & Confirmations

8 Chapter 7: Derivatives

7.1 Derivatives: Role, Underlying Assets & Users 7.2 Options Fundamentals: Calls, Puts & Moneyness 7.3 Option Strategies & Risk Management 7.4 Forward & Futures Contracts 7.5 Rights & Warrants

9 Chapter 8: Corporations and their Financial Statements

8.1 Corporate Structures & Corporate Governance 8.2 The Annual Report, Accounting Standards & the Auditor's Report 8.3 The Balance Sheet & Income Statement 8.4 The Cash Flow Statement & Earnings Quality 8.5 Public Company Disclosure, Investor Rights, Take-Over Bids & Insider Trading

10 Chapter 9: Financing and Listing Securities

9.1 Government & Corporate Financing: Underwriting and Syndicates 9.2 The Prospectus Process, Stabilization & Purchaser Rights 9.3 The Exempt Market & Private Placements 9.4 The Listing Process: TSX, TSXV & Capital Pool Companies 9.5 Continuous Disclosure, Material Changes & Insider Reporting

11 Chapter 10: Investment Analysis

10.1 Methods of Equity Analysis & Macroeconomic Analysis 10.2 Fundamental Industry Analysis 10.3 Company Analysis: Competitive Advantages, Governance & the Dividend Discount Model 10.4 Discounted Cash Flow & Relative Valuation Multiples 10.5 Financial Statement Ratio Analysis 10.6 Assessing Preferred Share Investment Quality 10.7 Technical Analysis: Charts, Trends & Patterns 10.8 Technical Indicators, Volume, Breadth & Sentiment

12 Chapter 11: Portfolio Analysis

11.1 Measuring Investment Return 11.2 Measuring Risk: Types of Risk, Standard Deviation & Downside Measures 11.3 Portfolio Risk & Return: Correlation and Diversification 11.4 Beta, the Capital Asset Pricing Model & the Security Market Line 11.5 Portfolio Manager Styles: Equity & Fixed Income 11.6 The Portfolio Management Process: Objectives, Constraints & the IPS 11.7 Asset Mix, Monitoring, Performance Evaluation & Rebalancing

13 Chapter 12: Alternative Investments, Other Managed, and Structured Products

12.1 Alternative Investments: Structures, Fees & Liquid Alternatives 12.2 Alternative Strategies, Performance Measurement & Due Diligence 12.3 Segregated Funds, Labour-Sponsored Funds & Listed Private Equity 12.4 Income Trusts, REITs & Closed-End Funds 12.5 Structured Products: PPNs & Market-Linked GICs 12.6 Split Shares & Asset-Backed Securities

14 Chapter 13: Mutual Funds

13.1 Managed Products & Mutual Fund Structure 13.2 Pricing Mutual Fund Units: NAVPS & Forward Pricing 13.3 Mutual Fund Fees, Sales Charges & Unit Series 13.4 Mutual Fund Regulation, Fund Facts & Account Opening 13.5 Types of Mutual Funds & Fund Management Styles 13.6 Redemptions, Withdrawal Plans & Measuring Fund Performance

15 Chapter 14: Exchange-Traded Funds (ETFs)

14.1 ETF Origins, Structure, Tax Efficiency & ETF Facts 14.2 ETF Creation, Redemption & Arbitrage 14.3 Types of ETFs & Advanced Strategies 14.4 Comparing ETFs, Mutual Funds & Individual Securities

16 Chapter 15: Working with the Institutional Client

15.1 The Institutional Marketplace & Institutional Clients 15.2 Institutional Investment Guidelines, Styles & Restrictions 15.3 Buy Side & Sell Side: Trading Desks, Revenue, Clearing & Best Execution 15.4 Block Trading, Dark Pools & Algorithmic Trading

17 Chapter 16: Fee-Based Accounts and Working with the Retail Client

16.1 Fee-Based Accounts: Managed & Non-Managed Models 16.2 Fee Transparency, CRM2 & Total Cost Reporting, and MWRR vs. TWRR 16.3 The Financial Planning Approach & the Life Cycle 16.4 Behavioral Finance, Sequence-of-Returns Risk & Client Coaching 16.5 Estate Planning Basics

18 Chapter 17: Canadian Taxation

17.1 The Canadian Taxation System 17.2 Taxation of Investment Income 17.3 Capital Gains, Losses & The Superficial Loss Rule 17.4 Registered vs Non-Registered Tax-Advantaged Accounts 17.5 Tax Planning Strategies, Pension Plans & the RDSP

4.1 Bond Pricing, Price–Yield Relationships & Accrued Interest

Key Takeaways Explain This Topic AI

A bond's price is the present value of its semi-annual coupons plus the present value of its par value at maturity.

A bond trades at a discount when market yields exceed its coupon rate and at a premium when yields are below the coupon.

Canadian accrued interest = annual coupon × days elapsed ÷ 365, counting from the last coupon date up to but not including settlement.

Canadian bond trades settle T+1, and the buyer pays the quoted (clean) price plus accrued interest.

Last updated: October 2026

The Discounted Cash Flow Framework for Bond Valuation

A fixed-income security represents a contractual promise by an issuer to pay a predetermined stream of cash flows over time. Valuing a bond therefore relies on the foundational financial principle of discounted cash flows (DCF) : the theoretical intrinsic value of any bond equals the sum of the present values of all future cash flows, discounted at the prevailing market interest rate (the required yield to maturity for securities of comparable term, credit quality, and liquidity).

The Anatomy of Bond Cash Flows

For a standard conventional bond in Canada, these future cash flows consist of two distinct elements:

Annuity Stream of Periodic Coupons: Regular semi-annual interest payments distributed every six months until maturity.

Lump-Sum Par Value: The repayment of the bond's principal (face value) at final maturity.

Semi-Annual Compounding and the Valuation Formula

Because Canadian government and corporate bonds pay interest semi-annually , the annual coupon is divided by 2, the annual discount rate (yield) is divided by 2, and the number of discounting periods equals twice the number of years to maturity ( 2 n 2n 2 n ):

P = ∑ t = 1 2 n C / 2 ( 1 + r / 2 ) t + M ( 1 + r / 2 ) 2 n P = \sum_{t=1}^{2n} \frac{C/2}{(1 + r/2)^t} + \frac{M}{(1 + r/2)^{2n}} P = ∑ t = 1 2 n ​ ( 1 + r /2 ) t C /2 ​ + ( 1 + r /2 ) 2 n M ​

Where:

• P P P = Theoretical market price (present value) of the bond
• C C C = Annual contractual coupon payment in dollars (Coupon Rate × \times × Face Value)
• C / 2 C/2 C /2 = Semi-annual coupon cash payment
• r r r = Annual required market yield (discount rate expressed as a decimal)
• r / 2 r/2 r /2 = Semi-annual discount rate
• n n n = Number of years to maturity
• 2 n 2n 2 n = Total number of semi-annual compounding periods
• M M M = Par value (face value) repaid at maturity (standardized to $1,000 in Canadian practice)

Using the standard present value formula for an ordinary annuity, this equation can be expressed compactly as:

P = C 2 [ 1 − ( 1 + r / 2 ) − 2 n r / 2 ] + M ( 1 + r / 2 ) 2 n P = \frac{C}{2} \left[ \frac{1 - (1 + r/2)^{-2n}}{r/2} \right] + \frac{M}{(1 + r/2)^{2n}} P = 2 C ​ [ r /2 1 − ( 1 + r /2 ) − 2 n ​ ] + ( 1 + r /2 ) 2 n M ​

Step-by-Step Worked Numerical Example: Pricing a Bond

Valuation Problem: An investor is evaluating a 5-year Canadian corporate bond with an annual coupon rate of 6.00% paid semi-annually and a par value of $1,000. Prevailing market yields for comparable 5-year corporate debt currently stand at 8.00%.

Input Parameters:

• Par Value ( M M M ) = $1,000
• Annual Coupon Rate = 6.00% ⟹ \implies ⟹ Annual Coupon ( C C C ) = $60.00
• Semi-Annual Coupon ( C / 2 C/2 C /2 ) = $30.00
• Years to Maturity ( n n n ) = 5 ⟹ \implies ⟹ Compounding Periods ( 2 n 2n 2 n ) = 10
• Market Yield ( r r r ) = 8.00% ⟹ \implies ⟹ Semi-Annual Yield ( r / 2 r/2 r /2 ) = 4.00% (0.04)

Step 1: Calculate the Present Value of the Semi-Annual Coupons ( P V coupons PV_{\text{coupons}} P V coupons ​ )

P V coupons = $ 30.00 × [ 1 − ( 1 + 0.04 ) − 10 0.04 ] PV_{\text{coupons}} = \$30.00 \times \left[ \frac{1 - (1 + 0.04)^{-10}}{0.04} \right] P V coupons ​ = $30.00 × [ 0.04 1 − ( 1 + 0.04 ) − 10 ​ ] P V coupons = $ 30.00 × [ 1 − 0.675564 0.04 ] PV_{\text{coupons}} = \$30.00 \times \left[ \frac{1 - 0.675564}{0.04} \right] P V coupons ​ = $30.00 × [ 0.04 1 − 0.675564 ​ ] P V coupons = $ 30.00 × [ 0.324436 0.04 ] = $ 30.00 × 8.110896 = $ 243.33 PV_{\text{coupons}} = \$30.00 \times \left[ \frac{0.324436}{0.04} \right] = \$30.00 \times 8.110896 = \$243.33 P V coupons ​ = $30.00 × [ 0.04 0.324436 ​ ] = $30.00 × 8.110896 = $243.33

Step 2: Calculate the Present Value of the Lump-Sum Par Value ( P V par PV_{\text{par}} P V par ​ )

P V par = $ 1 , 000 ( 1 + 0.04 ) 10 = $ 1 , 000 × 0.675564 = $ 675.56 PV_{\text{par}} = \frac{\$1,000}{(1 + 0.04)^{10}} = \$1,000 \times 0.675564 = \$675.56 P V par ​ = ( 1 + 0.04 ) 10 $1 , 000 ​ = $1 , 000 × 0.675564 = $675.56

Step 3: Sum the Present Values to Determine Total Bond Price

P = P V coupons + P V par = $ 243.33 + $ 675.56 = $ 918.89 P = PV_{\text{coupons}} + PV_{\text{par}} = \$243.33 + \$675.56 = \$918.89 P = P V coupons ​ + P V par ​ = $243.33 + $675.56 = $918.89

In Canadian dealer quotes, this bond would be quoted as 91.89 (meaning 91.89% of par value). Because the market required yield (8.00%) exceeds the bond's contractual coupon (6.00%), the bond trades at a discount of $81.11 below par value.

Price-Yield Relationships: Par, Discount, and Premium Bonds

A bond's coupon rate is contractually fixed at issuance in the trust indenture. However, macroeconomic conditions, inflation expectations, and Bank of Canada monetary policy adjustments cause prevailing market yields to fluctuate continuously. The relationship between the bond's fixed coupon rate and prevailing market yields determines whether the bond trades at par, at a discount, or at a premium. Prevailing Market Yield vs. Fixed Coupon Rate

• ├── Yield == Coupon Rate ──> Par Bond (Price == 100)
• ├── Yield > Coupon Rate ──> Discount Bond (Price < 100)
• └── Yield < Coupon Rate ──> Premium Bond (Price > 100)
• The Par Bond ( P = 100 P = 100 P = 100 )

When prevailing market interest rates equal the bond's coupon rate, the present value of future cash flows discounted at that rate exactly matches the par value. The bond trades at 100.00 ($1,000 per $1,000 par unit). An investor purchasing a par bond earns an investment return derived entirely from coupon payments, with zero capital gain or loss at maturity.

The Discount Bond ( P < 100 P < 100 P < 100 )

When market interest rates climb above the bond's fixed coupon rate, newly issued bonds offer higher cash payments. To entice investors to purchase the existing lower-coupon bond in the secondary market, its price must fall below par value (e.g., 94.50 , or $945.00 per $1,000 bond). For a discount bond:

Coupon Rate < Current Yield < Yield to Maturity \text{Coupon Rate} < \text{Current Yield} < \text{Yield to Maturity} Coupon Rate < Current Yield < Yield to Maturity

The total return on a discount bond consists of two components: the ongoing semi-annual coupon income, plus a built-in capital gain realized as the bond's price pulls upward toward par ($1,000) as maturity approaches.

The Premium Bond ( P > 100 P > 100 P > 100 )

When market interest rates drop below the bond's fixed coupon rate, the bond's above-market cash flows become highly desirable. Investors bid up the price above par value (e.g., 106.25 , or $1,062.50 per $1,000 bond). For a premium bond:

Yield to Maturity < Current Yield < Coupon Rate \text{Yield to Maturity} < \text{Current Yield} < \text{Coupon Rate} Yield to Maturity < Current Yield < Coupon Rate

The total return on a premium bond is dampened by an inevitable capital loss as the bond's market price pulls downward toward par at maturity.

Summary of Bond Pricing Relationships

Pricing Status Price vs. Par Coupon vs. Market Yield Yield Hierarchy Source of Investor Return

Par Bond Price = 100.00 \text{Price} = 100.00 Price = 100.00 Coupon Rate = Market Yield \text{Coupon Rate} = \text{Market Yield} Coupon Rate = Market Yield Coupon = Current Yield = YTM \text{Coupon} = \text{Current Yield} = \text{YTM} Coupon = Current Yield = YTM 100% coupon cash flow; zero capital gain/loss

Discount Bond Price < 100.00 \text{Price} < 100.00 Price < 100.00 Coupon Rate < Market Yield \text{Coupon Rate} < \text{Market Yield} Coupon Rate < Market Yield Coupon < Current Yield < YTM \text{Coupon} < \text{Current Yield} < \text{YTM} Coupon < Current Yield < YTM Coupon cash flow + capital appreciation to par

Premium Bond Price > 100.00 \text{Price} > 100.00 Price > 100.00 Coupon Rate > Market Yield \text{Coupon Rate} > \text{Market Yield} Coupon Rate > Market Yield YTM < Current Yield < Coupon \text{YTM} < \text{Current Yield} < \text{Coupon} YTM < Current Yield < Coupon Coupon cash flow - capital depreciation to par

Clean Price vs. Dirty Price and Canadian Accrued Interest

When a bond is traded between its scheduled semi-annual coupon payment dates, interest is continuously accumulating for the seller who held the security since the last payment date. The buyer receives the full semi-annual coupon on the next scheduled payment date, even though they only held the bond for a portion of the period. Consequently, market conventions require the buyer to reimburse the seller for the interest accrued up to the settlement date.

Definitions: Clean vs. Dirty Price

Clean Price (Quoted Price): The price of the bond published on exchange boards, Bloomberg screens, and dealer quote sheets. It reflects the pure present value of future cash flows and excludes accrued interest.

Dirty Price (Gross Price / Settlement Price): The actual total dollar amount the buyer must deliver to the seller on the settlement date. It comprises the clean quoted price plus accrued interest:

Dirty Price = Clean Price + Accrued Interest \text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest} Dirty Price = Clean Price + Accrued Interest

The Canadian Accrued Interest Convention: Actual/365 Days

In Canadian fixed-income markets, accrued interest for both Government of Canada bonds and Canadian corporate bonds is calculated using the actual/365-day convention (counting the actual number of calendar days elapsed divided by 365 days):

Accrued Interest = Annual Coupon Dollar Amount × Actual Days Elapsed 365 \text{Accrued Interest} = \text{Annual Coupon Dollar Amount} \times \frac{\text{Actual Days Elapsed}}{365} Accrued Interest = Annual Coupon Dollar Amount × 365 Actual Days Elapsed ​

For a $1,000 par bond with coupon rate c c c :

Accrued Interest = ( $ 1 , 000 × c ) × Actual Days Elapsed 365 \text{Accrued Interest} = (\$1,000 \times c) \times \frac{\text{Actual Days Elapsed}}{365} Accrued Interest = ( $1 , 000 × c ) × 365 Actual Days Elapsed ​

Important Distinction: While the U.S. corporate bond market utilizes a 30/360-day convention, Canadian financial practice standardizes on actual/365 for all domestic government and corporate bonds.

Settlement Timing: Standard T+1 Settlement

Securities transactions in Canada follow a standard T+1 settlement cycle (effective May 27, 2024), meaning that a trade executed on Monday settles on Tuesday. When calculating accrued interest, the elapsed period runs from and including the previous coupon date up to, but not including, the settlement date .

Bonds Trading "Flat"

If an issuer defaults on its contractual interest payments, or if the security is an income bond where interest payments are contingent upon corporate earnings, the bond trades "flat" . When a bond trades flat, no accrued interest is added to the clean price. The buyer pays strictly the quoted clean price, and any potential past-due coupon rights transfer to the buyer.

Comprehensive Step-by-Step Worked Example: Canadian Accrued Interest & Settlement

Settlement Scenario: An institutional portfolio manager in Toronto purchases $200,000 par value of an 8.00% Government of Canada marketable bond at a quoted clean price of 103.50 . The bond pays semi-annual coupons on March 15 and September 15 .

• Trade Date: Wednesday, June 10 (non-leap year)
• Settlement Standard: T+1 ⟹ \implies ⟹ Settlement Date: Thursday, June 11
• Step 1: Calculate the Actual Days Elapsed from Previous Coupon to Settlement Date
• Previous coupon date: March 15
• Settlement date: June 11 (accrued interest accumulates through June 10)

We count the actual calendar days, including the previous coupon date and excluding the settlement date:

• March: 17 days (March 15 through March 31, counting March 15)
• April: 30 days (full month)
• May: 31 days (full month)
• June: 10 days (June 1 through June 10)

Total Days Elapsed: 17 + 30 + 31 + 10 = 88 17 + 30 + 31 + 10 = 88 17 + 30 + 31 + 10 = 88 days (check: day 162 minus day 74 of a non-leap year)

Step 2: Calculate Total Annual Coupon Payment

Annual Coupon = $ 200 , 000 × 8.00 % = $ 16 , 000.00 \text{Annual Coupon} = \$200,000 \times 8.00\% = \$16,000.00 Annual Coupon = $200 , 000 × 8.00% = $16 , 000.00

Step 3: Calculate Accrued Interest (Actual/365)

Accrued Interest = $ 16 , 000.00 × 88 365 = $ 16 , 000.00 × 0.241096 = $ 3 , 857.53 \text{Accrued Interest} = \$16,000.00 \times \frac{88}{365} = \$16,000.00 \times 0.241096 = \$3,857.53 Accrued Interest = $16 , 000.00 × 365 88 ​ = $16 , 000.00 × 0.241096 = $3 , 857.53

Step 4: Calculate Clean Dollar Principal Amount

Clean Principal = $ 200 , 000 × 103.50 100 = $ 207 , 000.00 \text{Clean Principal} = \$200,000 \times \frac{103.50}{100} = \$207,000.00 Clean Principal = $200 , 000 × 100 103.50 ​ = $207 , 000.00

Step 5: Calculate Total Settlement Amount (Dirty Price)

Gross Settlement Invoice = Clean Principal + Accrued Interest \text{Gross Settlement Invoice} = \text{Clean Principal} + \text{Accrued Interest} Gross Settlement Invoice = Clean Principal + Accrued Interest Gross Settlement Invoice = $ 207 , 000.00 + $ 3 , 857.53 = $ 210 , 857.53 \text{Gross Settlement Invoice} = \$207,000.00 + \$3,857.53 = \$210,857.53 Gross Settlement Invoice = $207 , 000.00 + $3 , 857.53 = $210 , 857.53

The purchasing dealer must wire $210,857.53 to the clearinghouse on Thursday, June 11.