Study guide
4.2 Yield Calculations & Return Measures
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
4.2 Yield Calculations & Return Measures
Key Takeaways Explain This Topic AI
Nominal yield (coupon rate) represents the contractual annual percentage paid on face value, whereas current yield measures annual coupon cash flow relative to current market price.
Yield to Maturity (YTM) is the internal rate of return equating the present value of all future cash flows to the bond's current market purchase price, factoring in both income and capital gains/losses.
The standard approximate YTM formula balances annual coupon income and annualized capital gain/loss over the average capital invested: Approximate YTM = Coupon + ( Par − Price ) / n ( Par + Price ) / 2 × 100 \text{Approximate YTM} = \frac{\text{Coupon} + (\text{Par} - \text{Price})/n}{(\text{Par} + \text{Price})/2} \times 100 Approximate YTM = ( Par + Price ) /2 Coupon + ( Par − Price ) / n × 100 .
YTM assumes all intermediate semi-annual coupons are reinvested at the same YTM rate; when market interest rates fall, realized total return will trail YTM due to reinvestment risk.
For discount bonds, the ascending yield hierarchy is Nominal Yield < Current Yield < Yield to Maturity; for premium bonds, the hierarchy reverses to Yield to Maturity < Current Yield < Nominal Yield.
Last updated: October 2026
The Spectrum of Fixed-Income Yield Measures
When assessing fixed-income securities in Canadian capital markets, relying solely on the stated contractual coupon rate is insufficient. Because bonds frequently trade at prices above or below their face value, financial professionals use several distinct yield measures to evaluate return, compare competing debt issues, and match client investment objectives.
1. Nominal Yield (Coupon Rate)
The nominal yield is simply the contractual annual coupon rate stated on the face of the bond certificate and established in the trust indenture:
Nominal Yield = Annual Dollar Coupon Par Value × 100 \text{Nominal Yield} = \frac{\text{Annual Dollar Coupon}}{\text{Par Value}} \times 100 Nominal Yield = Par Value Annual Dollar Coupon × 100
For example, a $1,000 par bond paying $65.00 in annual interest has a nominal yield of 6.50%. The nominal yield never changes throughout the life of a fixed-rate bond, regardless of where its price trades in the secondary market.
Current Yield: Cash Flow Relative to Market Price
The current yield measures the annual cash income generated by a bond expressed as a percentage of its current secondary market price:
Current Yield = Annual Contractual Dollar Coupon Current Market Price × 100 \text{Current Yield} = \frac{\text{Annual Contractual Dollar Coupon}}{\text{Current Market Price}} \times 100 Current Yield = Current Market Price Annual Contractual Dollar Coupon × 100
Worked Calculations: Discount vs. Premium Bonds
Case A: Discount Bond An investor purchases a $1,000 par bond with a 6.00% coupon ($60.00 annual interest) trading at a discount price of 92.00 ($920.00).
Current Yield = $ 60.00 $ 920.00 × 100 = 6.52 % \text{Current Yield} = \frac{\$60.00}{\$920.00} \times 100 = 6.52\% Current Yield = $920.00 $60.00 × 100 = 6.52%
Because the investor paid less than face value, the cash income yield ( 6.52 % 6.52\% 6.52% ) is higher than the nominal coupon rate ( 6.00 % 6.00\% 6.00% ).
Case B: Premium Bond An investor purchases a $1,000 par bond with an 8.00% coupon ($80.00 annual interest) trading at a premium price of 108.00 ($1,080.00).
Current Yield = $ 80.00 $ 1 , 080.00 × 100 = 7.41 % \text{Current Yield} = \frac{\$80.00}{\$1,080.00} \times 100 = 7.41\% Current Yield = $1 , 080.00 $80.00 × 100 = 7.41%
Because the investor paid more than face value, the cash income yield ( 7.41 % 7.41\% 7.41% ) is lower than the nominal coupon rate ( 8.00 % 8.00\% 8.00% ).
Limitations of Current Yield
While current yield is useful for income-oriented investors seeking immediate cash flow, it has major analytical flaws:
Ignores Capital Gains or Losses: It completely omits the built-in capital gain earned on a discount bond or the capital loss incurred on a premium bond when redeemed at par at maturity.
Ignores the Time Value of Money: It treats a coupon received in year 1 identically to a coupon received in year 20.
Ignores Reinvestment Return: It assumes cash flows sit idle without compounding.
Yield to Maturity (YTM): The True Internal Rate of Return
The Yield to Maturity (YTM) is the most comprehensive and universally accepted rate of return measure in global bond markets. It represents the internal rate of return (IRR) earned by an investor under three explicit conditions:
The bond is purchased at the current secondary market price.
The bond is held until its final maturity date.
All intermediate semi-annual coupon cash flows are fully reinvested at an interest rate exactly equal to the YTM itself.
Mathematically, YTM is the discount rate ( y y y ) that equates the present value of all scheduled future cash flows to the bond's clean market price:
Market Price = ∑ t = 1 2 n C / 2 ( 1 + y / 2 ) t + Par ( 1 + y / 2 ) 2 n \text{Market Price} = \sum_{t=1}^{2n} \frac{C/2}{(1 + y/2)^t} + \frac{\text{Par}}{(1 + y/2)^{2n}} Market Price = ∑ t = 1 2 n ( 1 + y /2 ) t C /2 + ( 1 + y /2 ) 2 n Par
Because solving this polynomial equation requires financial calculators, computer algorithms, or trial-and-error interpolation, analysts utilize the standard fixed-income approximation formula for rapid estimation.
The Standard Approximate YTM Formula
The standard formula balances annual coupon income and the annualized capital gain or loss over the average capital invested across the holding period:
Approximate YTM = Annual Dollar Coupon + Par Value − Market Price n Par Value + Market Price 2 × 100 \text{Approximate YTM} = \frac{\text{Annual Dollar Coupon} + \frac{\text{Par Value} - \text{Market Price}}{n}}{\frac{\text{Par Value} + \text{Market Price}}{2}} \times 100 Approximate YTM = 2 Par Value + Market Price Annual Dollar Coupon + n Par Value − Market Price × 100
Where:
Annual Dollar Coupon \text{Annual Dollar Coupon} Annual Dollar Coupon = Total contractual coupon cash received per year ( C C C )
- Par Value \text{Par Value} Par Value = Face value redeemed at maturity (standardized to $1,000 or 100)
- Market Price \text{Market Price} Market Price = Clean market purchase price
- n n n = Number of years to final maturity
Par Value − Market Price n \frac{\text{Par Value} - \text{Market Price}}{n} n Par Value − Market Price = Annualized capital gain (if positive) or annualized capital loss (if negative)
Par Value + Market Price 2 \frac{\text{Par Value} + \text{Market Price}}{2} 2 Par Value + Market Price = Average capital invested over the life of the bond
- Detailed Worked Numerical Examples: Approximate YTM
- Example 1: Calculating Approximate YTM for a Discount Bond
Problem: A client purchases an 8-year Canadian corporate bond with a 7.00% coupon at a market price of 94.00 ($940.00 per $1,000 par bond). Calculate the bond's approximate Yield to Maturity.
- Step 1: Identify Given Variables
- Annual Coupon ( C C C ) = 7.00% × $1,000 = $70.00
- Par Value = $1,000
- Market Price = $940.00
- Years to Maturity ( n n n ) = 8
- Step 2: Calculate the Annualized Capital Gain
Annual Capital Gain = $ 1 , 000 − $ 940.00 8 = $ 60.00 8 = $ 7.50 \text{Annual Capital Gain} = \frac{\$1,000 - \$940.00}{8} = \frac{\$60.00}{8} = \$7.50 Annual Capital Gain = 8 $1 , 000 − $940.00 = 8 $60.00 = $7.50
Step 3: Calculate the Total Annual Return (Numerator)
Numerator = $ 70.00 + $ 7.50 = $ 77.50 \text{Numerator} = \$70.00 + \$7.50 = \$77.50 Numerator = $70.00 + $7.50 = $77.50
Step 4: Calculate the Average Capital Invested (Denominator)
Denominator = $ 1 , 000 + $ 940.00 2 = $ 1 , 940.00 2 = $ 970.00 \text{Denominator} = \frac{\$1,000 + \$940.00}{2} = \frac{\$1,940.00}{2} = \$970.00 Denominator = 2 $1 , 000 + $940.00 = 2 $1 , 940.00 = $970.00
Step 5: Compute the Approximate YTM
Approximate YTM = $ 77.50 $ 970.00 × 100 = 7.9897 % ≈ 7.99 % \text{Approximate YTM} = \frac{\$77.50}{\$970.00} \times 100 = 7.9897\% \approx 7.99\% Approximate YTM = $970.00 $77.50 × 100 = 7.9897% ≈ 7.99%
The approximate YTM is 7.99% , which appropriately exceeds both the nominal coupon (7.00%) and current yield ($70 / $940 = 7.45%).
Example 2: Calculating Approximate YTM for a Premium Bond
Problem: An investor purchases a 6-year provincial bond with a 9.00% coupon at a market price of 106.00 ($1,060.00 per $1,000 par bond). Calculate the bond's approximate Yield to Maturity.
- Step 1: Identify Given Variables
- Annual Coupon ( C C C ) = 9.00% × $1,000 = $90.00
- Par Value = $1,000
- Market Price = $1,060.00
- Years to Maturity ( n n n ) = 6
- Step 2: Calculate the Annualized Capital Loss
Annual Capital Loss = $ 1 , 000 − $ 1 , 060.00 6 = − $ 60.00 6 = − $ 10.00 \text{Annual Capital Loss} = \frac{\$1,000 - \$1,060.00}{6} = \frac{-\$60.00}{6} = -\$10.00 Annual Capital Loss = 6 $1 , 000 − $1 , 060.00 = 6 − $60.00 = − $10.00
Step 3: Calculate the Total Annual Return (Numerator)
Numerator = $ 90.00 + ( − $ 10.00 ) = $ 80.00 \text{Numerator} = \$90.00 + (-\$10.00) = \$80.00 Numerator = $90.00 + ( − $10.00 ) = $80.00
Step 4: Calculate the Average Capital Invested (Denominator)
Denominator = $ 1 , 000 + $ 1 , 060.00 2 = $ 2 , 060.00 2 = $ 1 , 030.00 \text{Denominator} = \frac{\$1,000 + \$1,060.00}{2} = \frac{\$2,060.00}{2} = \$1,030.00 Denominator = 2 $1 , 000 + $1 , 060.00 = 2 $2 , 060.00 = $1 , 030.00
Step 5: Compute the Approximate YTM
Approximate YTM = $ 80.00 $ 1 , 030.00 × 100 = 7.7669 % ≈ 7.77 % \text{Approximate YTM} = \frac{\$80.00}{\$1,030.00} \times 100 = 7.7669\% \approx 7.77\% Approximate YTM = $1 , 030.00 $80.00 × 100 = 7.7669% ≈ 7.77%
The approximate YTM is 7.77% , which is lower than both the nominal coupon (9.00%) and current yield ($90 / $1,060 = 8.49%) due to the annual amortization of the premium.
Yield to Call (YTC) and Yield to Worst (YTW)
Many Canadian corporate and municipal debt issues feature call provisions allowing the issuer to redeem the bonds prior to maturity. When market interest rates fall, issuers exercise these calls to refinance expensive high-coupon debt with newly issued lower-cost debt.
Yield to Call (YTC)
When a bond is likely to be called, calculating YTM to final maturity is misleading. Instead, analysts calculate Yield to Call (YTC) by substituting the call price for par value and the number of years until the call date for total maturity:
Approximate YTC = Annual Coupon + Call Price − Market Price n call Call Price + Market Price 2 × 100 \text{Approximate YTC} = \frac{\text{Annual Coupon} + \frac{\text{Call Price} - \text{Market Price}}{n_{\text{call}}}}{\frac{\text{Call Price} + \text{Market Price}}{2}} \times 100 Approximate YTC = 2 Call Price + Market Price Annual Coupon + n call Call Price − Market Price × 100
Yield to Worst (YTW)
Institutional bond desks quote callable debt on a Yield to Worst (YTW) basis. Yield to Worst is defined as the lowest potential yield generated among all possible scenarios:
- Yield to maturity
- Yield to first call date
- Yield to subsequent intermediate call dates
- Yield to par call date
If a bond trades at a substantial premium, YTC is almost always lower than YTM, making YTC the Yield to Worst . Conversely, if a callable bond trades at a discount, the issuer has no incentive to call the bond, making YTM the Yield to Worst .
Reinvestment Risk and Semi-Annual Compounding Mechanics
A critical, frequently misunderstood concept on Canadian licensing exams is the reinvestment assumption inherent in Yield to Maturity.
The Reinvestment Risk Trap
YTM mathematically presumes that every single semi-annual coupon payment received over 5, 10, or 30 years is reinvested immediately at an interest rate equal to the original YTM. In the real world, interest rates change continuously:
If Interest Rates Decline After Purchase: Future coupon payments must be reinvested at lower prevailing yields. The portfolio suffers from reinvestment risk , and the investor's actual realized compound return will be lower than the initial YTM .
If Interest Rates Rise After Purchase: Future coupon payments are reinvested at higher prevailing yields. The investor earns a realized compound return higher than the initial YTM (assuming the bond is held to maturity so capital losses are not realized). Impact of Interest Rate Shifts on Realized Return vs. YTM
- ├── Market Rates Fall ──> Reinvestment at lower rates ──> Realized Return < YTM
- └── Market Rates Rise ──> Reinvestment at higher rates ──> Realized Return > YTM
- Zero Reinvestment Risk in Strip Bonds
Because strip bonds (zero-coupon bonds) pay no periodic cash coupons prior to maturity, they carry zero reinvestment risk . An investor purchasing a 10-year Government of Canada strip bond at an agreed YTM locks in that exact compound return to maturity with absolute certainty.
Holding Period Return (HPR)
Investors often sell bonds prior to final maturity. The Holding Period Return (HPR) measures the total percentage return earned over the specific timeframe the bond was actually held:
HPR = Total Coupon Income Received + ( Sale Price − Purchase Price ) Purchase Price × 100 \text{HPR} = \frac{\text{Total Coupon Income Received} + (\text{Sale Price} - \text{Purchase Price})}{\text{Purchase Price}} \times 100 HPR = Purchase Price Total Coupon Income Received + ( Sale Price − Purchase Price ) × 100
Worked Example: Holding Period Return
An investor purchases a $1,000 par bond for $960.00 . Over a 2-year holding period, the investor collects four semi-annual coupon payments totaling $120.00 ($30 every six months). At the end of year 2, market interest rates have declined, and the investor sells the bond for $1,020.00 .
HPR = $ 120.00 + ( $ 1 , 020.00 − $ 960.00 ) $ 960.00 × 100 \text{HPR} = \frac{\$120.00 + (\$1,020.00 - \$960.00)}{\$960.00} \times 100 HPR = $960.00 $120.00 + ( $1 , 020.00 − $960.00 ) × 100 HPR = $ 120.00 + $ 60.00 $ 960.00 × 100 = $ 180.00 $ 960.00 × 100 = 18.75 % \text{HPR} = \frac{\$120.00 + \$60.00}{\$960.00} \times 100 = \frac{\$180.00}{\$960.00} \times 100 = 18.75\% HPR = $960.00 $120.00 + $60.00 × 100 = $960.00 $180.00 × 100 = 18.75%
The total holding period return over the two-year period is 18.75% .
The Complete Yield Hierarchy: Discount, Par, and Premium
The mathematical relationship among nominal yield, current yield, yield to maturity, and yield to call forms a strict, predictable hierarchy depending on whether the bond trades at a discount, at par, or at a premium. Yield Hierarchies
- ├── Discount Bond: Nominal Yield < Current Yield < Yield to Maturity < Yield to Call
- ├── Par Bond: Nominal Yield == Current Yield == Yield to Maturity
- └── Premium Bond: Yield to Call < Yield to Maturity < Current Yield < Nominal Yield
- Comprehensive Yield Comparison Table
Feature Discount Bond ( P < 100 P < 100 P < 100 ) Par Bond ( P = 100 P = 100 P = 100 ) Premium Bond ( P > 100 P > 100 P > 100 )
- Nominal Yield (Coupon) Lowest yield metric Equal to all metrics Highest yield metric
- Current Yield Intermediate (Above coupon) Equal to all metrics Intermediate (Below coupon)
- Yield to Maturity (YTM) Highest standard metric Equal to all metrics Lowest standard metric
Yield to Call (YTC) Highest overall (if call ≥ \ge ≥ par) Equal to YTM Lowest overall (accelerates premium loss)
Ascending Hierarchy Nominal < Current < YTM \text{Nominal} < \text{Current} < \text{YTM} Nominal < Current < YTM Nominal = Current = YTM \text{Nominal} = \text{Current} = \text{YTM} Nominal = Current = YTM YTM < Current < Nominal \text{YTM} < \text{Current} < \text{Nominal} YTM < Current < Nominal