15.2.1 Rate Of Return

Learn the in-depth analysis of the rate of return and its importance in the context of Canadian Securities Course. Understand various related concepts such as capital loss, real rate of return, cash flow, and risk-free rate of return.


In this section, we will delve into various fundamental concepts critical to understanding portfolio approaches and investment strategies. These concepts are pivotal for those pursuing the Canadian Securities Course (CSC). Below is a glossary of terms that will be extensively discussed:

  • Rate of Return: The percentage gain or loss on an investment over a specified period.
  • Capital Loss: The loss incurred when the value of a security decreases below its purchase price.
  • Real Rate of Return: The return on an investment adjusted for inflation.
  • Cash Flow: The total amount of money being transferred into and out of a business, especially affecting liquidity.
  • Risk-Free Rate of Return: The return on an investment with zero risk, typically represented by Treasury bills.
  • Correlation: A statistical measure that describes the degree to which two securities move in relation to each other.
  • Sector Rotation: A strategy that involves shifting investments among different sectors of the economy to take advantage of sector performance.
  • Default Risk: The risk that a borrower will not be able to make required payments on their debt.
  • Specific Risk: The risk associated with a particular company or security.
  • Diversification: A risk management technique that mixes a wide variety of investments within a portfolio.
  • Standard Deviation: A measure of the amount of variability or dispersion of a set of values.
  • Ex-Ante: Based on forecasts rather than actual results, expected returns.
  • Systematic Risk: Risk inherent to the entire market or an entire market segment.
  • Ex-Post: Based on actual results, historical returns.
  • Top-Down Analysis: An investment analysis strategy that first looks at broad economic factors before diving into specific companies.
  • Foreign Exchange Rate Risk: Risk of value fluctuation due to changes in exchange rates.
  • Volatility: A statistical measure of the dispersion of returns for a given security or market index.
  • Holding Period Return: The total return received from holding an asset or portfolio of assets over a period.
  • Yield: The earnings generated and realized on an investment over a particular period, usually expressed as a percentage.
  • Indexing: An investment strategy that attempts to replicate and track a market index.

Table of Contents


No perfect security exists that meets all the needs of every investor. If it did exist, there would be no need for investment and portfolio management, and no need to measure the return and risk of investments.

t might signal a poor investment choice.

The more common practice is to express returns as a percentage, called the rate of return or yield. To convert a dollar amount to a percentage, divide the total dollar returns by the amount invested. $$ \text{Return %} = \frac{\text{Cash Flow} + (\text{Ending Value} - \text{Beginning Value})}{\text{Beginning Value}} \times 100 $$

Rate of Return Calculation

Consider the following three scenarios to calculate rate of return:

  1. Scenario 1: You purchase a stock for $10 and sell it one year later for $12.

$$ Rate of Return = \frac{0 + (12 - 10)}{10} \times 100 = 20% $$

  1. Scenario 2: You purchase a stock for $20 and sell it one year later for $22, and during this period, you receive $1 in dividends.

$$ Rate of Return = \frac{1 + (22 - 20)}{20} \times 100 = 15% $$

  1. Scenario 3: You purchase a stock for $10 and receive $2 in dividends, but one year later you sell it for only $9.

$$ Rate of Return = \frac{2 + (9 - 10)}{10} \times 100 = 10% $$

These examples show how cash flow and capital gains or losses are used in calculating a rate of return. All trading periods in the examples are set for one year, hence the percentage of return is also called the annual rate of return. If the transaction period were longer or shorter than a year, the return would be called the holding period return.

Nominal and Real Rates of Return

So far, we have looked only at a simple rate of return, otherwise known as the nominal rate of return. Besides that, the real rate of return takes into consideration the effects of inflation.

$$ Real Return = Nominal Rate - Annual Inflation Rate $$

Example: If a client earns a 10% nominal return on an investment with a 2% inflation rate over the same period: $$ Real Return = 10% - 2% = 8% $$

The Risk-Free Rate of Return

T-bills often represent the risk-free rate of return, given that there is essentially zero risk with this type of investment. Other securities must pay at least the T-bill rate plus a risk premium to compensate investors for the added risk.

Historical Returns

You can gain important insights into the market and determine appropriate investments and investment strategies by studying historical data.

The more common practice is to express returns as a percentage, called the rate of return or yield. To convert a dollar amount to a percentage, divide the total dollar returns by the amount invested. $$ \text{Rate of Return} = \frac{\text{Ending Value} - \text{Beginning Value} + \text{Income}}{\text{Beginning Value}}\times 100 $$

Figure 15.3: Risk and Return Relationship

    graph TD;
	    LowRisk[Low Risk / Low Return]
	    ModerateRisk[Moderate Risk / Moderate Return]
	    HighRisk[High Risk / High Return]
	    Tbills(T-Bills) --> LowRisk
	    Bonds(Bonds) --> ModerateRisk
	    Reits(REITs) --> ModerateRisk
	    Stocks(Stocks) --> HighRisk
	    Crypto(Cryptocurrencies) --> HighRisk
	    style LowRisk fill:#f9f,stroke:#333,stroke-width:2px
	    style ModerateRisk fill:#ccf,stroke:#333,stroke-width:2px
	    style HighRisk fill:#cff,stroke:#333,stroke-width:2px

Key Takeaways

  • Rate of Return: Always express investment returns as a percentage to better grasp the significance of the return relative to the amount invested.

  • Real Rate of Return: Adjust nominal returns for inflation to understand the true earning power of an investment.

  • Risk-Free Rate of Return: Represents the base return with zero risk upon which other investments with higher risks are compared.

  • Historical Returns: While useful for insights, always remember that historical returns do not guarantee future performance.

  • Diversification: Essential to risk reduction by spreading investments across various securities or sectors. Did You Know?

  • The return on an investment is often referred to as the expected return to emphasize the non-guarantee of returns.

  • Capital gains and losses contribute significantly to the overall return on an investment.

Rates of return can be defined as Ex-Ante or Ex-Post:

  • Ex-Ante: These are expected returns based on forecasts.
  • Ex-Post: These are returns evaluated after the investment has matured, showing historical performance.

Understanding the intricate relationship between risk and return is crucial for anyone involved in the Canadian Securities Course. This knowledge allows for better portfolio diversification and, ultimately, better client outcomes.

📚✨ Quiz Time! ✨📚

🧐 Assess and Solidify Your Understanding

Welcome to the Knowledge Checkpoint! You’ll find 10 carefully curated quizzes designed to reinforce the key concepts covered. These questions will help you gauge your grasp of the material, identify areas that need further review, and ensure you’re on the right track towards mastering the content for the Canadian Securities certification exams. Take your time, think critically, and use these quizzes as a tool to enhance your learning journey. 📘✨

Good luck! 🍀💪

## What is the formula to calculate the expected return of a single security? - [ ] (Expected Cash Flow - Expected Capital Gain) / Beginning Value - [x] (Expected Cash Flow + Expected Capital Gain) / Beginning Value - [ ] (Expected Cash Flow - Expected Capital Gain + Expected Ending Value) / Beginning Value - [ ] (Expected Cash Flow + Expected Ending Value) / Beginning Value > **Explanation:** The expected return of a single security is calculated using the sum of the expected cash flow and expected capital gain or loss divided by the beginning value of the investment. ## What is the nominal rate of return? - [ ] Return on investment adjusted for inflation - [x] Return on investment without adjustment for inflation - [ ] Return after adjusting for taxes - [ ] Return after adjusting for fees > **Explanation:** The nominal rate of return is the return on investment without adjusting for inflation. It is the simple percentage gain calculated from the initial investment. ## How does one calculate the real rate of return? - [x] Nominal Rate - Annual Inflation Rate - [ ] Nominal Rate - Taxes and Fees - [ ] Nominal Rate + Annual Inflation Rate - [ ] Nominal Rate + Expected Return Rate > **Explanation:** The real rate of return is calculated by subtracting the annual inflation rate from the nominal rate of return, indicating the purchasing power gain. ## What does the risk-free rate of return typically represent? - [x] The yield on Treasury bills (T-bills) - [ ] The return on corporate bonds - [ ] The return on equities - [ ] The return on government bonds > **Explanation:** The risk-free rate of return usually represents the yield on Treasury bills (T-bills) because they are considered to have negligible risk. ## Which type of risk can be reduced through diversification? - [ ] Systematic risk - [x] Specific risk - [ ] Market risk - [ ] Inflation risk > **Explanation:** Specific risk, or unsystematic risk, can be reduced through diversification by investing in a variety of securities, unlike systematic risk which affects the entire market. ## What is capital gain? - [ ] The return received in the form of dividends or interest - [x] Selling a security for more than its purchase price - [ ] Selling a security for less than its purchase price - [ ] The regular payment received from fixed-income securities > **Explanation:** Capital gain is the profit earned by selling a security for more than its purchase price. ## What does "standard deviation" measure in portfolio management? - [ ] Expected return - [ ] Inflation rate - [ ] Nominal rate of return - [x] The volatility or risk of the investment’s return > **Explanation:** Standard deviation measures the volatility or risk of an investment’s return. It indicates how much the return can deviate from the expected return. ## What is the significance of the holding period return? - [x] It represents the return over the entire holding period, regardless of the length. - [ ] It represents the annualized return of the investment. - [ ] It represents the minimum return obtained on investment. - [ ] It represents the difference between the nominal and real rate of return. > **Explanation:** Holding period return represents the total return earned over the entire period an investment is held, irrespective of the length of the holding period. ## What does a higher standard deviation indicate about an investment? - [ ] Lower risk and lower expected return - [ ] Lower risk and higher expected return - [x] Higher risk and higher expected return - [ ] Higher risk and lower expected return > **Explanation:** A higher standard deviation indicates higher risk, which can potentially lead to higher returns, reflecting more uncertainty and greater fluctuations in the investment’s returns. ## Why might an investor consider the Treasury bill rate while choosing an expected rate of return? - [x] As a benchmark for the risk-free rate - [ ] To compare with inflation rates - [ ] To calculate capital gain - [ ] To determine standard deviation > **Explanation:** Investors use the Treasury bill rate as a benchmark for the risk-free rate while choosing an expected rate of return because T-bills are considered to carry negligible risk.

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Saturday, July 13, 2024