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7.3.2 Yield Curve

Understand the significance of the yield curve in bond markets, including the key theories explaining its shape: expectations theory, liquidity preference theory, and market segmentation theory.

7.3.2 Yield Curve

The Yield Curve

The yield curve represents the relationship between short-term and long-term bond yields. This relationship is known as the term structure of interest rates. It can be graphed to show a continually changing line called the yield curve. Below is a depiction of a hypothetical yield curve for Government of Canada bonds, presented as an upward-sloping line, also known as a normal yield curve.

Example: Government of Canada Yield Curve

	    dateFormat  YYYY-MM-DD
	    title Government of Canada Yield Curve
	    section Bond Yields
	    1 month, 1%      :active, 2023-01-01, 30d
	    3 months, 1.5%   :active, 2023-02-01, 90d
	    6 months, 2%     :active, 2023-04-01, 180d
	    12 months, 2.5%  :active, 2023-07-01, 365d
	    2 years, 3%      :active, 2024-01-01, 730d
	    3 years, 3.5%    :active, 2025-01-01, 1095d
	    5 years, 3.75%   :active, 2027-01-01, 1825d
	    7 years, 4%      :active, 2029-01-01, 2555d
	    10 years, 4.5%   :active, 2032-01-01, 3650d
	    Long, 5%         :active, 2040-01-01, 7300d

Theories Explaining the Shape of the Yield Curve

There are three key theories to explain the shape of the yield curve:

Expectations Theory

The expectations theory posits that long-term interest rates reflect future short-term rates. This theory suggests that investors forecasting long-term investments expect to earn equal returns from investing in either long-term or short-term sequential bonds.

Example Calculation

Assume a two-year investment scenario:

  • Two-year bond rate: 5%
  • One-year bond rate: 4%

We’ll find out the return needed for a one-year bond in the second year using the equation:

$$2\text{-Year Return} = \left(1 + \frac{\text{1-Year Rate}}{100}\right) \left(1 + \frac{\text{Expected 1-Year Rate Next Year}}{100}\right)$$

Using this calculation:

$$1.1025 = (1.04) + (1 + r)$$

Solving for r:

$$\frac{1.1025}{1.04} = 1.0601\Rightarrow r = 0.0601 ≈ 6%$$

This means that for current one-year rates of 4%, one-year bonds in the subsequent year should rate 6% for an equivalent two-year bond return.

Liquidity Preference Theory

This theory suggests that investors prefer short-term bonds due to higher liquidity and relatively lower volatility. Longer-term investments demand higher returns for assumed risks, manifesting often in an upward yield curve, like the one depicted in Figure 7.8.

Market Segmentation Theory

According to market segmentation theory, supply and demand for varying bond terms shape the yield curve. Different institutional investors target specific maturity sectors, affecting rates and creating various yield curve shapes, such as normal, inverted, and humped curves.

Key Takeaways

  • Yield Curve: A graphical representation of the term structure of interest rates depicting various maturities relative to yields on bonds of similar credit quality.
  • Term Structure of Interest Rates: Describes the various interest rates on bonds of different maturities.
  • Expectations Theory: Long-term rates are average future short-term rates.
  • Liquidity Preference Theory: Investors prefer short-term bonds and require premiums for longer maturities.
  • Market Segmentation Theory: Specific market participants shape the yield curve according to the supply and demand of bond terms.

Frequently Asked Questions

Q: What does a normal yield curve indicate?

A: A normal yield curve, which slopes upward from left to right, suggests that longer-term bonds have higher yields than shorter-term bonds, indicating future expectations of rising interest rates.

Q: How can investors use the expectations theory?

A: According to expectations theory, investors can infer future interest rates from the current shape of the yield curve, helping make informed decisions about investment durations.

Q: What impact does liquidity have on the yield curve?

A: The demand for liquidity by investors leads them to favor short-term over long-term investments, requiring higher returns for increased investment horizons and contributing to an upward sloping yield curve.


  • Yield Curve: A graphical representation useful for showing interest rates varying over different bond maturities.
  • Term Structure of Interest Rates: Describes how bond yields of differing maturities relate to one another.
  • Expectations Theory: Economic hypothesis predicting future bond yields based on current long-term interest rates.
  • Liquidity Preference Theory: Theorizes investors require additional return (premium) for locking money in a less liquid, long-term investment.
  • Market Segmentation Theory: Contends the yield curve is composed of varying demands from different types of institutional investors across all maturity sectors.

📚✨ 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! 🍀💪

## Which of the following best describes the yield curve? - [ ] It indicates the performance of the stock market. - [ ] It shows the trends in inflation rates over time. - [x] It shows the relationship between bond yields and their terms to maturity. - [ ] It reflects the profitability of banks. > **Explanation:** The yield curve plots the interest rates of bonds having equal credit quality but differing maturity dates, representing the term structure of interest rates. ## What is the expectations theory? - [ ] It states that short-term interest rates are always higher than long-term rates. - [x] It suggests that current long-term interest rates predict future short-term interest rates. - [ ] It means long-term investors prefer less liquid bonds. - [ ] It indicates bonds of different terms have no relationship. > **Explanation:** The expectations theory posits that long-term rates are forecasts of future short-term rates, implying that the shape of the yield curve reflects market expectations. ## According to the expectations theory, what does an upward-sloping yield curve suggest? - [x] Future interest rates are expected to rise. - [ ] Future interest rates are expected to fall. - [ ] Interest rates will remain constant. - [ ] The economy is in a recession. > **Explanation:** An upward-sloping yield curve indicates a market consensus that future interest rates will increase. ## What choice does not align with the liquidity preference theory? - [ ] Investors need additional yield for holding less liquid, long-term bonds. - [ ] Short-term bonds are preferred for being more liquid and less volatile. - [ ] Liquidity preference can explain upward-sloping yield curves. - [x] A downward-sloping yield curve is easily explained by this theory. > **Explanation:** The liquidity preference theory explains an upward-sloping curve by the additional yield for long-term bond risks but does not explain downward-sloping yield curves. ## The market segmentation theory is based on: - [ ] Economic growth predictions. - [ ] Investor risk preferences. - [x] Supply and demand within specific maturity segments influenced by different institutional players. - [ ] Government interventions in the bond market. > **Explanation:** This theory posits that the yield curve represents supply and demand within different maturity segments influenced by predominant institutional investors in each sector. ## Using the calculation in the expectations theory example, what is the implied one-year rate if the current one-year bond yields 4% and the two-year bond yields 5%? - [ ] 3% - [ ] 4% - [x] 6% - [ ] 7% > **Explanation:** The calculation (1.05² = (1.04) × (1 + r)) indicates that r = 6%, meaning the second year's one-year bond rate must be 6%. ## What does a humped yield curve indicate according to expectations theory? - [ ] Rates will continuously fall. - [x] Rates will rise initially then fall. - [ ] Rates will continuously rise. - [ ] Rates will stay the same. > **Explanation:** A humped yield curve shows that rates are expected to rise initially before eventually falling, indicating fluctuating market expectations. ## Which theory postulates that investors require extra yield for holding less liquid and more volatile longer-term bonds? - [x] Liquidity preference theory - [ ] Expectations theory - [ ] Market segmentation theory - [ ] Random walk theory > **Explanation:** The liquidity preference theory argues that investors need more yield to compensate for the higher risk of lower liquidity and higher price volatility in long-term bonds. ## Which theory can explain all types of yield curves, including normal, inverted, and humped shapes? - [ ] Liquidity preference theory - [ ] Expectations theory - [x] Market segmentation theory - [ ] Arbitrage pricing theory > **Explanation:** The market segmentation theory can account for normal, inverted, and humped yield curves by considering the supply and demand dynamics within each bond maturity segment. ## What is the implication of the expectations theory for a two-year investment decision? - [ ] It is better to always choose the shorter-term bonds. - [x] The return from a two-year bond should equal the combined returns of two consecutive one-year bonds. - [ ] Longer-term bonds always provide better compensation. - [ ] Short-term bonds are riskier than long-term bonds. > **Explanation:** The expectations theory suggests that in an efficient market, the return on a two-year bond should match the returns from rolling over consecutive shorter-term bonds.

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Saturday, July 13, 2024