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

    gantt
	    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.

Glossary

• 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.