Introduction

Understanding the term structure of interest rates is crucial for analyzing the relationship between different maturities of bonds and their corresponding interest rates. Various theories have been proposed to explain the shape of the yield curve, which plots interest rates against the maturity of bonds. In this chapter, we will delve into the major theories that shed light on this complex relationship.

Expectations Theory

The Expectations Theory posits that the current yield curve reflects market participants’ expectations of future short-term interest rates. This theory assumes that investors are indifferent between holding short-term bonds and rolling them over, or investing in longer-term bonds. Consequently, long-term interest rates are simply the average of expected future short-term rates.

Mathematically, the Expectations Theory can be expressed as follows:

$$ \left(1+r_n\right)^n=\left(1+r_1\right)\left(1+f_{1,1}\right)\left(1+f_{2,1}\right) \ldots\left(1+f_{n-1,1}\right) $$ Where:

• $r_n$ is the yield of a bond with maturity $n$.
• $r_1$ is the current short-term interest rate.
• $f_{i, 1}$ is the one-year forward rate at time $i$. Example: If the current short-term rate is $3 \%$ and the one-year forward rates for the next three years are $4 \%, 4.5 \%$, and $5 \%$, respectively, the Expectations Theory would predict the yield for a three-year bond as $(1+0.03)^3=(1+0.04)(1+0.045)(1+0.05)$, resulting in a yield of approximately $5.09 \%$.

Liquidity Preference Theory

The Liquidity Preference Theory, proposed by John Maynard Keynes, asserts that investors require a premium for holding longer-term bonds due to their lower liquidity compared to short-term bonds. As a result, the yield curve slopes upward to compensate investors for the increased risk of holding longer-term securities.

Market Segmentation Theory

The Market Segmentation Theory argues that investors have specific preferences for different maturity bonds and do not necessarily switch between them. This leads to segmented markets, with interest rates determined independently for each maturity based on supply and demand factors.

Preferred Habitat Theory

Building upon the Market Segmentation Theory, the Preferred Habitat Theory acknowledges that investors might be willing to move out of their preferred maturity “habitats” if compensated with higher returns. This theory recognizes that investors have different risk preferences and may be enticed to invest in longer-term bonds if the yield compensates for the added risk.