Interest rates vary based on time to maturity, forming the term structure. This concept is crucial for understanding how different securities are priced and how economic expectations impact the financial markets.

Three main theories explain the term structure: expectations, liquidity preference, and market segmentation. The yield curve's shape offers insights into economic outlook, while spot and forward rates help in pricing various financial instruments.

Term Structure of Interest Rates

Theories of interest rate structure

• Expectations theory proposes interest rates reflect market participants' expectations about future interest rates, with long-term rates being an average of current and expected future short-term rates (Treasury bills, commercial paper)
• Liquidity preference theory suggests investors prefer short-term securities (certificates of deposit) and demand a premium for holding long-term securities (corporate bonds), resulting in higher long-term rates due to the liquidity premium
• Market segmentation theory argues different investors have distinct investment horizons and preferences, with supply and demand in each maturity segment (short-term, intermediate-term, long-term) determining the interest rates for that segment

Yield curve shape and implications

• Normal yield curve has long-term rates higher than short-term rates, indicating expectations of economic growth and rising interest rates
  • Upward sloping curve suggests a favorable economic outlook (expansion)
• Inverted yield curve occurs when short-term rates exceed long-term rates, suggesting expectations of economic slowdown and falling interest rates
  • Downward sloping curve may signal an impending recession
• Flat yield curve shows similar short-term and long-term rates, implying uncertainty about future economic conditions and interest rates
  • Horizontal curve indicates a transitional phase in the economy

Spot rates and forward rates

• Spot rates represent interest rates for borrowing or lending money for a specific period, starting immediately, and are used to price zero-coupon bonds (Treasury STRIPS)
• Forward rates are interest rates for borrowing or lending money for a specific period, starting at a future date, and are implied by the term structure of spot rates
• Relationship between spot rates and forward rates:
  1. Long-term spot rates are a geometric average of current and expected future short-term forward rates
  2. $\left(1 + R_n\right)^n = \left(1 + R_1\right) \times \left(1 + f_2\right) \times \ldots \times \left(1 + f_n\right)$
     • $R_n$: n-period spot rate
     • $R_1$: one-period spot rate
     • $f_i$: forward rate for period $i$

Limitations of expectations theories

• Pure expectations theory assumes investors are risk-neutral and have no preference for maturity, ignoring the potential impact of liquidity preferences on interest rates (term premium)
  • May not fully explain the observed shape of the yield curve
• Liquidity premium theory assumes investors are risk-averse and prefer short-term securities, accounting for the liquidity premium in long-term rates
  • May overstate the importance of liquidity preferences in determining interest rates
• Both theories have limitations:
  • They do not consider the impact of market segmentation on interest rates (institutional investors, pension funds)
  • They assume investors have homogeneous expectations about future interest rates, which may not always be the case