Chapter 9 Interest Rates

Learning Objectives

  • Understand money market prices and rates

  • Learn about rates and yields on fixed-income securities

  • Explore Treasury STRIPS and the term structure of interest rates

  • Differentiate between nominal and real interest rates

Introduction to Interest Rates

  • Different interest rates are reported in the financial press and influence various economic activities.

  • Important to understand how interest rates are calculated, quoted, and what factors determine them.

U.S. Interest Rate History (1800-2021)

  • Historical trends of U.S. interest rates for bills and bonds provide insight into economic conditions.

  • Interest rates have varied significantly over two centuries.

Money Market Rates

Key Interest Rates

  • Prime Rate: Basic short-term interest rate for loans to creditworthy corporate customers.

  • Federal Funds Rate: The rate banks charge each other for overnight loans.

  • Discount Rate: Interest rate for loans from the Federal Reserve to commercial banks.

  • Banker’s Acceptance: A financial instrument used in international trade, guaranteed by a bank.

  • Call Money Rate: Interest rate for loans to brokerage firms.

Recent Developments

  • LIBOR: Previously the benchmark rate for short-term loans, it is being replaced by SOFR (Secured Overnight Financing Rate).

    • SOFR: Reflects financing costs based on repurchased treasury securities.

    • Eurodollars and Euro LIBOR refer to deposits outside the U.S. and in euros respectively.

Money Market Prices and the Rates

  • Pure Discount Security: Only pays the face value at maturity with no interim payments.

  • Different methods for quoting interest rates include:

    • Bank Discount Basis

    • Bond Equivalent Yields (BEY)

    • Annual Percentage Rates (APR)

    • Effective Annual Rates (EAR)

Bank Discount Basis

  • Quoting method using a formula based on a 360-day year.

Bond Equivalent Yields (BEY)

  • Relevant formula for converting bank discount yields. Only applies for maturities of six months or less.

  • Example calculation of BEY from given discount rates.

Converting APRs to EARs

  • Converts nominal APR to EAR based on compounding frequency.

Rates and Yields on Fixed-Income Securities

  • Includes long-term debt from various issuers (e.g., U.S. government, corporations).

  • Distinction between fixed-income securities (more than one year) and money market securities (less than one year).

The Treasury Yield Curve

  • Represents the relationship of Treasury yields over various maturities.

  • Crucial for understanding bond market behaviors.

The Term Structure of Interest Rates

  • Describes the relationship between interest rates and time to maturity, illustrating investor expectations.

    • Also known as the zero-coupon yield curve.

  • STRIPS: These are created by separating coupon and principal payments from Treasury securities.

Nominal vs. Real Interest Rates

  • Nominal Interest Rates: Quoted rates not adjusted for inflation.

  • Real Interest Rates: Nominal rates adjusted to account for inflation effects.

    • Formula: Real Interest Rate ≈ Nominal Interest Rate - Inflation Rate.

  • Fisher Hypothesis: Suggests nominal rates reflect general inflation levels over time, staying above inflation rates.

Inflation-Indexed Treasury Securities

  • Designed to ensure returns exceed inflation.

  • Adjusts principal according to inflation rates, resulting in variable coupon payments.

Theories of Term Structure

Traditional Theories

  • Expectations Theory: The yield curve reflects market expectations on future rates.

  • Market Segmentation Theory: Interest rates vary by market segment based on maturity.

  • Maturity Preference Theory: A maturity premium is necessary for longer-term loans due to increased risk.

Problems with Traditional Theories

  • The assumptions of traditional theories do not always hold true in the market.

Modern Term Structure Theory

  • Incorporates interest rate risk, inflation premium, and possibly liquidity and default risk into understanding bond pricing.

  • The formula: NI = RI + IP + RP + LP + DP

    • Where NI = nominal interest rate, RI = real interest rate, IP = inflation premium, RP = risk premium, LP = liquidity premium, DP = default premium.