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.