Interest Rates Summary

Interest Rates

  • Critical Concepts: Types of Interest Rates, Continuous Compounding, Zero Rates, Bond Pricing, Forward Rates, Duration, Convexity.

Types of Interest Rates

  • Treasury Rate

  • LIBOR

  • Fed Funds Rate

  • Repo Rate

  • SOFR

Treasury Rates

  • Rates on government-issued instruments. Types include:

    • Treasury Bills: 1 month to 1 year

    • Treasury Notes: 2 to 10 years

    • Treasury Bonds: Over 10 years

Overnight Rates

  • Unsecured bank borrowing/lending; known as Fed Funds Rate in the U.S.

  • Central banks may adjust this rate through interventions.

Repo Rate

  • Interest rate from repurchase agreements; reflects short-term loans.

LIBOR

  • London InterBank Offered Rate, used for various currencies and maturities.

    • Phase-out and replacement with transaction-based rates (e.g., SOFR) due to manipulation concerns.

New Reference Rates

  • SOFR (U.S.), SONIA (GBP), ESTER (EU), SARON (Switzerland), TONAR (Japan).

Risk-Free Rate

  • Treasury rate viewed as artificially low; SOFR used as the reference risk-free rate.

Continuous Compounding

  • Formula: A=100eRTA = 100e^{RT} for growth, and A=100e−RTA = 100e^{-RT} for discounting.

Bond Valuation

  • Zero rates applied to calculate the present value of cash flows.

  • Bond yield is the discount rate equating market price with present value.

Duration and Convexity

  • Duration measures bond price sensitivity; key relationship: D=−ΔBBΔyD = -\frac{\Delta B}{B \Delta y} .

  • Modified duration accounts for different compounding frequencies.

Forward Rates

  • Future zero rates implied by current term structure.

Forward Rate Agreements (FRA)

  • OTC agreements exchanging predetermined rates with actual market rates.

SVB Case Study

  • Collapse initiated by rising rates and liquidity issues. Regulatory failures from Dodd-Frank rollback.

Theories of Term Structure

  • Expectations Theory: forward rates equal expected future rates.

  • Market Segmentation: rates determined independently.

  • Liquidity Preference Theory: higher forward rates than expected future rates.

Inverted Yield Curve

  • Indicative of recession; short-term rates exceed long-term, signaling expected rate drops in the future.