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The Term Structure and Interest Rate Dynamics

2024 Curriculum CFA Program Level II Fixed Income

Introduction

Interest rates are both a barometer of the economy and an instrument for its control. The term structure of interest rates—market interest rates at various maturities—is a vital input into the valuation of many financial products. The quantification of interest rate risk is of critical importance to risk managers. Understanding the determinants of interest rates, and thus the drivers of bond returns, is imperative for fixed-income market participants. Here, we explore the tools necessary to understand the term structure and interest rate dynamics—that is, the process by which bond yields and prices evolve over time.

Section 1 explains how spot (or current) rates and forward rates, which are set today for a period starting in the future, are related, as well as how their relationship influences yield curve shape. Section 2 builds upon this foundation to show how forward rates impact the yield-to-maturity and expected bond returns. Section 3 explains how these concepts are put into practice by active fixed-income portfolio managers.

The swap curve is the term structure of interest rates derived from a periodic exchange of payments based on fixed rates versus short-term market reference rates rather than default-risk-free government bonds. Sections 4 and 5 describe the swap curve and its relationship to government yields, known as the swap spread, and explains their use in valuation.

Section 6 describes traditional theories of the term structure of interest rates. These theories outline several qualitative perspectives on economic forces that may affect the shape of the term structure.

Section 7 describes yield curve factor models. The focus is a popular three-factor term structure model in which the yield curve changes are described in terms of three independent movements: level, steepness, and curvature. These factors can be extracted from the variance-covariance matrix of historical interest rate movements.

Section 8 builds on the factor model and describes how to manage the risk of changing rates over different maturities. Section 9 concludes with a discussion of key variables known to influence interest rates, the development of interest rate views based on forecasts of those variables, and common trades tailored to capitalize on an interest rate view. A summary of key points concludes the reading.

Learning Outcomes

The member should be able to:

  • describe relationships among spot rates, forward rates, yield to maturity, expected and realized returns on bonds, and the shape of the yield curve;
  • describe how zero-coupon rates (spot rates) may be obtained from the par curve by bootstrapping;
  • describe the assumptions concerning the evolution of spot rates in relation to forward rates implicit in active bond portfolio management;
  • describe the strategy of rolling down the yield curve;
  • explain the swap rate curve and why and how market participants use it in valuation;
  • calculate and interpret the swap spread for a given maturity;
  • describe short-term interest rate spreads used to gauge economy-wide credit risk and liquidity risk;
  • explain traditional theories of the term structure of interest rates and describe the implications of each theory for forward rates and the shape of the yield curve;
  • explain how a bond’s exposure to each of the factors driving the yield curve can be measured and how these exposures can be used to manage yield curve risks;
  • explain the maturity structure of yield volatilities and their effect on price volatility;
  • explain how key economic factors are used to establish a view on benchmark rates, spreads, and yield curve changes.

Summary

  • The spot rate for a given maturity can be expressed as a geometric average of the short-term rate and a series of forward rates.
  • Forward rates are above (below) spot rates when the spot curve is upward (downward) sloping, whereas forward rates are equal to spot rates when the spot curve is flat.
  • If forward rates are realized, then all bonds, regardless of maturity, will have the same one-period realized return, which is the first-period spot rate.
  • If the spot rate curve is upward sloping and is unchanged, then each bond “rolls down” the curve and earns the forward rate that rolls out of its pricing (i.e., an N-period zero-coupon bond earns the N-period forward rate as it rolls down to be a N – 1 period security). This dynamic implies an expected return in excess of short-maturity bonds (i.e., a term premium) for longer-maturity bonds if the yield curve is upward sloping.
  • Active bond portfolio management is consistent with the expectation that today’s forward curve does not accurately reflect future spot rates.
  • The swap curve provides another measure of the time value of money.
  • Swaps are an essential tool frequently used by investors to hedge, take a position in, or otherwise modify interest rate risk.
  • Bond quote conventions often use measures of spreads. Those quoted spreads can be used to determine a bond’s price.
  • Swap curves and Treasury curves can differ because of differences in their credit exposures, liquidity, and other supply/demand factors.
  • Market participants often use interest rate spreads between short-term government and risky rates as a barometer to evaluate relative credit and liquidity risk.
  • The local expectations theory, liquidity preference theory, segmented markets theory, and preferred habitat theory provide traditional explanations for the shape of the yield curve.
  • Historical yield curve movements suggest that they can be explained by a linear combination of three principal movements: level, steepness, and curvature.
  • The volatility term structure can be measured using historical data and depicts yield curve risk. The sensitivity of a bond value to yield curve changes may make use of effective duration, key rate durations, or sensitivities to parallel, steepness, and curvature movements. Using key rate durations or sensitivities to parallel, steepness, and curvature movements allows one to measure and manage shaping risk.
  • The term bond risk premium refers to the expected excess return of a default-free long-term bond less that of an equivalent short-term bond or the one-period risk-free rate
  • Several macroeconomic factors influence bond pricing and required returns such as inflation, economic growth, and monetary policy, among others.
  • During highly uncertain market periods, investors flock to government bonds in a flight to quality that is often associated with bullish flattening, in which long-term rates fall by more than short-term rates.
  • Investors expecting rates to fall will generally extend (shorten) portfolio duration to take advantage of expected bond price increases (decreases)
  • When investors expect a steeper (flatter) curve under which long-term rates rise (fall) relative to short-term rates, they will sell (buy) long-term bonds and purchase (sell) short-term bonds.

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