Term Structure

Section: Term Structure of Interest Rates Estimated study time: 60 minutes Content: The term structure of interest rates describes the relationship between bond yields and time to maturity for otherwise identical bonds. At CFA Level 2, candidates must master the spot rate curve (also called the zero curve), the forward rate curve, the par curve, and the swap rate curve, and understand the theories that explain why the yield curve takes its observed shape. The spot rate for maturity T (denoted z_T) is the yield on a zero-coupon bond maturing at time T. The par rate for maturity T is the coupon rate that makes a T-period bond priced at par. Forward rates are the rates implied by the spot curve for loans beginning in the future. The relationship between spot rates and forward rates is governed by the no-arbitrage condition. A forward rate f(j,k) represents the annualized rate for a loan beginning in j years and maturing in k years. The key formula: (1 + z_k)^k = (1 + z_j)^j * (1 + f(j,k))^(k-j), where z_j and z_k are the j-year and k-year spot rates. Solving for the forward rate: (1 + f(j,k)) = [(1 + z_k)^k / (1 + z_j)^j]^(1/(k-j)). Bootstrapping is the process of deriving spot rates from par bond prices: starting with the 1-year spot rate from the 1-year par bond, then extracting the 2-year spot rate from the 2-year par bond price given the known 1-year spot rate, and so on. Spot rates and forward rates together allow pricing of any fixed cash flow stream. Three main theories explain the shape of the yield curve. The Pure Expectations Theory (PET) holds that forward rates…