The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

FORWARD RATES

We described how a default-free theoretical spot rate curve can be extrapolated from the Treasury yield curve. Additional information useful to market participants can be extrapolated from the default-free theoretical spot rate curve: forward rates. A forward rate is the fundamental unit of yield curve analysis. Forward rates are the building blocks of interest rates just as atoms are the building blocks of solid matter in physics. A forward rate is the discount rate of a single cash flow over a single period. Under certain assumptions, these rates can be viewed as the market’s consensus of future interest rates.²⁸²

Examples of forward rates that can be calculated from the default-free theoretical spot rate curve are the:

• Six-month forward rate six months from now

• Six-month forward rate three years from now

• One-year forward rate one year from now

• Three-year forward rate two years from now

• Five-year forward rates three years from now

We begin by showing how to compute the six-month forward rates. Then we explain how to compute any forward rate between any two periods in the future.

Deriving Six-Month Forward Rates

To illustrate the process of extrapolating six-month forward rates, we use the yield curve and the corresponding spot rate curve from Exhibit 18.1. Suppose an investor has a one-year anticipated investment horizon. In general, an investor has three basic ways to satisfy this maturity preference. First, an investor can purchase a security ...