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3.9 The Maturity Structure of Interest Rates

3.9.1 Forward Rates

Forward rate is the interest rate on a bond or money market instrument traded in a forward market (future delivery).

Most common market practice is to name forward rates as: "2y5y" – pronounced "the two- year into five-year rate." The first number (two) refers to the length of the forward period in years from today, and the second number (five) refers to the tenor (time-to-maturity) of the underlying bond.

An implied forward rate (also known as a forward yield) is calculated from spot rates and is a break-even reinvestment rate. It links the return on an investment in a shorter-term zero- coupon bond to the return on an investment in a longer-term zero-coupon bond.

3.9.2 Determination of Spot rates from Forward rates, Forward Rates from Spot Rates,

and the Price of a Bond Using Forward Rates The formula might be used to calculate an implied forward rate from two spot rates or a spot rate from another spot rate and a forward rate.

3.9.3 Yield Spread Measures

The spread is the difference between the yield-to-maturity and the benchmark. The spread captures the microeconomic factors specific to the bond issuer and the bond itself: the credit risk of the issuer and changes in the quality rating on the bond, liquidity and trading in comparable securities, and the tax status of the bond.

The benchmark is often called the "risk-free rate of return." Fixed-rate bonds often use a government benchmark (on-the-run) security with the same time-to-maturity as, or the closest time-to-maturity to, the specified bond. A frequently used benchmark for floating-rate notes is Libor. As a composite interbank rate, it is not a risk-free rate.

The most recently issued government bond is called the "on-the-run security." Yield-to-Maturity Building Blocks YTM = Benchmark + Spread (Risk-free rate of return) (Risk Premium)

Spread – Accounts for Taxation, Liquidity and credit risk.

Benchmark ("Risk-free" rate of return) represents: Expected inflation rate and Expected real rate.

Types of Spreads

  • G-spread – The yield spread in basis points over an actual or interpolated government bond.
  • I-spread or interpolated spread to the swap curve – The yield spread of a specific bond over the standard swap rate in that currency of the same tenor. This yield spread over Libor (I- spread) allows comparison of bonds with differing credit and liquidity risks against an interbank lending benchmark.
  • A zero volatility spread (Z-spread) of a bond: Calculated as a constant yield spread over a government (or interest rate swap) spot curve – as opposed to the G-Spread and the I- Spread, which use the same discount rate for each cash flow.

PV = PMT/(1+Z1+Z)1 + PMT/(1+Z2+Z)2 + … + (PMT + FV)/(1+Zn+Z)n

  • Option-Adjusted Spread (OAS): The Z-spread is also used to calculate the Option-Adjusted Spread (OAS) on a callable bond.

OAS = Z-Spread – Option Value (in basis points per year)

Lesson Wrap-Up

This lesson should leave you able to explain the the maturity structure of interest rates in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain forward rates in your own words.
  2. Explain determination of spot rates from forward rates, forward rates from spot rates, in your own words.
  3. Explain yield spread measures in your own words.
  4. State one exam-style risk, valuation, or market implication of the the maturity structure of interest rates.