Key Rate Duration: A Granular Approach to Managing Yield Curve Risk

The Limitations of a Single Duration Number

Effective duration is a effective tool, but it has a significant weakness: it assumes that all yields along the term structure move by the same amount (a parallel shift). This is rarely the case. The yield curve can steepen, flatten, or develop a "hump," meaning different parts of the curve move by different amounts. A single duration number cannot capture a portfolio's sensitivity to these non-parallel shifts. To address this, sophisticated managers use a more granular set of risk measures: key rate durations.

Defining Key Rate Duration

Key rate duration (also known as partial duration) measures a bond's sensitivity to a shift in a single point on the yield curve, holding all other rates constant. A set of key rate durations consists of sensitivities to several "key" rates, typically the 2-year, 5-year, 10-year, and 30-year points on the spot curve. For example, the 5-year key rate duration of a bond measures the percentage price change of that bond for a 1% change in the 5-year spot rate, assuming all other spot rates do not change.

The sum of a bond's key rate durations is approximately equal to its effective duration. By breaking down the total duration into these components, a manager can see exactly where along the curve the portfolio's interest rate sensitivity lies.

Using Key Rate Durations in Portfolio Management

Key rate durations allow for a much more precise management of yield curve risk. A portfolio manager can analyze the key rate duration profile of their portfolio and compare it to the profile of their benchmark.

• Identifying Exposures: A manager might find that their portfolio has a much higher 10-year key rate duration than the benchmark. This means the portfolio is effectively making a bet that the 10-year part of the curve will rally (yields will fall). If the manager does not intend to make this bet, they can adjust the portfolio to reduce this exposure.

• Hedging Non-Parallel Shifts: Key rate durations are essential for hedging against specific changes in the shape of the yield curve. If a manager expects the 5-year to 10-year part of the curve to steepen (10-year yields rise more than 5-year yields), they could structure a hedge that is short 10-year duration and long 5-year duration. This could be done by selling 10-year Treasury futures and buying 5-year Treasury futures. The goal is to create a "key rate neutral" position for the part of the curve the manager is concerned about.

• Constructing Curve Trades: Key rate durations are the building blocks of yield curve trading strategies. A "flattener" trade, which profits from a flattening of the yield curve, would involve being long duration in the long end of the curve and short duration in the short end. The net effective duration of the trade might be zero, but it would have a large positive 10-year key rate duration and a large negative 2-year key rate duration, for example.

A Practical Example

Consider a portfolio with an effective duration of 6.5 years. This single number tells us little about the portfolio's structure. Now consider its key rate duration profile:

• 2-Year KRD: 0.5
• 5-Year KRD: 2.5
• 10-Year KRD: 3.0
• 30-Year KRD: 0.5

This profile tells us that the portfolio is heavily concentrated in the 5- to 10-year part of the curve. It is essentially a "bullet" portfolio. Now consider a benchmark with the same effective duration of 6.5 years, but with this profile:

• 2-Year KRD: 1.5
• 5-Year KRD: 1.5
• 10-Year KRD: 1.5
• 30-Year KRD: 2.0

This benchmark is much more of a "barbell." The portfolio is underweight the short and long ends of the curve and overweight the middle. This is a significant bet on the shape of the yield curve. If the curve flattens, the portfolio will underperform the benchmark. By analyzing the key rate durations, the manager can see this risk and decide whether it is an intended part of their strategy. Without key rate durations, this important exposure would be hidden within a single, misleading duration number.