The Term Structure of Interest Rates and its Impact on Duration

Beyond Parallel Shifts

Duration is a effective concept, but its standard calculation assumes a "parallel shift" in the yield curve—that is, all interest rates, from overnight to 30 years, move up or down by the same amount. In reality, this rarely happens. The yield curve, or the term structure of interest rates, is constantly changing its shape. It can steepen (long-term rates rise more than short-term rates), flatten (long-term rates rise less than short-term rates), or even invert (short-term rates are higher than long-term rates). These non-parallel shifts have significant implications for portfolio management that are not captured by a single duration number.

Duration and the Shape of the Yield Curve

The Macaulay duration of a bond is the weighted average of the times to receipt of its cash flows, where the weights are the present values of those cash flows. The discount rates used to calculate these present values are taken from the spot yield curve. Therefore, the shape of the yield curve itself is an input into the duration calculation. An upward-sloping yield curve will result in a slightly lower duration than a flat yield curve, because the later cash flows are discounted at higher rates, giving them a lower present value and thus a lower weight in the duration calculation.

More importantly, different bonds are sensitive to changes in different parts of the yield curve. A 2-year note is primarily sensitive to changes in the 2-year spot rate. A 30-year bond is sensitive to the entire long end of the curve. A portfolio's performance depends not just on the overall direction of rates, but on how the curve shifts.

Positioning for Yield Curve Shifts

Active managers can structure their portfolios to profit from anticipated changes in the shape of the yield curve. The three primary strategies are:

1. Bullet Strategy: The portfolio is concentrated in a single maturity or a narrow range of maturities (e.g., all 5-year bonds). This strategy will perform best if the yield curve makes a parallel shift, or if the part of the curve where the portfolio is concentrated has the most favorable move (e.g., a rally in 5-year rates).

2. Barbell Strategy: The portfolio holds a combination of very short-maturity and very long-maturity bonds, with nothing in between. A barbell portfolio has higher convexity than a bullet portfolio of the same duration. This strategy will outperform a bullet if the yield curve flattens (long rates fall more than short rates, or short rates rise more than long rates). The long-end bonds provide capital gains while the short-end bonds provide a stable anchor.

3. Ladder Strategy: The portfolio has equal amounts invested across a range of maturities (e.g., equal amounts in 1-year, 2-year, 3-year... up to 10-year bonds). This is a more conservative strategy that diversifies a portfolio across the yield curve. It avoids betting on a particular change in the shape of the curve. As the shorter-term bonds mature, the proceeds are reinvested at the long end of the ladder, which can help to increase yield in a normal, upward-sloping yield curve environment.

Example: Flattening vs. Steepening

Consider a manager who must maintain a portfolio duration of 7 years. The manager can choose a bullet strategy (holding all 7-year bonds) or a barbell strategy (holding 2-year and 10-year bonds). If the manager expects the yield curve to flatten, the barbell is the superior choice. For example, if 10-year yields fall by 50 basis points and 2-year yields are unchanged, the long end of the barbell will generate significant capital gains, and the portfolio will outperform the bullet. If the manager expects the curve to steepen (10-year yields rise more than 2-year yields), the bullet would be the safer, and likely better-performing, choice, as it avoids the heavy losses on the long end of the barbell.

Understanding the term structure is important for any fixed-income trader. Relying on a single duration number is insufficient. A more granular analysis, considering how a portfolio is positioned across the yield curve, is necessary to manage risk and generate alpha in a world of non-parallel shifts.