The Same Average Maturity Can Hide Different Yield-Curve Exposures

Maturity dates locate the risk along the curve

FINRA's yield-curve discussion describes the relationship between maturity and yield. A portfolio summary that compresses several maturities into one average can lose information about where payments occur. To see the gap, compare two portfolios with the same initial market value and the same market-value-weighted average maturity. Their payments can occupy different parts of the curve and respond differently when those parts move in opposite directions.

This exercise prices fictional zero-coupon claims at annual effective spot yields. A spot yield discounts one payment at its exact horizon. It is not necessarily the quoted yield on a coupon-bearing Treasury of the same maturity. All changes occur instantaneously, so no time passes and no carry is earned. That controlled setup lets the table isolate curve shape rather than mixing shape changes with interest accrual.

Supporting references: 1. FINRA: Understanding Bond Yield and Return

Construct two portfolios that share the headline number

Portfolio A has USD 5,000 of present value in a one-year zero and USD 5,000 in a five-year zero. Portfolio B has USD 10,000 of present value in a three-year zero. Initially all spot yields are 4 percent. The required face payments are USD 5,200 at year one, approximately USD 6,083.26 at year five and USD 11,248.64 at year three. Each portfolio therefore costs USD 10,000.

Using initial market-value weights, A's average maturity is one-half times one year plus one-half times five years, or three years. B's is three years directly. In this flat-yield zero-coupon example their modified-duration summaries also initially coincide at three divided by 1.04. This carefully constructed similarity makes the missing shape exposure easier to identify; it does not imply average maturity generally substitutes for duration.

Twist the ends while leaving the middle unchanged

In the first stress, the one-year spot yield rises to 5 percent, the five-year spot yield falls to 3 percent and the three-year yield stays at 4 percent. A's short claim loses about USD 47.62, but its long claim gains about USD 247.48. Its total value rises to about USD 10,199.86. B stays at USD 10,000 because its own discounting point has not changed.

The arithmetic uses each original face payment divided by the new spot-rate growth factor for its maturity. There is no need to guess which single portfolio yield should represent the twist. The gain arises because a five-year payment is more sensitive to its local rate decline than a one-year payment is to an equal-sized local rate increase. The average of the two rate changes being zero does not make the dollar effects cancel.

Reverse the twist and compare a parallel move

Reverse the stress: the one-year yield falls to 3 percent, the five-year yield rises to 5 percent and the three-year yield remains 4 percent. A's value becomes approximately USD 9,814.94, while B again stays at USD 10,000. The opposite twist does not produce exactly the opposite dollar result because discounting is nonlinear. That asymmetry can be measured directly rather than assigned to a mysterious residual.

For another comparison, raise all three spot yields to 5 percent. Both portfolios lose value, but their exact losses differ slightly even though initial first-order duration coincides. The table shows both outcomes and the A-minus-B difference in USD. This additional scenario separates a curve-shape mismatch from higher-order effects that can matter even under a parallel move. A single sensitivity estimate answers only the movement it was designed to approximate. The signed difference column compares portfolio values at one instant. It is not an annual return, a probability-weighted expectation or compensation that either portfolio promises to deliver over the remaining years.

Relate the shape exposure to actual spending dates

An investor owing USD 11,248.64 in three years has a direct scheduled match in B if the payment is made as assumed. A has no principal maturity at year three. It would require holding early proceeds and selling or borrowing against the five-year claim. Equal average maturity therefore does not establish equivalent funding capacity for a particular bill, even if broad interest-rate sensitivity looks similar.

The counterexample also works in the other direction. If two separate obligations fall at years one and five, B does not match those dates just because its average maturity sits between them. A pricing comparison needs a cash-use comparison. Identify whether the portfolio is intended to meet dated liabilities, track a market index or tolerate a specified family of shocks before selecting the risk summary.

Use a small scenario grid before a more elaborate model

Treasury's STRIPS description provides an example of individual maturity payments that can be analyzed separately. Our amounts remain fictional and omit transaction constraints. For real coupon portfolios, each coupon belongs to its own date and may load on several curve points. A practical model can allocate sensitivities by maturity region and then test whether the allocation adequately reproduces exact repricing under the shocks that matter.

The decision boundary is whether the proposed exposure remains acceptable when neighboring curve regions move differently. If the answer depends on one assumed parallel shift, document that restriction. The table does not rank barbells and middle maturities universally: it shows why a shared headline statistic cannot settle their equivalence. Credit, callable features, funding costs and changing liabilities would require additional scenarios beyond these clean single-payment claims.

Supporting references: 2. TreasuryDirect: STRIPS

Limits of this analysis

• Spot yields are supplied model inputs, not observed Treasury par yields.
• Three points and zero-coupon claims simplify the full curve.
• Initial average maturity equivalence does not imply equivalent liabilities, convexity or credit exposure.