Portfolio Duration:
Two Methods, One Right Answer

A worked example comparing the cash flow yield method against the weighted average method — and the one condition under which they always agree.

📅 2026 ⏱ 8 min read 📊 1 interactive widget

Two Roads to the Same Number

There are two ways to calculate the duration of a bond portfolio. They give different answers — unless one special condition holds. Understanding the difference is essential for anyone managing or analysing fixed income.

METHOD 1 Cash Flow Yield

Aggregate all cash flows from every bond in the portfolio into a single stream. Solve for the IRR of that combined stream — this is the cash flow yield (CFY). Then compute the Macaulay duration of the aggregate stream using the CFY as the single discount rate.

✓ Theoretically precise. Treats the portfolio as a single bond with one yield and one duration. No simplifying assumption is made about the shape of the yield curve.
METHOD 2 Weighted Average

Calculate the modified duration of each bond individually using its own YTM. Then take a weighted average of these individual durations, where each weight = bond's market value ÷ total portfolio market value.

≈ Approximation only. Implicitly assumes the yield curve is flat — i.e., all bonds share the same yield. In practice this is rarely true, so the result is an approximation that is easy to compute but theoretically imprecise.

A Worked Example — Try It Yourself

Below is a 3-bond portfolio with a normal upward-sloping yield curve. Edit any field to test your own numbers, or toggle to a flat yield curve to see the two methods converge.

Portfolio Duration Calculator — RUQQI Interactive
Yield Curve
Portfolio — 3 Bonds (edit any field)
Face ($) Coupon % YTM % Maturity (yrs) Units held
Bond A
Bond B
Bond C
Step 1 — Individual Bond Results
Bond Market Value Weight Mac. Duration Mod. Duration Weighted Contrib.
Method 2 — Weighted Average of Mod. Durations
—
= Σ (Weight × Individual Mod. Duration)
Step 2 — Aggregate Portfolio Cash Flows (Method 1)
Solving for IRR of aggregate cash flows…
Method 1 — Cash Flow Yield (Precise)
—
= Mac. Duration of aggregate cash flows ÷ (1 + CFY)
Annual coupon · Annual compounding · Face value as entered · IRR solved via Newton-Raphson

Which Method Is Better — and Why?

Why Method 1 is more precise
›It treats the portfolio as a single instrument with one unified yield and one Macaulay duration. No information is discarded.
›It does not assume all bonds face the same yield. Each bond's cash flows are aggregated at their actual timing, then a single IRR is solved.
›The resulting duration correctly measures the portfolio's sensitivity to a parallel shift in the yield curve — which is exactly what duration is supposed to capture.
Why Method 2 is used in practice
›Computationally simple. You only need each bond's individual modified duration and market value — no IRR solving required.
›Additive and decomposable. You can immediately see which bonds contribute most to portfolio duration risk — useful for risk attribution and hedging decisions.
›Industry standard. Bloomberg, portfolio management systems, and the CFA curriculum all use the weighted average as the working definition of portfolio duration.
When the two methods give the same answer

The two methods produce identical results if and only if the yield curve is flat — meaning every bond in the portfolio has the same YTM.

The reason: when all YTMs are equal, the IRR of the aggregate cash flow stream equals that common YTM. Discounting all cash flows at the same rate, the weighted-average duration calculation and the full Macaulay duration calculation become mathematically equivalent.

Try it yourself: switch to the "Flat" yield curve in the widget above and watch both results converge to the same number.

RUQQI STUDY STRATEGY — PORTFOLIO DURATION
  • Know both methods by name and formula: the cash flow yield (CFY) method and the weighted average method.
  • The weighted average is what is actually used in practice and in most exam questions — but you must be able to explain why it is an approximation.
  • The two methods are equal only under a flat yield curve. This single fact is a favourite testing point — know it cold.
  • If asked to justify which method is "more correct," the answer is always Method 1 (cash flow yield) — it makes no simplifying assumption about the yield curve shape.