Bond ETF Duration Math: Why 1.46%p Meant -21%

A bond ETF with a modified duration of 17 years falls roughly 17% in price when market rates rise by one percentage point. Korea's 30-year government bond (gukgochae) yield climbed from 3.255% at the start of this year to 4.714% on 11 September — a move of 1.459%p. Over the same stretch, ETFs tracking that maturity returned an average of -25.39%, according to Asia Today.

The gap between the phrase "safe asset" and a double-digit loss is created by one number: duration. Funds holding the same 30-year government bonds diverged by more than 13 percentage points — TIGER's 30-year STRIP Active fell 34.57% while KIWOOM's 30-year Active fell 21.35%. The labels differ, but what really differs is duration.

Duration is not decorative fine print in a fact sheet. It is the only input that tells you, in advance, how much your account moves when yields move.

How much does price move per 1%p of yield?

Duration is the weighted-average time to recover the money invested in a bond, counting the present value of both coupons and principal. Longer maturities push it up; larger interim coupons pull it down. A zero-coupon or STRIP bond, which pays nothing along the way, has a duration close to its maturity, as Korea Investment & Securities explains.

The sensitivity formula, in the form set out by Quarterback Asset Management, is:

Price change = -duration × change in yield ÷ (1 + market yield)

If the market yield rises from 10% to 11%, a bond with duration 2.735 moves -2.735 × 0.01 ÷ 1.1 = -0.0249, a 2.49% decline. Modified duration simply bakes that (1 + r) division in ahead of time, so practitioners multiply modified duration by the yield change and stop there. At yields of 4-5%, the denominator adjustment is under 5%, which makes the mental shortcut accurate enough for real decisions.

Spread that single line into a grid and fund selection becomes arithmetic. The table below computes price change by modified duration across a range of rate moves; the rightmost column plugs in the 1.459%p that actually happened this year.

What duration does -21% imply?

The equation runs backwards too. Given a return and a yield move, you can solve for duration. One adjustment is needed first: a year-to-date ETF return blends price change with accrued interest. Roughly 4% a year collected over eight and a half months adds about 2.8%, so that carry has to be stripped out to isolate price.

Implied modified duration = (return minus carry) ÷ 1.459%p

Returns are as of 11 September; the 2.8% carry is an assumption. Two things fall out. First, even a portfolio of 30-year maturities lands at a modified duration of 16-17 years once coupons are counted — the 13-year gap between maturity and duration is exactly what the interim interest buys you. Second, stripping the coupons away pushes duration into the mid-20s, so the same rate move hits about 1.5 times harder. Words like "STRIP" and "Enhanced" in a fund name are, in practice, duration multipliers.

This back-solve ignores convexity, so it understates true duration slightly. Over a move as large as 1.46%p, convexity works in the holder's favour and cushions part of the loss.

Maturity is printed on the label. Duration is not. The second one is what moves your account.

How much of a rate rise can the coupon absorb?

Holding a bond still earns interest while the price falls, which makes a more useful question: how large a rate rise does one year of income offset? The answer is short.

Break-even rate rise = annual yield ÷ modified duration

Using the 4.714% 30-year yield from 11 September as the income rate:

At a duration of 17, a 0.28%p rise wipes out a full year of income. This year delivered more than five times that. The table applies the same 4.714% across every bucket, so short-dated funds — whose actual yields are lower — defend slightly less well than shown. The order of magnitude, though, holds.

The arithmetic points to one conclusion: a long-duration bond ETF is a bet on falling rates, not a deposit substitute. An individual bond held to maturity pays its contracted coupon and principal regardless of interim prices, but an ETF has no maturity and continuously rolls its holdings, so price change is the return. That distinction is why investors planning to hold to maturity often compare the fee and yield structure of buying individual bonds over the counter.

Why yields are not falling with policy rates

This year's long-end selloff is not a monetary policy story alone. Shrinking demand from insurers and worries about fiscal deterioration did much of the work. Lim Jae-kyun, an analyst at KB Securities, noted that despite historically attractive yields, weaker buying from insurers and foreign investors has left a supply-demand overhang — meaning long rates may not follow even if the policy rate is cut.

That also strains the assumption behind the tables above, which presume every maturity moves in parallel. When short rates fall while long rates hold, the curve steepens and a 30-year ETF does not rally on rate-cut headlines. That is precisely the regime this year has been in.

What to watch

• The duration figure in the fund fact sheet — modified duration, published monthly. A 30-year maturity is not a 30-year duration.
• Suffixes like STRIP or Enhanced — check whether coupon stripping or leverage has extended duration.
• The 3-year versus 30-year yield spread — in a steepening curve, policy cuts do not reach long bond prices.
• Net buying by insurers and foreign investors — the supply-demand axis that pushed long yields up this year.
• Your holding period against the duration — shorter than duration is a directional rate bet; longer is an income strategy.
• Fees and tracking error — over a long hold, the real cost ratio hiding behind the headline fee compounds against you.

Sources

• Government bond ETFs disappoint retail buyers — Asia Today
• What is bond duration? — Quarterback Asset Management
• Bond duration explained — Korea Investment & Securities