The 2020 30-year Treasury is worth 46 cents on the dollar
Treasury sold a 1.375% 30-year bond on August 13, 2020. At the long yields of October 16, 2026 (20-year 5.47%, 30-year 5.43%) it prices near 46. Duration is the reason.
- What happened
- On August 13, 2020 the Treasury auctioned a 30-year bond with a 1.375% coupon at a high yield of 1.406% and a price of 99.243. On October 16, 2026 the Treasury par yield curve put the 20-year yield at 5.47% and the 30-year at 5.43%. At 5.45%, that 2020 bond, with 23.8 years left, prices at about 46.00 per 100 of face value.
- Why
- A bond's price is the present value of fixed coupons and principal. When market yields rise, the discount applied to every future payment rises, and payments far in the future shrink most. Duration measures that sensitivity: the 2020 bond has a modified duration of about 17.7, so each percentage point of yield moves its price by roughly 17.7% at the margin.
- The numbers that matter
- 1.375%Coupon on the 30-year bond auctioned August 13, 2020, high yield 1.406% (TreasuryDirect)5.43%30-year Treasury par yield, October 16, 2026 (20-year: 5.47%)46.00Computed clean price per 100 of the 1.375% bond of August 2050 at a 5.45% yield, settlement October 20, 202617.7Computed modified duration of that bond; a 2-year par note at 4.74% has a duration of 1.9
- Why it matters
- The same yield move that costs a 2-year note about 2% costs a 30-year bond about 13% to 16%. Long-bond funds carry that exposure every day; a holder of the bond itself gets par back in 2050.
- What happens nextas we saw it on 20 Oct 2026
- The Treasury posts the par yield curve each business day; October 16, 2026 was the latest row available when this piece was prepared on October 20, 2026. The 1.375% bond pays its next coupon on February 15, 2027 and matures on August 15, 2050.
The further out the cash flows, the larger the price move; the low-coupon 2020 bond moves most of all.
| 2-year par note at 4.74% | -1.9% |
|---|---|
| 10-year par note at 5.09% | -7.4% |
| 20-year par bond at 5.47% | -11.1% |
| 30-year par bond at 5.43% | -13.2% |
| 1.375% bond of Aug 2050 at 5.45% | -15.9% |
On August 13, 2020 the U.S. Treasury sold $26.0 billion of a new 30-year bond. The coupon was 1.375%, the high yield was 1.406%, and buyers paid 99.243 per 100 of face value. Six years later the bond has not missed a payment, cannot default in any ordinary sense, and is worth about 46 cents on the dollar.
Nothing went wrong with the bond. What changed is the yield the market demands on long government debt. On October 16, 2026 the Treasury's par yield curve put the 30-year yield at 5.43% and the 20-year at 5.47%. Reprice a 1.375% coupon stream at those yields and roughly half the value disappears. The number that said so in advance is called duration, and this piece works through it with the real bond.
The bond, in the Treasury's own figures
TreasuryDirect's auction results press release of August 13, 2020 describes a 30-year bond, CUSIP 912810SP4, “Bonds of August 2050”, interest rate 1-3/8%, high yield 1.406%, price 99.243433, issued August 17, 2020, maturing August 15, 2050. $55.5 billion was tendered for $26.0 billion accepted, a bid-to-cover ratio of 2.14. The coupon is paid on February 15 and August 15: $68.75 twice a year per $10,000 of face value.
The Treasury's daily par yield curve for August 13, 2020 shows the 2-year at 0.16%, the 10-year at 0.71%, the 20-year at 1.20% and the 30-year at 1.42%. For October 16, 2026 it shows the 2-year at 4.74%, the 10-year at 5.09%, the 20-year at 5.47% and the 30-year at 5.43%, a rise of about 4.0 percentage points at the long end.
Pricing the bond by hand
A bond's price is the present value of what it pays. The payments are fixed: 48 more half-coupons of 0.6875 per 100 of face value, from February 15, 2027 to August 15, 2050, and 100 of principal on the last date. The only question is the discount rate, and on October 16, 2026 the market's rate for 20- to 30-year Treasury cash flows was between 5.43% and 5.47%.
Formula, semiannual compounding: Price = Σ (C ÷ 2) ÷ (1 + y ÷ 2)^(w + k) for k = 0 to 47, plus 100 ÷ (1 + y ÷ 2)^(w + 47). Inputs: C = 1.375; y = 0.0545 (the October 16, 2026 par yields of 5.47% at 20 years and 5.43% at 30 years, interpolated to 23.8 years); settlement October 20, 2026; next coupon February 15, 2027, so w = 118 ÷ 184 = 0.641 of a period. Result: full price 46.245, less accrued interest of 0.6875 × (1 − 0.641) = 0.247, a clean price of 46.00. At 5.43% it is 46.16; at 5.47%, 45.84. Check: the same formula with y = 0.01406 and 60 coupons gives 99.243, the auction price to three decimals.
A buyer at the August 2020 auction paid 99.243 per 100. The bond has since paid 12 half-coupons, February 2021 to August 2026: 12 × 0.6875 = 8.25. Market value at 5.45% is 46.00. Sum: 46.00 + 8.25 − 99.24 = −44.99 per 100, a 45.3% loss on the purchase price, before any interest earned on reinvested coupons and before tax. On $10,000 of face value: $9,924 paid, $825 of coupons received, about $4,600 of market value.
The bond still pays $137.50 a year per $10,000 of face value, and on August 15, 2050 it pays $10,000. The October 2026 yield changes none of that. It changes what someone else pays for those cash flows in the meantime.
Duration: the number that said this in advance
Duration is the weighted average time, in years, until a bond's cash flows arrive, each weighted by its present value. A 1.375% coupon pays little along the way, so nearly all the value sits in the principal 24 years out, and the duration is long. Modified duration, which divides by (1 + y ÷ 2), turns that into a price sensitivity: the percentage change in price per 1 percentage point change in yield, for a small move.
Macaulay duration = Σ t × PV(cash flow at t) ÷ Price, with the cash flows and 5.45% yield above, equals 18.1 years. Modified duration = 18.1 ÷ (1 + 0.0545 ÷ 2) = 17.65, so the linear estimate for a 1 point rise is a 17.7% fall. Exactly: at 6.45% the full price is 38.91, down 15.9% from 46.25; at 4.45% it is 55.36, up 19.7%. The gap is convexity: the price-yield curve bends, so a bond loses less on a rise and gains more on a fall than duration alone says.
| Bond | Yield and coupon | Modified duration | Price if yield +1 point | Price if yield −1 point |
|---|---|---|---|---|
| 2-year note | 4.74% | 1.89 | 98.14 (−1.86%) | 101.91 (+1.91%) |
| 10-year note | 5.09% | 7.76 | 92.59 (−7.41%) | 108.14 (+8.14%) |
| 20-year bond | 5.47% | 12.07 | 88.87 (−11.13%) | 113.13 (+13.13%) |
| 30-year bond | 5.43% | 14.73 | 86.78 (−13.22%) | 116.51 (+16.51%) |
| 1.375% bond of Aug 2050 (23.8 yrs left) | 5.45% | 17.65 | 38.91 (−15.87%) | 55.36 (+19.72%) |
The new 30-year par bond carries a 5.43% coupon, so a large share of its value arrives in the first decade and its duration is 14.7. The 2020 bond pays 1.375%, so almost everything is in the 2050 principal, and its duration is 17.7. Two things lengthen duration: more years to maturity and a lower coupon. A buyer in 2020 got both at once.
The 2-year note is the other end of the scale. A duration of 1.9 means a full point of yield is worth under 2% of price, and the note returns par within two years whatever happens in between. That is why short Treasuries behave like cash with a lag and long Treasuries like a leveraged position in interest rates. The whole curve in October 2026 is in the site's 10-year piece.
What a fund's stated duration implies
The iShares product page for the 20+ Year Treasury Bond ETF (TLT), as of October 16, 2026, lists an effective duration of 14.84 years, a weighted average maturity of 26.05 years, a weighted average coupon of 3.36%, an average yield to maturity of 5.49%, 47 holdings, net assets of $47,007,128,833 and an expense ratio of 0.15%. The fact sheet dated June 30, 2026 showed 15.31 years.
Price change ≈ −(duration) × (change in yield). For a 1.00 point rise: −14.84 × 1.00 = about −14.8%, roughly $1,484 on a $10,000 holding; a 0.50 point rise is about −7.4%, or $742. A fall in yields gives a gain of similar size, slightly larger because of convexity. These are first-order estimates, and a fund's duration drifts: it moved from 15.31 to 14.84 years between June 30 and October 16, 2026.
The difference between the fund and the single bond is that the fund never matures. It sells bonds as they fall below 20 years and buys new long ones, so its duration stays near 15 indefinitely, while a single bond's duration shrinks every year to zero. A saver who wants par on a known date gets it from the bond; the fund is a standing exposure to long yields, a different thing even when the holdings overlap.
Coupons, reinvestment and holding to maturity
- Par at maturity. The 1.375% bond pays 100 on August 15, 2050 regardless of its price in between. A holder from the 2020 auction who keeps it receives 60 half-coupons totaling 41.25 per 100 plus 100 of principal, against 99.24 paid. Their realized yield is the 1.406% they locked in, because none of the cash flows changed. The 46.00 price is the cost of leaving early.
- Reinvestment. The 1.406% auction yield assumes each coupon is reinvested at 1.406%. Coupons received in 2026 can be reinvested at 2-year yields near 4.7%, which lifts the holder's total cash at 2050 above what the 2020 yield implied. The effect is small because the coupons are small: the whole 30-year coupon stream is 41.25 per 100.
- The buyer at 46. Whoever buys the bond at 46.00 on October 20, 2026 locks in a 5.45% yield to maturity by construction, most of it from the pull of 46 toward 100 over 23.8 years rather than from the coupon. The price can move a long way before 2050; the destination cannot.
What it means for your money
The practical content of duration is one multiplication: the duration of what you hold, times the yield change you want to stress, is the approximate percentage move in price. From the October 16, 2026 curve:
- A 2-year note at 4.74%: duration 1.9. A full point of yield is about 1.9% of price, and the note returns par in October 2028.
- A 10-year note at 5.09%: duration 7.8. A full point is 7.4% to 8.1% of price. A 10-year note bought in August 2020 at a 0.71% par yield has under four years left and a short duration; it returns par in 2030.
- A 30-year bond at 5.43%: duration 14.7. A full point is 13% to 17% of price. A long-Treasury fund with a 14.84-year duration behaves the same way and does not shorten with time.
- The 2020 bond at 1.375%: duration 17.7. It already shows what a 4 point rise does to a low-coupon long bond: 99.24 to 46.00.
None of this says which way yields go from 5.43%. A 1 point fall would lift the 2020 bond about 19.7%; a 1 point rise would cut it 15.9%. The arithmetic is silent on direction. What a saver controls is the duration they hold and whether a bond's maturity matches the date they need the money. The loss-recovery tool shows that a 45.3% loss needs an 82.8% gain to recover. How the auctions work is in the auction explainer; what nominal yields price in for inflation is in the breakeven piece.
Sources
- Daily Treasury Par Yield Curve Rates, October 2026U.S. Department of the Treasury · Oct 20, 2026 · Primary source
- Daily Treasury Par Yield Curve Rates, August 2020U.S. Department of the Treasury · Oct 20, 2026 · Primary source
- Treasury Auction Results: 30-Year Bond, CUSIP 912810SP4, Bonds of August 2050 (press release, August 13, 2020)TreasuryDirect / Bureau of the Fiscal Service · Oct 20, 2026 · Primary source
- iShares 20+ Year Treasury Bond ETF (TLT), product page, characteristics as of October 16, 2026BlackRock / iShares · Oct 20, 2026 · Primary source
- iShares 20+ Year Treasury Bond ETF Fact Sheet as of June 30, 2026BlackRock / iShares · Oct 20, 2026 · Primary source
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