Why a 1% Rise Costs a 30-Year 15%

A bond's price and its yield always move in opposite directions, and the size of that move is set by one number. Here is how to read it — and why today's higher yields are good news for the next buyer.

The same promise, two prices

Somebody promises you $100. Not today — 10 years from today. What is that promise worth right now?

You have to discount it. Money you cannot touch for a decade is worth less than money you can, so you divide the $100 down, once for every year you have to wait. The rate you divide by is the whole subject of this lesson.

At a 1% rate, that promise is worth $90.53 today. At a 5% rate, the same $100 promised on the same date is worth $61.39.

Nothing about the promise changed. Same amount, same date, same borrower. Only the rate moved — and that was worth a 32% difference in what you would pay for it.

Why the price has to do the adjusting

Bonds already exist, and they trade. Once a bond is issued, its payout is fixed in dollars. The borrower owes you that coupon and that face value, and no news changes it.

So if the market's rate moves, the payout cannot. The only thing left to move is the price.

If rates rise, a buyer can get a better payout on a new bond, so the old one has to get cheaper to compete. Its price falls. If rates fall, the old bond's fixed payout looks generous by comparison, so it gets more expensive.

Price and yield therefore always move in opposite directions. That is not a market opinion. It is arithmetic performed on a fixed number of dollars.

The number that tells you how much

Some bonds barely notice a rate move. Others get hit hard. What separates them is duration — roughly, how long you are waiting for your money, weighted by when each payment arrives.

You do not need the formula to use it. You need the table. One percentage point is the standard unit of a rate move, so here is what a rise of one point, from today's levels, does to a plain bond of each maturity:

Read the bars as: if yields rise by one percentage point, that is roughly what happens to the price. A 2yr loses about 2%. A 30yr loses about 15%.

Same news, same morning, same bond market — and the 30yr holder loses about eight times as much as the 2yr holder. That single ratio is why investors care so much about where on the curve they sit.

One bond, 1 decade

Now put the mechanics next to recent history, which is the part that tends to surprise people.

In July 2020, the US 10yr Treasury yield averaged 0.62% — the low point of a series that runs back to 1953. In September 1981 it averaged 15.32%. Those two prints sit 38.8 years apart, and almost everything in between went one direction.

Buy a 10yr bond at the 2020 low, then. You collect 0.62% a year and wait for 2030. That bond has about 4 years left to run, and today it is marked against a market where the 10yr yields 4.96%. Its price is roughly 85, down about 15% from the 100 you paid.

Hold it to maturity and none of that matters: you get your 100 back, plus 6.20 in coupons along the way. The fall in price only bites the investor who has to sell.

Nobody defaulted. No company blew up. The rate changed, and the price followed. That is the entire story.

The other side of the seesaw

Here is the half that is usually left out, and the reason this is not a warning.

Run the arithmetic backwards. A 10yr bond bought at the 1981 peak paid 15.32% every year for a decade. As yields collapsed it became valuable in the market as well: by 1986, with 5 years left to run, it was worth about 132, roughly a third more than the 100 it cost.

And held to the end, it did not need a falling-rate market to pay off at all. 10 years of coupons plus your principal returned 253 on a 100 investment.

Falling rates made the old bond a winner. Rising rates make it a loser. It is the identical mechanism running in the opposite direction, and which one you experience depends entirely on when you bought.

For the person buying today, the direction is the friendly one. The 10yr pays 4.96%. Subtract expected inflation of about 2.36% and a real yield of roughly 2.6% is left — and the market's own inflation-protected bond, which prices this directly, yields 2.55% (as of 10 September).

That second number is the one to sit with. Over the past 15 years, an inflation-protected 10yr Treasury has spent roughly a quarter of its time yielding less than nothing — and it arrived in waves, not as one strange moment: through the euro crisis years of 2011 to 2013, again through 2020 and 2021, and briefly in 2022. In each of those windows, the only way to protect yourself against inflation was to accept a guaranteed real loss.

Paying to lend is the unusual state. Being paid to lend is the normal one.

That is the positive version of this story, and it is worth stating plainly: the waiting is finally paid. A saver can now earn a real return on the safest asset there is, without taking anyone's credit risk or anyone's equity risk.

Where Bitcoin fits

Bitcoin has no coupon. It promises you no dollars in 10 years, or in fifty, so there is nothing to discount — the calculation above does not apply to it, and you should be sceptical of anyone who claims to run it.

What it shares with a long bond is the waiting, and the sensitivity. Bitcoin is around $77,700 today: about 32.6% lower than a year ago, and about 23% higher than a month ago. That is a wider swing than the 30yr bond's 15% entry above, and there is no coupon arriving while you wait for it to come back.

So why bring it up in a lesson about discounting? Because the two assets answer the same question in opposite ways. A bond now pays you to be patient. Bitcoin pays you nothing and asks you to be patient anyway.

That contrast is the useful part. When the risk-free rate is 4.96%, patience has a price on it for the first time in years — and an asset that offers no yield has to justify itself against a real alternative. Worth knowing whether or not you own any.

How to read it from here

Three things to take away, and you can check each of them in the numbers on this site:

• The level. The 10yr is 4.96% and the 30yr is 5.35%. Higher yields mean the same bonds are cheaper to buy than they were.
• The direction. A rising yield costs someone who already holds the bond. The 2yr rose 29 basis points this week — but it is a short bond, so the damage to its price was small. Maturity is what decides that, not the size of the move.
• The wait. If you may need the money soon, duration is a real risk, because you might have to sell at whatever price the market offers. If you can hold to maturity, the price in between matters much less — you get your dollars back on a fixed date regardless.

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