Article 01 · Bond Math · Coupons · Yields · Central Banks
The Bond Seesaw
Why Prices and Yields Move in Opposite Directions
Every headline about central banks, government debt, and interest rates rests on one piece of arithmetic that takes five minutes to learn: a bond’s payout is fixed, but its price is not. Once you see that, the entire machinery of modern monetary policy (from quantitative easing to the Bank of Japan’s trap) stops being mysterious.
The Machine
A Bond Is a Fixed Promise With a Floating Price
A government bond is the simplest financial contract there is. The government borrows money from you today and makes two promises in writing:
- : the amount repaid at maturity. Call it $1,000.
- : a fixed annual payment, set as a percentage of par on the day the bond is born. A 5% coupon means $50 per year, every year, until maturity.
Here is the detail everything else hangs on: the $50 never changes. Wars, elections, inflation, panics: the coupon is contractual. What does change is the price at which that bond trades between investors in the . And when a fixed payout meets a moving price, the effective interest rate (the ) has no choice but to move in the opposite direction.
The Math
One Bond, Three Prices
Take that 5% bond ($1,000 par, $50 fixed coupon) and watch what happens to its yield as the market price moves. Nothing about the bond changes. Only the price of admission does.
At par: $50 / $1,000 = 5.0% yield
the bond yields exactly its coupon rate: the seesaw is level
Price crashes to $500: $50 / $500 = 10.0% yield
sellers panic, the price halves, and the fixed $50 now buys new investors twice the return
Price soars to $2,000: $50 / $2,000 = 2.5% yield
buyers stampede in, the price doubles, and the same $50 is now a rounding error
That is the whole seesaw. Price up, yield down. Price down, yield up. It is not a market tendency or a historical correlation: it is division. The numerator ($50) is bolted down; only the denominator moves.
The full story adds one refinement. A bond bought at $500 also repays $1,000 at maturity, a built-in capital gain on top of the coupons. The measure that captures both is the , and it is the number quoted in every headline about “10-year yields.” The refinement sharpens the seesaw; it never reverses it.
The Core Mechanism
The Evidence
The Seesaw in Live Market Data
Below, the two ends of the seesaw side by side since 2018, in real, current data. The left panel is the price of TLT, an ETF holding 20+ year US Treasury bonds. The right panel is the 10-year Treasury yield over the exact same window. When the Federal Reserve began hiking in March 2022, yields surged, and the price of every existing low-coupon bond collapsed. Two views of a single mechanical fact.
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The Application
Why Central Banks Buy Bonds
Now run the seesaw backwards. Suppose you are a central bank and you want long-term interest rates lower: to cheapen mortgages, corporate borrowing, and above all your own government’s debt service. You cannot decree the 10-year yield. But you do not need to.
You walk into the bond market with a printing press and start buying. Buying pressure raises the price. And because yield is coupon ÷ price, pushing the price toward the ceiling mathematically forces the yield toward the floor. There is no persuasion involved, no announcement effect required: just the arithmetic of division, executed at scale. This is the entire engine of .
Central bank buys → demand ↑ → price ↑ → yield ↓
a price ceiling is a yield floor: the same fact stated twice
BOJ target (2016–2024): 10-year JGB yield ≈ 0%
achieved by standing ready to buy at whatever price pins the yield ("yield curve control")
The Bank of Japan took this logic to its terminus: it announced a yield target and committed to buy in unlimited quantity at the corresponding price. The seesaw does not argue with a buyer who cannot run out of money. How a central bank is legally allowed to do this, and why commercial banks happily sold it bonds yielding nothing, is the subject of the next article.
Key Numbers
$50
Fixed coupon on a 5% / $1,000 bond
Contractual. Never changes, whatever the price does.
10.0%
Yield if the price falls to $500
Half the price, double the yield: pure division.
2.5%
Yield if the price rises to $2,000
Double the price, half the yield. The seesaw never breaks.
−3.4 pp
US 10Y yield, 2018 peak → 2020 trough
QE-era buying drove prices to the ceiling and yields to ~0.5%.