In this lesson · 7 sections
Almost everyone can recite that bond prices and yields move in opposite directions. Far fewer can say why, and the gap shows up the moment something unusual happens — a central bank cuts and the long bond falls, or yields rise and a portfolio of "safe" government paper loses more in a year than a diversified equity fund. The recitation is a slogan. The mechanism is arithmetic, and once you have done the arithmetic once, the slogan stops being something you remember and becomes something you can derive.
The confusion has a specific source: people carry equity intuition into a market where the cash flows are fixed. In equities, a higher expected return usually reflects a better business or a cheaper price, and the two travel together in the mind. In bonds, the payments are written into the contract and cannot change. The only variable left is what you pay for them. So the entire adjustment to a change in required return has to happen through price, and it has to happen in the opposite direction, because a fixed sum of money bought for less delivers more.
The seesaw, derived rather than asserted
Consider a bond with CHF 100 nominal, a 2% annual coupon and ten years to maturity, issued at par. It pays CHF 2 a year for ten years, then CHF 100. Nothing about that schedule will ever change.
Now suppose that a year later, comparable new bonds are being issued with a 3% coupon. Nobody will pay CHF 100 for a 2% stream when CHF 100 buys a 3% stream. The old bond must fall until a buyer earns 3% on it. Where does it stop?
Discount every cash flow at 3%. The ten annual coupons of CHF 2 are worth CHF 17.06 in present value. The CHF 100 principal, discounted ten years at 3%, is worth CHF 74.41. Total: CHF 91.47.
That is not a market opinion. It is the only price at which the fixed schedule delivers 3% a year, and the market enforces it by arbitrage. The seesaw is simply this calculation running continuously.
Run it the other way. If comparable yields fall to 1%, the same coupons are worth CHF 18.94 and the principal CHF 90.53, for a price of CHF 109.47.
Now look at the two results side by side, because they contain something the slogan never mentions. A one-percentage-point rise in yield cost 8.53. A one-percentage-point fall gained 9.47. Identical shock, different magnitude — the gain is larger than the loss. That asymmetry is convexity, and it is a real, structural feature of any instrument whose price is a sum of terms like 1/(1+y)ⁿ. Discounting is a curved function of the yield, not a straight line, and the curve bends in the owner's favour. The sibling lesson on duration and convexity measures it; here it is enough to see that it falls out of the arithmetic without anyone adding it.
Maturity is the amplifier
Repeat the exercise with a thirty-year bond: 2% coupon, yield moves to 3%. The coupons are now worth CHF 39.20 and the principal, discounted thirty years at 3%, only CHF 41.20. Price: CHF 80.40.
The same one-point move that cost 8.53 on the ten-year costs 19.60 on the thirty-year. The reason is not that long bonds are riskier borrowers. It is that discounting compounds: a change in the annual rate applies once for each year of waiting, so a franc due in thirty years is far more sensitive to the rate than a franc due in three.
This is the single most under-appreciated fact in retail fixed income. "Government bonds" is not a risk category. A three-month Confederation bill and a thirty-year Confederation bond have the same credit quality and completely different risk profiles. In 2022, when policy rates rose sharply across developed markets, long-dated sovereign bonds delivered drawdowns comparable to equity bear markets — not because anyone doubted the issuers, but because the exponent did its work. Investors who had bought duration in search of safety discovered they had bought a leveraged position on the level of interest rates.
The coupon size matters too, in the same direction. A high-coupon bond returns more of its value early, so its average waiting time is shorter and its price moves less for a given yield change. A zero-coupon bond, which pays nothing until maturity, is the most rate-sensitive instrument of its maturity that exists.
Why the loss is not the loss
Here is the part that genuinely trips up sophisticated people. If you own that ten-year bond and yields rise from 2% to 3%, your price drops from 100 to 91.47 immediately. But your return over a long enough holding period may be unchanged or better.
The reason is that two effects move in opposite directions. Higher yields reduce the present value of the remaining cash flows — that is the price hit, and it is instant. Higher yields also raise what every future coupon earns when reinvested — that is the income benefit, and it accumulates slowly. For a buy-and-hold investor these two effects offset, and they offset almost exactly at a horizon equal to the bond's duration.
Put concretely: buy the bond at 91.47 and hold to maturity and, provided the issuer pays, you receive 3% a year. The price recovers to 100 by contract — the pull to par covered in the first lesson — and the coupons compound at the new higher rate. The mark-to-market loss was a repricing of the timing of your return, not a destruction of it.
This is why a rise in yields is bad news for someone who must sell soon and good news for someone accumulating. It is also why pension funds — including Swiss Pillar 2 institutions, whose liabilities stretch decades — care about the relationship between asset duration and liability duration far more than about the price move in isolation. When rates rise, both sides of their balance sheet fall in value. Whether that is a problem depends entirely on which side falls further.
What actually moves the yield
The price follows the yield, so the causal question is what moves yields. Four things, roughly in order of how quickly they act.
Expected policy rates. Short-dated yields are close to an average of expected central bank rates over the instrument's life. When the SNB shifts its policy rate, or the market revises what it thinks the SNB will do, short yields respond immediately. Long yields respond only to the extent the change is expected to persist.
Expected inflation. A lender who expects prices to rise 2% a year requires compensation for that erosion before any real return. Swiss nominal yields have historically sat well below those of most other developed markets, and a persistently lower inflation record is a large part of the explanation. The lesson on inflation-linked bonds separates the nominal and real components properly.
Term premium. Extra compensation demanded for committing capital for a long time under uncertainty. It is not directly observable — it must be estimated — and it can be negative when investors want long duration badly enough, which is what happened during the era when the entire Confederation yield curve traded below zero.
Credit and liquidity. For anything other than a top-rated sovereign, the yield includes compensation for default risk and for the difficulty of selling. The credit spread lesson takes this apart.
Reading the seesaw correctly
Three practical consequences follow.
A falling bond price is not automatically bad news, and a rising one is not automatically good. What matters is your horizon relative to the bond's duration, and whether the yield move was driven by rates or by credit. A price fall caused by rising risk-free rates is a repricing you eventually earn back; a price fall caused by deteriorating creditworthiness is a genuine expected-loss revision, and no amount of holding to maturity fixes it if the issuer defaults.
Quoted headline yields say nothing about the risk you are taking to get them. A 5% yield built from a 2% risk-free rate plus a 3% credit spread is a different instrument from a 5% yield on a long-dated government bond, even though both print the same number.
And the pull to par is the anchor that makes bonds behave unlike equities. However violently a solvent issuer's bond moves in the interim, its price converges on a known number on a known date. There is no equivalent gravitational point in equities, which is precisely why "it will come back" is a defensible statement about a Confederation bond and a hope about a share.
What to take away
- Bond cash flows are fixed by contract, so the only way the market can change the return on offer is to change the price — the inverse relationship is arithmetic, not convention.
- A 2% ten-year bond repriced from a 2% to a 3% yield falls to 91.47; the identical move to 1% takes it to 109.47, and that asymmetry in favour of the holder is convexity, not a rounding artefact.
- Sensitivity scales with how long you wait for the money: the same one-point yield move costs roughly 8.5 points on a ten-year 2% bond and roughly 19.6 points on a thirty-year one.
- For a holder, a yield rise trades an immediate price loss for a permanently higher reinvestment rate, and the two roughly cancel at a horizon equal to the bond's duration.
- A price fall from rising risk-free rates is recoverable by waiting; a price fall from deteriorating credit is not, so always ask which component moved before deciding whether anything is wrong.
Sources
- Bruce Tuckman and Angel Serrat, Fixed Income Securities: Tools for Today's Markets — first-principles derivation of bond pricing and the price/yield relationship.
- Frank J. Fabozzi, Bond Markets, Analysis, and Strategies — worked mechanics of discounting, coupon effects and maturity effects.
- Antti Ilmanen, Expected Returns (2011) — evidence on term premia and the decomposition of bond returns into rate, inflation and premium components.
- Frederick Macaulay (1938), NBER — the original study introducing the duration concept underlying the horizon-offset result.
- Swiss National Bank — policy rate decisions, monetary policy assessments and the Monthly Statistical Bulletin for Swiss yield series.
- Swiss Federal Finance Administration (EFV) — Confederation bond issuance and outstanding maturity structure.
- Bank for International Settlements, Quarterly Review — analysis of the 2022 repricing in global sovereign bond markets.