Bond commentary assumes the reader already understands the price-yield relationship. Many people reading it do not, and the confusion makes the rest of the coverage unreadable.
The mechanical relationship
A bond pays fixed amounts on fixed dates. Those payments do not change.
What changes is what somebody will pay for the right to receive them.
If the price falls, the same fixed payments represent a higher return to the new buyer. That return is the yield.
So price down means yield up, and it is not a coincidence or a market convention. It is arithmetic.
Coupon against yield
The coupon is the stated interest on the face value, fixed at issue.
The yield is the return based on the current price.
A bond issued with a low coupon during a low-rate period, trading in a higher-rate environment, will trade below face value, and its yield will exceed its coupon.
Which is why holders of long-dated low-coupon bonds took large losses when rates rose. The bonds still pay what they always paid. What people will pay for them fell.
Duration
The measure of how sensitive a bond's price is to a change in rates.
Longer maturity means higher duration, because more of the value sits in payments far in the future, which are discounted more heavily as rates move.
Lower coupon also means higher duration, for the same reason — less value arrives early.
Duration is quoted as a number of years, and it approximates the percentage price change for a one percent move in rates.
A bond with duration of eight loses roughly eight percent if rates rise one percent, which is a large number for something described as a safe asset.
The safety confusion
Government bonds are described as safe, and the word covers two different things.
Credit safety — the likelihood of being repaid — is genuinely high for major sovereign issuers in their own currency.
Price safety — the stability of the market value before maturity — is not high at all for long-dated bonds.
Someone holding to maturity receives what was promised regardless of interim price. Someone who must sell earlier does not.
Conflating these two produced a great deal of surprise when long bond prices fell sharply.
The yield curve
Plotting yield against maturity produces a curve, normally upward sloping, since lenders generally demand more for lending longer.
When short yields exceed long yields, the curve is inverted, which has historically preceded recessions with a reasonable record and a long and variable lag.
The interpretation is that markets expect rates to fall, which usually implies expecting economic weakness.
Whether the relationship remains reliable is debated, since central bank bond purchases distorted long yields for an extended period.
Real against nominal
A nominal yield is the stated return. A real yield subtracts expected inflation.
Inflation-linked bonds trade on real yields directly, with the principal adjusting for inflation.
The difference between the nominal yield and the real yield on comparable maturities gives a market-implied inflation expectation, which is one of the more useful numbers available and is quoted daily.
Credit spreads
Corporate bonds yield more than government bonds of the same maturity, and the difference is the credit spread.
It compensates for default risk and for liquidity, and it widens when the economic outlook deteriorates.
Which makes spreads a market view on corporate health, moving faster than any published economic data.
The lowest-rated categories have spreads that move violently, and the yield on offer in those categories reflects a genuine probability of not being repaid rather than a free lunch.
Why this is worth the effort
Bond markets are considerably larger than equity markets and drive most of the pricing across everything else.
Mortgage rates, corporate borrowing costs, pension scheme valuations and equity discount rates all trace back to these yields.
Which means understanding the price-yield relationship is the entry point to understanding why unrelated things move together.
None of this is a recommendation about holding bonds or anything else. It is a description of a mechanism, and decisions involving money should involve someone regulated to advise on them.
Convexity
The refinement to duration that matters at large rate moves.
Duration assumes a linear relationship between rates and price, which is an approximation.
The actual relationship curves, so a bond gains slightly more when rates fall than it loses when they rise by the same amount.
That curvature is convexity, and it is generally favourable to the holder, which is why it commands a small premium in pricing.
Bonds with embedded options behave differently. A callable bond can be redeemed early by the issuer, which caps the price gain when rates fall, producing negative convexity — the worst combination for a holder.
Ratings and what they measure
Credit ratings assess the probability of default and, in some scales, the expected recovery if it occurs.
They do not assess price volatility, liquidity or suitability, which are separate questions frequently conflated with credit quality.
Rating changes tend to lag market pricing, since spreads move on information before agencies act, which limits their usefulness as a trading signal while retaining their role in regulatory and mandate frameworks.