Bonds and interest rates: price, yield and the curve

A borrower, usually a government or a company, raises money by issuing bonds. Each bond has a face value, a rate of interest called the coupon, and a date of repayment called its maturity. Whoever holds the bond receives the coupons and, at maturity, the face value.

Once issued, a bond is traded between investors at whatever price they agree. The borrower’s promise does not change; the price of the promise does.

The coupon is fixed in money. The yield is the return a buyer earns at the price actually paid. Pay less for the same payments and the return is higher; pay more and it is lower. That is the whole of the relationship, and it is arithmetic, not a tendency.

It follows that when interest rates in general rise, existing bonds fall in price. Nobody will pay full price for an old bond when a new one, just as safe, pays more. The old bond’s price falls until its yield is in line with the new ones. When rates fall, the reverse happens and existing bonds gain.

A holder who keeps a bond to maturity, and whose borrower pays, still receives exactly what was promised. The change in price in between matters to anyone who sells before then, or whose holdings are valued every day.

How far a price moves for a given change in yield depends mostly on how long the money is tied up. If rates rise by one point, the holder of a one-year bond is paid too little for one year; the holder of a twenty-year bond is paid too little for twenty. The second bond’s price must fall much further to make up for it.

Duration is the measure of that sensitivity. As a rule of thumb, it is the percentage by which a bond’s price changes for a change of one percentage point in its yield: a duration of 7 means a fall of about 7 per cent in price if the yield rises by one point, and a similar rise if it falls. The approximation is good for small changes and less so for large ones.

Credit risk is the risk that the borrower does not pay in full or on time. A government borrowing in a currency it issues itself is treated as the reference for that currency. Every other borrower pays more, and the extra is called the credit spread.

Rating agencies grade borrowers, and the grades fall into two broad groups, investment grade and high yield. A rating is an opinion, not a guarantee, and ratings have been wrong. Spreads usually widen when investors are anxious and narrow when they are confident, so the bonds of a weak borrower can fall in price even when government yields have not moved.

Take one government’s bonds, set their yields out by maturity from a few months to thirty years, and the line through them is the yield curve.

The short end is tied closely to the central bank’s policy rate and to what is expected of it over the coming months. The long end reflects what investors expect of rates and inflation over many years, plus something extra for the uncertainty of lending for so long.

The curve usually slopes upwards, because lenders ask more for a longer wait. It flattens, or inverts so that short yields stand above long ones, when investors expect the policy rate to be lower in future than it is now. An inverted curve has come before a number of recessions, notably in the United States, which is why it is watched. It has also given false alarms, and it says nothing about timing.

Money can move between currencies. If the safe bonds of one currency pay more than those of another, holding the first is better rewarded, other things being equal, and money tends to move towards it. The gap between the two is the interest-rate differential, and it is one of the things a currency pair follows most closely.

What moves an exchange rate is a change in that gap against what was expected. A rate rise that everyone foresaw is already in the price; a decision or a sentence from a central bank that changes the expected path is what moves yields, and the currency with them. Yields at shorter maturities, such as two years, are widely watched for this reason, because they sum up where the policy rate is expected to go.

The link is not mechanical. A yield can rise because investors expect stronger growth and higher policy rates, and the currency commonly rises with it. A yield can also rise because investors fear inflation or doubt the borrower, and then the currency can fall while the yield climbs. In times of stress, money moves towards the currencies and bonds regarded as safe havens whatever they yield. What is left after expected inflation, the real yield, is often the more telling figure, and it is the one commonly set beside the price of gold, which pays no interest.