↓ Today
You pay £98.01 for each £100 of face value.
The rate
What the yield is
How do we compare gilts of different coupon and maturity? What is your actual return on the gilt of a fixed coupon and maturity at the market price? This is where yield comes into play. There are various ways to think of yield, here we will be using the conventional "Yield to Maturity". In plain terms, Yield to Maturity is the annualised return you earn if you buy at today’s market price, hold to maturity, receive every coupon, get par back at the end, and reinvest those coupons at the same yield. It is not the coupon, and it is not a forecast of what you will earn if you sell early — the price can still move. It is the conventional way the market quotes “what this gilt returns at this price” henceforth referred to simply as yield.
What the gilt pays
Take a conventional gilt with a 4% coupon and two years left. For each £100 of face value it pays £2 every six months, four times. The last payment also returns the £100. Suppose the price today is £98.01.
↑ 6 months, 1 year, 18 months
Coupon, £2 each time.
↑ 2 years
The last coupon, £2, and the principal, £100.
The yield is the rate that gets you back to the price
A pound in two years is worth less today than a pound in six months, because you have to wait. The yield is the single rate that, used on every payment, makes the four future pounds add up to the £98.01 you pay now. UK gilts compound that rate twice a year, because the coupon arrives twice a year. At 5.06% a year, each half-year multiplies by 1 + 5.06% / 2, which is 1.0253.
£2 in 6 months
Divide by 1.0253. Worth £1.95 today.
£2 in 1 year
Divide by 1.0253 squared. Worth £1.90 today.
£2 in 18 months
Divide by 1.0253 cubed. Worth £1.86 today.
£102 in 2 years
Divide by 1.0253 to the fourth. Worth £92.30 today.
£98.01
£1.95 + £1.90 + £1.86 + £92.30. That is the price. The rate that does it is the yield, 5.06%.
When the price falls, the yield rises
A gilt is bought and sold at a price, in pounds for each £100 of face value. The yield is the rate that makes the payments still to come worth that price. Pay less for the same coupons and the same money back, and the rate is higher. Pay more, and the rate is lower.
Dealers and investors usually talk in yield, because a yield can be compared across coupons and maturities, and a move is quoted as a change in that rate. The gilt is still transacted at a price. Experiment by changing the price, coupon, and maturity of a hypothetical bond below:
The key thing to remember is that as prices go down, yield goes up, and vice versa. In other words, if there is less demand for gilts, the price goes down, and the return goes up. This makes sense as we know that the coupons and final payments are fixed, so if we pay less for these fixed cashflows (price down) the return we are getting is higher (yield up). Equivalently, if the perceived risk of UK debt goes up, investors demand a higher return.
A key component of yield comes from inflation, or more accurately, expected inflation. We can see that for a conventional gilt the cash flows are fixed by the coupon and the maturity. But what if those cashflows fixed into the future give us pounds that buy less than we expected?
Expected inflation is the largest piece of a ten-year gilt. The next page opens that yield into its pieces, and sets the term premium beside the expected path of short rates.