# Bonds

## Bond yields

### Coupon payments

A coupon payment is the regular payment that the holder of a bond gets over the life-time of the bond, until it finally matures, say in 5 years’ time. Coupon payments are typically made twice yearly by the bond issuer to the bond holder. The ‘face value’ (called par value) of a bond is determined when the bond is issued and is the value of the bond at the point it matures.

Bonds can be categorised in terms of their life to maturity, with short-term bonds maturing in less than 3 years, medium-term between 4 and 10 years, and long-term bonds greater than 10 years.

Before technological advances removed the need to physically cash-in coupons, the issuer would sell a bond and provide the number of coupons appropriate to the length of the bond to maturity. For example, a 5-year bond would typically have 10 coupons attached, given that coupon payments are commonly paid twice a year.

### Coupon rates

The coupon rate is the percentage of the value of the coupon paid in relation to the bond’s par value. Not all bonds have a fixed coupon rate – zero coupon bonds do not pay regular rate of interest, but pay the par value at maturity. For these to be attractive to buyers of bonds they are sold at a discounted price below the par value.

Floating rate coupons have a variable interest rate, which can be changed on a periodic basis. The rate on these is usually tied (pegged) to another security – typically Treasury Bills. As bill rates change, bond rates are adjusted in the same direction.

For example, a fixed rate government bond issued at a par value of £1,000 may receive two coupon payments each year of £50 each, giving an annual return of £100. In this case the coupon rate is 100/1,000, which is 10%. The coupon rate will stay at a fixed rate, irrespective of the market interest rate.

### The current yield and bond prices

Of course, the actual return to the investor (the current yield) depends upon the actual price paid for the bond, which can rise or fall as a result of being traded in the secondary bond market. Bond prices can vary over the life of the bond, with bond prices depending on demand and supply-side factors, such as the yields on alternative bond or other investments, which can make them more or less attractive.

So, if the market price of the nominal £1,000 bond falls to £950, the current yield would rise to 10.53% (100/950). Hence, the ** price of a bond and its current yield vary inversely**. If an investor pays more than the face value, par rate – i.e. pays a premium – the yield will fall. For example, if the investor pays £1050 for the bonds, the yield will fall to 9.52% (100/1050).

### Yield to maturity

If an investor wishes to purchase an existing bond, they are likely to want to assess the yield they will gain between the purchase date and the maturity date* – *shortened to* ‘yield to maturity’* (YTM). While the coupon rate is the rate which is paid out per year as a percentage of the bond’s par value, the yield to maturity is the *total appreciation* which takes place over the life of the bond remaining at the point of purchase, expressed as an annual % figure. The YTM indicates how much an investor will earn if the bond is held until it matures, including the value of the remaining coupon payments as well as the return (the capital gain, or loss) of the principal sum upon maturity.

This value will take into account when the bond is purchased and the years left to maturity, and the price paid. YTM is widely used to compare different bonds.

In our example, if an investor pays £950 for a par value bond of £1000, with two years to maturity, as well as receiving the fixed £100 per year for two years, the investor will also benefit from the movement in the bond price paid, from £950 back to the par value of £1000 at maturity. When we add this £50 increase to the (remaining) coupon payments of £100 per year, and spread this out over the two years left, we can calculate the YTM.

In practice, there are plenty of software programmes and spreadsheets to enable the yield to maturity to be calculated.