There are lots of different definitions of 'yield'- it's easy to get confused. Here's the textbook
The general idea...
A bond with a face value of £100 may pay interest of £4 every year. £4 as a percentage of £100 is 4%, and this is described as a 'yield'.
This particular yield might be described as a 'face value yield', but it isn't. Traditionally it has the much shorter name of 'coupon'.
There are other types of yield.
'Current yield' is.....
When this same bond is traded in the market, it will change hands at a price agreed between buyer and seller. This reflects prevailing interest rates and perceptions of the bond's default risk.
Let's say this price is £80. The fixed annual interest of £4 now represents 5% of the bond's market price of £80. This 5% is the 'current yield' or 'current annual yield' or 'running yield' or 'income yield'.
'Yield to Redemption' is......
...... often called 'yield to maturity'.
Most bonds have a redemption date - a date at which the full face value will be paid to the owner (unless the owner defaults). The bond is said to 'mature' on that date.
Suppose, in the previous example, that the bond has 10 years to redemption. A buyer at £80 will then get £4 of interest per year for 10 years and £100 at the end of year 10. The £100 represents a premium of £20 over cost, or £2 per year spread over 10 years. When added to the coupon this gives an annual gain of £6. £6 as a percentage of £80 is 7.5% and is an approximation of the 'yield to redemption' (YTR).
In reality the YTR is calculated in a more sophisticated way to take account of the time value of money (or compounding). The true YTR in the above example is 6.8%.
The YTR is the only really meaningful yield measure for term bonds. We can expect all bonds with comparable terms and risks to have similar YTRs at any one time. Look at any list of actual bond yield and price quotations and see how the YTRs cluster together. Whereas the income yields are all over the place.
An irredeemable bond has, by definition, no redemption promise and therefore the YTR and the running yield are the same.
When interest rates change, so do capital values
The mathematics of yields determines how bond values fluctuate, and explains the capital risk inherent in a bond.
Back to our familiar 4% coupon bond. Let's say it's irredeemable. When issued at par (ie the buyer paid face value) the market rate of interest for this type of bond would have been 4%. If interest rates then move up (in response to changing economic conditions) to 5%, the current yield on this bond will also move to 5%. That means the price will go to 80 (the £4 coupon is 5% of 80)- a 20% loss. That's one reason why bonds are riskier than they look.
Long-term bonds are less risky than irredeemable bonds, and short-term bonds are less risky than long-term bonds. Play with the maths and see.
When redemption periods change, so do interest rates
Two bonds, identical in every respect except their time to redemption, will have different yields to redemption. The longer-period bond is slightly riskier than the shorter-period bond (more chance of bad things happening) and so will have a slightly higher yield to redemption. But not always. See Yield Curve