So we have seen what a bond is, we have talked a little about who issues bonds and why, and we have identified some of the key risks associated with holding bonds. Now the interesting stuff starts.

As we have seen, ‘the higher the risk of default, the higher the return the bond’s issuer will need to offer to compensate for that risk’. But what is a bond’s return? The key word here is yield.

Yield is the percentage return your bond investment promises at any given price. In its most simple form - known as ‘current yield’ or ‘coupon yield’ - it can be expressed with this formula:

Take a ‘straight bond’ with a face value of $1000 paying a 5% coupon. If you were to buy it for $1,000, the current yield would simply be 5% ($50 / $1,000). So, when you buy a bond for face value, the yield is simply the coupon, or interest rate.

Unfortunately, it gets more complicated. In the real world, when people talk about yield, they are usually talking about "yield to maturity." This represents the total return you can expect if you buy a bond at a given price and hold it until it matures. It is a complicated calculation without a spreadsheet or a bond calculator but the principle is pretty straightforward.

The return on a bond is composed of three elements:

1. the interest paid on the bond - the coupon          
2. the return on interest paid on the bond that is reinvested - i.e. interest on interest    
3. the capital gain or loss on the bond in terms of its price

Taking our 5% coupon bond again, if you had bought it in the market for $950 rather than $1000 (i.e. 95 rather than 100), a ‘yield to maturity’ calculation would take account of the fact that the bond you bought at 95 will pay you 100 when it is due. What is more, it would also assume that you reinvest the coupons at the same rate as is paid on the bond and calculate the compounding effect.

Now obviously, this is going to give you a much better idea of the real return on your investment. If you lend someone $950 and get $1000 back you are making a return of some kind. Similarly, if you are reinvesting coupon interest you are making a return too.

Now in fact, even though it is a widely used measure, professionals don't consider 'yield to maturity' to be particularly accurate either - preferring something called 'total return analysis' - but to be honest, you really don't need to know about this.

What you do need to know about though is the inverse relationship between price and yield and the 'yield curve'.

The inverse relationship

A bond’s price and a bond’s yield are inversely related; that is to say, when a bond’s price falls its yield rises and vice-versa. Why?

Let's look at our 5% coupon bond again. If you were to buy it for $1000, the current yield would simply be 5% ($50 / $1,000). But if the price drops to $950, the yield - for anyone who bought the bond for $950 - rises to 5.26% ($50 / $950). Intuitively, this is because the guaranteed coupon - $50 - is now a greater percentage of the price of the bond.

Conversely, if you buy the bond for $1000 and its price rises to $1050, the yield  - for anyone who buys the bond at $1050 - falls to 4.76% ($50 / $1050). This is because the guaranteed coupon - $50 - is now a smaller percentage of the price of the bond.

This simple relationship raises all sorts of important questions. For now though we will consider just one: If yields and prices move in opposite directions, why are both high yields and high prices considered good things? The answer depends on your perspective.

If you are a bond buyer, high yields are what you want, because you want to pay $950 for that $1,000 bond.

Once you own the bond, however, you want its price to rise. You have already locked in your yield, and if the price rises, it can only be a good thing - especially if you need cash and want to sell the bond to get it.

Now let's look at the yield curve.