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Bonds are a form of IOU issued by governments or firms, to financial institutions, the BoE (or other central banks), or private investors. They are issued as a method of financing growth and expansion, or perhaps to improve a firms cash flow. The seller of the bond asks for a certain amount of money which they promise to pay back, along with interest, at a fixed date. The interest is the buyer's return, it is also known as the yield which is the percentage of interest on the original sum of money. For example I could issue a bond for £10 with an interest of £1, redeemable in a year; the yield on this bond is 10%. The yield usually takes in to account the risk of the bond; if a company is perceived unlikely to be able to repay the bond then investors will demand a higher yield, and the current interest rate as well as inflation. 

If the yield on other assets such as shares or bank accounts is higher than bonds than few people will purchase the bonds and hence demand will fall. From basic demand and supply we know that the yield of the bond will have to rise as supply is constant and yet demand has fallen. So the current interest rate is the opportunity cost of holding a bond (the yield is paying you for not investing your money in other assets). Inflation also affects the yield, as if inflation is high then the real return (after inflation is taken into account) will be lower, and so a high yield will be demanded to offset the effects of inflation.
Bond buyers may also demand a higher yield the longer the length of time the bond is in issue. This is because they have to guess what they believe interest rates will be over time and so want a fair rate as their money is effectively 'locked-in' (although they could potentially sell the bond).

Bonds can usually be sold on. For example if I buy a bond from Company X for £10 (with a yield of 10% = £1) I can sell this to Investor 2 for an agreed price. If the bond becomes more risky then I may only be able to sell the bond for £9 to Investor 2. I would want to sell it as it reduces my exposure (the risk I face if the bond isn't repaid) and at £9 the yield increases. This is because the interest is still £1 but the bond price is lower, the calculation would be [(Interest/Bond Price) * 100] which would equal 11%, which is a better yield and may entice Investor 2 to purchase the bond (which I perceive as risky) from me.

The bond market works similarly for governments who issue debt to financial public spending. The UK government issues debt which is known as Gilts (the US issues US Treasuries, the Germans issue Bunds and the Japanese issue JGBs). The yield of government bonds are usually a lot lower than the yields for bonds issued by firms - the reason for this is that government yields are generally seen as being safer (although some countries are an exception) as they are less likely to default and hence it is a safe place to 'store' one's wealth.

As mentioned above bonds can be traded on the bond market and can also be speculated. If speculation drives the yield on existing bonds higher (as a result of a lower price) then issuers will have to increase the face-value yield (the initial interest they pay) in order to attracted demand for the bond. Therefore the bond market has profound influence on the economy.

Page last updated on 20/10/13