The bid-offer spread is simply the difference between the price at which you can buy a share and the price at which you can sell it. There is a difference between the two prices because this is how the people who ensure there is a market for the shares (known as market makers') make money.
The bid price is what the market maker will pay you to sell your shares to them (it's what they'll bid for it). The offer price is what you have to pay to buy shares from them. The offer price is usually higher than the bid price so that the market maker can make a profit.
The bid-offer spreads on large companies in the FTSE 100 which trade in huge volumes every day tend to be tiny. Smaller companies can have very big spreads, as they are harder to trade, so an investment in a very small company can easily be worth 10%-15% less than the price you paid for it as soon as you have bought it.
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Bid-offer spreads are also a feature of investment trusts and exchange-traded funds (ETFs) and represent an extra initial cost of investing in them. In the case of certain funds having large bid-offer spreads it might be worth the effort of finding an alternative in order to minimise your investment costs.
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