I was wondering how to backtest using stock indices. For example, the FTSE100 has had changes in its components over time. How does one go about testing a time period from i.e. 2000 - 2018, even if there have been changes in the FTSE100 components in between the time? I.e., would it make sense to use the initial components of the FTSE100 (say at 2000) and continue using those components even if they have been removed from the FTSE later on?
You need to use the proper index constituents each point in time, recording index entrance, exit, splits, corporate actions etc. otherwise you will end up with sampling bias. If you are backtesting a trading strategy consider that your equity line will be affected by all those movements and you will need to rebalance as index constituents change. This will also likely materialize in transition costs, which should be included in backtesting together with stop loss and limits. This also explains why a backtest just considering the index returns is useless. To summarize, the data for the backtest should be the closest possible to the strategy.
Why would you want to use the components that were removed at an earlier point.Indices are supposed to be a representative of a market or a particular security type. If some company due to loss in market share or other reasons gets removed from the index, it means that the company is not a broad representative of the market, you would not want to keep it in present terms.