In most indices the weights are free float market capitalisation of each constituent. Why is it that the core reading use the following formula most of the way through the notes: I(t) = sum N(t,i) x P(t,i) / B(t) where N(t,i) = number of shares issues for constituent i at time t This is weighting by number of shares, rather than market capitalisation, not quite sure why you would want to do this (since number of shares is kind of meaningless, it's the total value of the shares that matters - e.g. scrip issues don't add any value!) I would have thought they should be saying something more like MV(t, i) instead or just leave it as a generic w(t,i)? It feels like I am missing the point here perhaps...
The intuitive formula is that on page 2 of Chapter 14, in which the wi's will be based on market capitalistions. You can then show (and doing so has never been required and so is not shown in the Course Notes), that after allowing for chain-linking, this formula becomes the one on page 4,ie: I(t) = sum N(t,i) x P(t,i) / B(t) where N(t,i) = number of shares issues for constituent i at time t. Note that B(t) itself will be based on the market capitalisations, after allowing for the chain-linking events since time zero. So, the index value does reflect the ratio of: (1) the total market capitalisation at time t (ie sum N(t,i) x P(t,i)) over (2) the total market capitalisation at the last chain-linking date/event (which will be relfected in the value of B(t))
