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What is the All Ordinaries Accumulation Index?

It is not easy to get a precise definition of how the All Ordinaries Accumulation index is calculated.

The All Ordinaries price index is a capitalisation weighted index of price for the 500 stocks in the index. It measures the overall price movement of the market, or if you like, the overall capital gain or capital loss over a period.

However, investing in shares is about the total return, not just the capital gain or loss. The total return is the stream of dividends plus the capital gain or loss. The All Ordinaries Accumulation index tries to measure the total return. As I understand it, it is calculated by assuming that the cash dividend is reinvested on the ex date for each dividend. This is unreal, in my opinion, because you can not reinvest the dividend on the ex date, only on the payment date, or as soon after the payment date that the dividend hits your bank account and is cleared if it is received by cheque. So, it would seem that the accumulation index slightly overstates the total return. However, it does not assume the reinvestment of franking credits. This is a difficult one conceptually, and is best left at that for this question.

I compare my investment results to the All Ordinaries Accumulation index because it is the closest measure we have of total return from investing in shares.