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So from what I've read, the adjusted close price on a stock is the close price taking into account any dividend and stock split events.

That would indicate to me that unless there is a stock split, the prices in between each dividend period same be equal. So for example, if the dividend for a stock was 20 cents, then the adjusted close between the dividend date and the last dividend date should be 20 cents.

However, this doesn't seem to be the case. For example, I'm looking at BHP (http://real-chart.finance.yahoo.com/table.csv?s=BHP&d=10&e=28&f=2016&g=d&a=4&b=29&c=1987&ignore=.csv).

Now this stock had a dividend event on 31/08/2016 which paid out 28 cents. I also know for sure there was no stock split event around this time.

That indicates to me that for everyday before that, the adjusted close price should be 28 cents lower than the close price.

However, as you can see from the screenshots, the diff between close and adjusted close is not the same each subsequent day. It's always slightly different.

enter image description here

Why isn't the difference always 28 cents? What is causing the small differences? How exactly is adjusted close worked out? I also tried this with a number of stocks and they also exhibited the same behaviour.

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Prices are adjusted for return and not payout. So if you take the ratio of the close price and the adjusted close price, it should remain constant.

The idea behind a total return (back-)adjustment is to give you a feeling how much money you would have needed back then to reach the price today under the premise that all distributions (dividends, spin-offs, etc.) are reinvested instantly and that reinvestment doesn't cost anything.

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