If I have adj.close and close, how to convert open to adj.open?

If I have adj.close and close values of a stock, and I want to calculate adj.open from open, should I just multiply the open prices with the percentage change (adj.close/close) or should I add the difference (close - adj.close) to each open price?

Thank you.

• There isn't enough information to do this. A stock split would be a multiplicative adjustment, while a dividend would be additive. – msitt Apr 10 '17 at 17:29
• I see. This is unfortunate lol. – moondra Apr 10 '17 at 19:30
• Is there any further information you require? I see you haven't accepted an answer. – David Addison Apr 25 '17 at 18:48
• Sorry, about that. I was meaning to get back to it, as I had to move onto another project. – moondra Apr 25 '17 at 19:10
• @Moondra. Thank you very much! Sorry to bother! I am happy to assist further if possible. – David Addison Apr 25 '17 at 19:42

Your first answer will get close enough for most practical applications; multiplicative factors are generally how adj. closes are calculated.

If you have dividend and split data, you can actually get a more granular answers as follows:

$P_{adj,\,t-1} = P_{adj, \,t} (1 + (\frac{P_{t-1}}{S} - P_t -D)\frac{1}{P_t})$

where $P$ is the actual price

$P_{adj}$ is the adjusted price

$S$ is the split ratio when $t$ is a split ex-date. Otherwise it is $1$.

and, $D$ is dividends per share if $t$ is a dividend ex-date. $D = 0$ when $t$ is not a dividend ex-date.

I hope this helps. I tested the formula and it appears to work. It may get more complicated if there are other kinds of corporate actions which affect share price. But then again, these corporate actions will be reflected in the adjusted close prices as published within most data sources which leads us back to the start: multiplication.

Factor = 1 + ( Close - Adjusted Close ) / Adjusted Close;
Adjusted Open = Open / Factor

It's important to remember that precision is lost since dividends are often given with 4 decimals and over multiple adjustments, the effect is significant. Many providers only give 2 decimals for prices which is the wrong approach when splits are taken into consideration.