Adjusting Stock Open Prices with the Adjusted-Close Factor
Summary
The note explains how to estimate a stock’s adjusted open price when raw open and close prices and adjusted close are available. Its practical approach is to apply the same multiplicative adjustment factor used for adjusted closing prices: scale the open by adjusted close divided by raw close. Adding the difference between the two closing prices is not the method recommended in the response.
With split and dividend data, the adjustment can instead be reconstructed from corporate actions on each ex-date, applying the split ratio and dividend amount to the prior price adjustment. The responses say that multiplying by the published adjustment factor is usually adequate and present the more detailed formula as an alternative. They also flag limits: other corporate actions may require additional treatment, and rounded dividend or price data can accumulate precision errors, particularly across multiple adjustments. The note offers a data-adjustment procedure, not a comparison of data vendors or an accuracy study.
Key ideas
- Estimate adjusted open by scaling raw open with adjusted close divided by raw close.
- A multiplicative adjustment reflects the common method used to construct adjusted closes.
- Split and dividend records can support a more detailed adjustment across ex-dates.
- Other corporate actions may require adjustments beyond splits and dividends.
- Rounded source data can cause precision loss across repeated adjustments.
Tags
Full text
# If I have adj.close and close, how to convert open to adj.open?
# 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.
## Answer by David Addison (score 3, accepted)
https://quant.stackexchange.com/a/33633
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.
## Answer by misantroop (score 3)
https://quant.stackexchange.com/a/33795
```
Factor = 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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.