Why Dividend-Adjusted Stock Prices Can Become Negative
Summary
The document investigates negative dividend-adjusted historical prices, using an example from an Indian listed company. The responses attribute the problem to an adjustment formula that subtracts a cash dividend as a fraction of the prior price. When the dividend exceeds that price, the resulting adjustment factor can become negative, making adjusted historical prices negative even though splits and proportional price changes should preserve positive prices.
One response gives an alternative reinvestment-based approach: adjust prices using multiplicative factors tied to dividends and prices, with backward adjustment applied before the ex-dividend date. Another suggests calculating split and dividend adjustment ratios and applying them to the original price series. The discussion says the alternative adjustment methods produce consistent returns, but it does not independently validate the data source or settle all conventions for unusual corporate actions. The central caveat is that adjusted prices depend on the vendor's methodology; researchers should inspect adjustment factors and verify that they reflect the intended dividend-reinvestment convention before using them downstream.
Key ideas
- Dividend and split adjustments are ordinarily proportional transformations that should preserve positive prices.
- A dividend larger than the prior price can make a subtraction-based adjustment factor negative.
- The responses describe multiplicative factors based on dividend reinvestment as an alternative adjustment approach.
- Researchers should inspect vendor adjustment conventions before relying on adjusted prices and returns.
Tags
Full text
# Asset Pricing and Negative Prices
# Asset Pricing and Negative Prices
I am running an asset pricing study. The data is from 1990 to 2020. When the data is adjusted for dividends and splits, stock prices of several firms become negative.
How does one handle negative prices and returns and the results downstream?
Sample Example
If you run this query - you shall be able to download data for SHANTIGEAR listedn on BSE - The adjusted price is negative (Obviously Adjusted close is the closing price after adjustments for all applicable splits and dividend distributions. Data is adjusted using appropriate split and dividend multipliers, adhering to Center for Research in Security Prices (CRSP) standards.) - https://in.finance.yahoo.com/quote/SHANTIGEAR.BO/history?period1=1026000000&period2=1624665600&interval=1d&filter=history&frequency=1d&includeAdjustedClose=true
## Answer by demully (score 3)
https://quant.stackexchange.com/a/66084
The methodology has to be wrong to generate negative prices. Dividends and splits both generate proportional shifts in nominal prices, that are positive. A proportional shift to any positive number generates a positive number.
The problem with the company given is that it seems to pay a >100% dividend to its previous close, which is why the previous adj close appears negative. Except this is Yahoo Finance's algo being lazy, being configured for US companies where this kind of thing does not happen.
What it should do with a company paying a dividend of 100% of price is not take the price to zero, but halve it! There in lies your problem.
## Answer by emot (score 1)
https://quant.stackexchange.com/a/66131
This has already been answered but I will try to provide more insight.
The formula that you should use for forward adjusting: $$P_{adj, j}=P_{unadj, j}*\prod_{i=1}^{j} f_i$$ $$f_i=1+\frac{d_i}{P_{unadj, i}}$$ where $d_i$ is a dividend paid on day $j$ and $P_{unadj, j}$ is unadjusted price for that day.
for backward adjusting we have: $$P_{adj, j}=P_{unadj,j}*\prod_{j}^{1} f_j$$ $$f_j=\frac{1}{1 + \frac{d_{j+1}}{p_{unadj,j}}}$$
where we adjust the prices BEFORE the exDate.
The idea with this formula is that we reinvest the dividend back into the stock and hold more units of that stock. Those two methods give us exactly the same returns. As you can see with those two methods above, you can't get negative prices, no matter what is the value of dividend. For the dividend 6 and price of 5.5 that you wrote in your comment, you would get $f=0.45$. This is the correct formula imho.
The formula Yahoo uses is: $$f_j=1 - \frac{d_j}{p_{unadj, j-1}}$$ which is obviously wrong. This formula can yield negative values as you have noticed, but for small dividends (compared to stock price) this method and backward method above yield similar results.
References: https://quantdare.com/approach-to-dividend-adjustment-factors-calculation/
## Answer by Joshua Ulrich (score 1)
https://quant.stackexchange.com/a/66168
This seems to work for me:
```
library(quantmod)
# import data
sym <- "SHANTIGEAR.BO"
x <- getSymbols(sym, auto.assign = FALSE)
div <- getDividends(sym)
spl <- getSplits(sym)
# calculate adjustment ratios
ratios <- adjRatios(close = Cl(x), dividends = div, splits = spl)
# apply adjustment ratios to original data
adjusted <- adjustOHLC(x, ratio = ratios$Split * ratios$Div)
# chart original series and add calculated adjusted close
chart_Series(x)
add_Series(Cl(adjusted), on = 1)
```
Notice that the `adjusted` values are lower at the beginning of the series because the return from dividends have been added, increasing the return.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.