A-Shares Pre-adjustment: How to Connect the Candlestick Data (The Core Issue)
With this domestic set of metrics, the public anchor points are actually not difficult to find. The SZSE has provided the reference price formula for ex-rights and ex-dividends:
$$ \text{Adjusted (Dividends/Rights) Reference Price}=\frac{(\text{Previous Closing Price}-\text{Cash Dividend})+\text{Rights Issue Price}\times\text{Share Change Ratio}}{1+\text{Share Change Ratio}} $$The formula for “adjusted forward division” written in the East Money Encyclopedia and this approach are basically on the same track:
$$ P'=\frac{(P-D)+K\times r}{1+r} $$Here, $P$ is the pre-adjusted price, $D$ is the cash dividend per share, $K$ is the rights issue or new stock price, and $r$ is the proportion of circulating shares change. The most important point about this formula is not whether it has division, but that the cash dividend is deducted based on a fixed amount.
Thus, if a company’s actions are limited to cash dividends—with no stock transfers or bonus share allocations—the formula will directly simplify to:
$$ P'=P-D $$The consequence of this matter is very direct: for A-shares listed many years ago with high accumulated dividends, if the historical price is continuously extrapolated backward in time, it can indeed be calculated as a negative number. Occasionally, you might see such extremely early negative values on East Money (Dongfang Caifu). This does not necessarily mean that they have calculated it incorrectly; it is more likely that they are simply adhering to this common set of domestic pre-adjustment definitions.
I now prefer to understand it as an approach that prioritizes “graphical continuity.” If you open the software today, and the current price remains stable while projecting downward from previous K-lines, the chart connects smoothly, and the technical indicators look more natural. This is very useful for market analysis, but it does not naturally equal the total return series.
HK/US Stocks Adjusted Close, First, how to calculate the total return
Yahoo’s official definition of Adjusted close is very straightforward: It adjusts for both stock splits and dividends, and the dividend multiplier is calculated based on “the proportion of the dividend to the price.” Yahoo also explicitly states that one of the main purposes of doing this is to avoid negative historical prices.
If written as a formula, the common approach is to first assign a multiplier to each company’s action:
- Stock split multiplier: e.g.,
2-for-1, historical price times0.5 - Dividend multiplier:
m=1-D/C_{t-1}
where $D$ is the cash dividend per share, and $C_{t-1}$ is the closing price before the ex-dividend date. Then, multiplying all subsequent corporate action multipliers sequentially yields the cumulative adjustment factor $F_t$:
$$ F_t=\prod_{j>t}(s_j\times m_j) $$Therefore, the adjusted price is:
$$
P_t^{adj}=P_t\times F_t
$$
The meaning of this approach is very clear: It approximates what the total return would be if dividends were continuously reinvested back into this stock. Therefore, it is naturally better suited for calculating rates of return, long-term backtesting, and cross-period comparisons. This methodology is fundamentally different from the domestic approach that simply deducts cash dividends directly from historical prices; even though both might appear to adjust the candlestick charts, they are not the same at their core.
I'll take this opportunity to add that the old article from June implied that Yahoo / yfinance's adjusted data and Tushare's qfq are "completely the same thing," which is not strictly accurate. A more precise way to put it is: **they belong to the same family, both being multiplicative or factor-type adjustments, but the normalization anchor point may not be the same.**
## Adjustment Factors Are Not a Universal Translator
The core issue lies right here. Many people, upon seeing the phrase "adjustment factor," assume that all markets can be abstracted into a single set of factors and then simply apply `price * factor` without question. This assumption is largely valid within the common adjusted close systems used by Hong Kong and US stocks, but it may not hold true in China's pre-adjustment system.
The reason is not complex. This set of precise reweighting formulas used domestically in China is actually an affine transformation, not purely multiplicative:
$$
P'=\frac{1}{1+r}P+\frac{Kr-D}{1+r}
$$
In other words, it is essentially:
$$
P'=aP+b
$$
If a cash dividend occurs, the constant term $b$ will not be zero. When multiple corporate actions stack up, what you get is not a single cumulative multiplier, but a series of multiplications and additions of affine transformations. At this point, **a single "adjustment factor" is insufficient**; you need at least event information such as cash dividends, ex-rights prices/book values, share change ratios, or the equivalent $(A, B)$ parameters.
Therefore, the answer is quite clear: **the concept of the adjustment factor cannot be directly generalized within these two sets of schemes.**
- In the commonly used adjusted close system abroad, the adjustment factor is the core focus.
- In this precise adjustment system domestically, the factor can only cover percentage changes related to "stock splits / bonus issues"; once it encounters cash dividends, a single factor cannot accommodate them.
This is also why directly comparing pre-adjusted domestic software data with Yahoo adjusted close using the same metric often leads to increasingly confusing results.
## Where Does Tushare Really Stand?
The official documentation actually writes it very clearly. The formula provided in Tushare's A-share adjusted closing price data is:
$$
\text{Pre-adjusted Price} = \text{Daily Closing Price} \times \text{Daily Adjustment Factor} / \text{Latest Adjustment Factor}
$$
The same page also clearly stated two things:
- It dynamically reprices/reweights based on your specified `end_date`
- It uses a "dividend reinvestment" model
These two sentences are sufficient for qualitative description. **Tushare's A-share `qfq` is conceptually closer to the multiplier/factor type adjusted close found overseas, rather than East Money’s precise adjustment pre-adjustment method.** However, it retains its own normalization approach: it does not always anchor to today, but anchors to the `end_date` of your current query window.
So, the positioning for Tushare can be condensed into a single sentence:
- It does not use the same pre-revised definition as East Money Fortune.
- It is more similar to Yahoo, but the values may not be identical at every point.
Tushare later also added adjusted factors and adjusted data interfaces for HK stocks and US stocks, with the official description remaining `price * adj_factor = Adjusted Price`. This further illustrates its product design thinking: fundamentally, it is based on multiplicative factors.
## Back to Backtesting: First Define the Parameters, Then Discuss Accuracy
Once you understand this matter, many of the debates will actually disappear automatically.
If you want:
- Aligned with screenshots from domestic financial charting software
- Current price remains unchanged, historical K-lines are connected (or 'aligned flatly')
- Viewing the "pre-adjusted graph" in the context of A-shares
In that case, you should use the domestic set of standards for precise re-weighting/adjustment.
If you are looking for:
- Backtest Return Rate
- Total Return from Dividend Reinvestment
- Long-Term Strategy Evaluation
You should better use the multiplicative factor metrics/basis, such as Tushare's `qfq` or Yahoo's `Adjusted close`.
The biggest problem with that old piece from June wasn't that it was entirely incorrect, but rather that it merged two distinct sets of definitions into a single "definitive standard." Looking back now, what you should truly remember isn't that "proportional methods are always correct and addition/subtraction methods are always wrong," but rather: **Are you trying to fit the data visually, or are you calculating returns.** If these two questions aren't separated first, everything that follows—backtesting results, candlestick comparisons, even 'why negative numbers appear'—will all become hopelessly tangled together.
## References
- [ChatGPT Shared Dialogue: Adjusted Price Calculation Difference Analysis](https://chatgpt.com/share/69e653e4-2814-83ea-bd7d-4233343ca9cf)
- [Tushare: A-Share Adjusted Price Data](https://tushare.pro/document/2?doc_id=146)
- [Tushare: US Stock Adjusted Price Data](https://tushare.pro/document/2?doc_id=338)
- [Yahoo Help: What is the adjusted close?](https://help.yahoo.com/kb/SLN28256.html)
- [Shenzhen Stock Exchange: How to Calculate Adjusted (Ex-Dividend) Price?](https://investor.szse.cn/institute/video/
## Writing Notes
### Original Prompt
```text
$blog-writer analyze the content here: https://chatgpt.com/share/69e653e4-2814-83ea-bd7d-4233343ca9cf, and also historical articles 27 - where to find backtesting data? First, outline the common pre-adjustment calculation formula used in China, then outline the common pre-adjustment calculation formula used overseas. Regarding the concept of adjustment factor/reversion factor, can it be general for both schemes? What type of method does Tushare's data belong to?