What Trade Data Can and Cannot Reveal About Shareholder Cost Basis

Summary

The document asks whether one can track, at a given time, how many shares were acquired at each historical price. It illustrates this with a small stockholding: shares purchased at one price and some later sold at another. It proposes representing each investor by share count and average cost, with the price distribution serving as information about other investors in a game-theoretic model.

The post does not answer whether such a distribution is available or give a method to estimate it. Its setup raises an important limitation: ordinary market transactions record trades, but they generally do not identify which holders bought or sold each share, so aggregate trade prices alone cannot reconstruct every investor’s current cost basis. The proposed distribution would require assumptions or investor-level data, and the document offers neither research references nor empirical evidence.

Key ideas

• The proposed function counts shares by their acquisition price at a particular time.
• The author frames investor holdings and average cost as states in a game-theoretic model.
• The document asks about terminology, research, and possible data sources without answering them.
• Public trade records do not by themselves identify each share's current owner or cost basis.

Tags

# How can I know the distribution of how many shares were bought in specific price?


# How can I know the distribution of how many shares were bought in specific price?












Given a stock and any time $t$, is there a way to find the distribution $f_t$ $$f_t: \text{price}\ p \rightarrow \text{in current time $t$, how many shares were bought in price $p$}$$

For example, a stock has 3 shares labeled as ($s1$, $s2$, $s3$).

In day1, ($s1$, $s2$, $s3$) are bought at price $\\\$1$, $f_{t_1}(1) = 3$ and all other $f_{t_1}(x) = 0$ for $x != 1$;

In day2, $s2$, $s3$ were sold at $\\\$2.5$, then $f_{t_2}(1) = 1$, $f_{t_2}(2.5) = 2$, $f_{t_2}(x) = 0$ for $x != 1, 2.5$;

I want to model stock as a game theory problem: every player as $(\text{number of shares}, \text{average cost})$ or $(0\ \text{shares})$, therefore given a specific player, its strategy will depend on personal state and the environment $f_t$ (encoding the information of all other players).

My questions:

- Is there any terminology for this $f_t$? Or is there any research in this area? Thank you so much.

- Where can I find the information of $f_t$ for a given stock? If there is no direct source, is there a way to derive this $f_t$ from open source?

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.