1. Review of Stochastic cost flow analysis for stock markets by Chun-Hun Chan, Alfred Ka Chun Ma

2. II.V Volume weighted average purchase price

3. II.V Volume weighted average purchase price

4. II.V Volume weighted average purchase price

5. II.V Volume weighted average purchase price

6. II.VI Effect of initial information
True estimate of
Suppose p0 : random variable but information is not enough to determine its distribution.

7. II.VII Effect of varying shares outstanding
Modified of R
The number of outstanding shares changes from time to time due to stock split, stock consolidation, rights issue scrip issue, share buybacks, stock dividends, M&A.
Suppose after some time J, the share outstanding K changes to i)
ii)

8. III. data
Dataset
In order to eliminate the effect of the uncertainly in the initial prices of the stocks we consider, Only IPOs from Jan 1, 1993
The information on equity new issues are obtained from Thomson Reuters SDC.
Among all IPOs from Jan 1, 1993 to Dec 31, 2004, only stocks that were offered in common shares are included.
New listings of investment funds and REITs are excluded in our dataset.
Considered the cost flow dynamics, the corresponding impact on the reference purchase price, and the disposition effects of the IPO stocks since the first trading day.
To avoid missing data, stocks delisted from NYSE within their first year of trading are filtered.
To eliminate the complexity due to varying shares outstanding discussed in II.VII, only stocks had unchanged shares outstanding during the first year since IPO are included.
Leave 51 stocks among 1182 IPOs on NYSE during the period.

9. III. data Manufacturing to insurance
About 20,000 transactions in a year give us sufficiently large sample for the empirical applications.(?)

10. IV. Empirical Applications
Three empirical applications
First, explore the differences between the reference purchase prices derived under traditional deterministic cost flow assumptions and the stochastic cost flow assumption.
Second, examine the value of high-frequency data by comparing the reference purchase prices computed using daily trading data and high-frequency trading data under the stochastic cost flow assumption.
Third, investigate the disposition effect under this framework and justify whether the use of the two ratios, namely the proportion of gains realized(PGR) and the proportion of losses realized(PLR), is appropriate for an empirical evidence of existence of disposition effect.

11. IV.I Comparison between representative purchase prices under different cost flow assumptions
Null hypotheses
The purchase price under the stochastic cost flow assumption is equal to that under FIFO, LIFO, HiFO, LoFO respectively.
The stochastic purchase price is equal to the volume weighted average price(VWAP) taking all transactions into account, and estimate of purchase price which does not require a cost flow assumption.

12. IV.I Comparison between representative purchase prices under different cost flow assumptions
The variance of the purchase price is very small
Estimates are mostly ranked third and fourth with 34 ranked.
Framework can be considered as a feasible and fair alternative to measure.

13. IV.I Comparison between representative purchase prices under different cost flow assumptions