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vertciel

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Although the following question involves some terms using finance, I post it here since it seems to involve some probability. I hope that it will be fine.

Thank you very much for your help.

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**Problem:**Suppose that John buys shares in only one company and he does so as follows:

Date 1. He buys 10 shares @ $10.

Date 2. He buys 5 shares @ $20.

Date 3. He sells 6 shares @ $15.

Date 4. He buys 10 shares @ $20.

After Date 4, what is the average price per share for John's holdings?

**Attempt at Solution :**

Before Date 3, the weighted average price is given by:

[itex]\frac{10}{15}$10 + \frac{5}{15}$20[/itex]

and the total amount before Date 3 is just $30.

At Date 3, John sells [itex] 6 \times $15 = $90 [/itex] of this stock

[itex]\Rightarrow[/itex] Total stock holdings = [itex] 200 - 90 = $110 [/itex].

Now, this is where I am having trouble. To calculate the average price, it appears that I would need to identify specifically the purchase dates of the 6 shares sold at Date 3, since Date 1 and Date 2 involve different purchase prices.

Is this correct? If so, how would I continue my calculation if I were to assume that the 6 shares sold were randomly chosen from the 15 shares from Date 1 and Date 2?