Close Short Accounting

[jalextowle]

Adds the accounting used to close shorts.

The short pnl is given by $s_{pnl} = c_0 \cdot z_0 - c_1 \cdot z_1 + loss$, where $c_0$ is the initial share price, $c_1$ is the share price when the short is closed, $z_0$ is the amount of shares the bonds were worth at opening, $z_1$ is the amount of shares the bonds are worth at closing, and $loss = y - c_0 \cdot z_0$. $y$ is the equal to the amount of bonds that were shorted. Thus, we can restate the short pnl as $s_{pnl} = y - c_1 \cdot z_1$. We can generalize this to allow the partial closing of shorts by assuming that we have $c_i$ as the share price of the ith transaction, $z_i$ as the shares paid in the ith transaction, and $y_i$ are the amount of shorts closed in the ith transaction with the sum of the all $y_i$ equal to $y$. Then we have the short pnl given as:

$$ s_{pnl} = \sum_{i = 1}^{n} (y_i - c_i \cdot z_i) $$

Aside from trading pnl, shorts also receive interest on their shorts. The initial shares value of the bonds being shorted is given by $\frac{y}{c_0}$. In general, we can calculate interest on shares as $(c_1 - c_0) \cdot z$, so the interest on the bonds being shorted is given by: $(c_1 - c_0) \cdot \frac{y}{c_0} = (\frac{c_1}{c_0} - 1) \cdot y$. To generalize this to the case of partial closing, we again assume that we have $y_i$ bonds shorted in the ith partial closing where the sum of the $y_i$ equal to $y$ and that we have $c_i$ as the share price at the time of the ith partial closing. Then, the interest proceeds are given by:

$$ s_{interest} = \sum_{i = 1}^{n} (\frac{c_i}{c_0} - 1) \cdot y_i $$

Finally, we have that the total pnl is given by:

$$ s_{total} = s_{pnl} + s_{interest} = \sum_{i = 1}^{n} (y_i - c_i \cdot z_i) + \sum_{i = 1}^{n} (\frac{c_i}{c_0} - 1) \cdot y_i $$

[jrhea]

A few questions/comments and I'm cornfused about the share reserve accounting

[jrhea]

lgtm. approved