A bit confused about how to think about trading cost as bps of the paper portfolio where there is also an opportunity cost.
For example: assume I want to trade 10,000 shares at $10/share (decision price), and assume for simplicity’s sake that arrival price = decision price, and that I actually buy 5,000 shares at a VWAP of $10.20.
The trading cost is ($10.20 - $10.00) x 5,000 = $1,000 which if I express as basis points on the paper portfolio would be $1,000 / ($10.00 x 10,000) x 10,000 = 100 bps
However, in reality, it really should be ($10.20 - $10.00) / $10.00 x 10,000 = 200 bps. Essentially, because I’m only actually filling the order for half of the shares, using the paper portfolio in the denominator makes it look as if the trading cost is only half of what it actually was on the shares I traded.
If we were asked to present the trading cost in bps terms, should it be 100 bps or 200 bps? And if we needed to do the market-adjusted trading price, presumably we have to do that agnostic of the number of shares traded (i.e. take the 200 bps as the true trading cost and subtract the market impact cost), but then would we need to adjust the answer for the delta between the total shares I wanted to trade and the number of shares I actually traded? (in this case, divide it by 2?)
Thanks for any help.