Trading cost as bps of paper portfolio cost


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.

Could you present with the original practical question? Thanks.

Hi. Please see here from the Kaplan Masterclass 9:

Specifically see quesion B(iv).

If I calculate on the basis of bps on total paper portfolio cost, the answer is ($25.4025* - $25.31) x 18,000 = $1,665 / ($25.21 x 25,000) x 10,000 = 26.32bps.

However, if I calculate on the basis of the actual traded volume (or just using the arrival price and VWAP), the answer is ($25.4025 - $25.31) / $25.31 x 10,000 = 36.55 bps.

The difference is driven by the discrepancy between 25,000 shares in the paper portfolio and 18,000 actually traded (i.e. 18,000 / 25,000 = 0.72 = 26.32 / 36.55.

Note: the correct answer as per their answers is 26 bps (i.e. methodology 1).

Now consider question C, below:

The market doesn’t care whether I’ve traded 18,000 or 25,000, so it must make sense to use the second methodology above when calculating the market-adjusted trading cost, which becomes:

($25.40* - $25.31) / $25.31 x 10,000 = 35.66 bps - [ (3,137 / 3,125 - 1) x 0.9 x 10,000 ] = 1.10 bps.

But the dollar cost would not be equivalent to the 1.10 bps x paper portfolio cost, again because of the mismatch between the number of shares traded and the number in the paper portfolio. Because I only incurred this market-adjusted trading cost on 18,000 / 25,000 = 0.72 of my paper portfolio, that would imply my true market-adjusted trading cost expresses as bps on the paper portfolio should be 1.10 bps x 0.72 = 0.79 bps.

So just to recap my question, if asked for the market-adjusted trading cost “in bps” do we assume they mean in actual basis points (i.e. the 1 bps) or in basis points of the paper portfolio (i.e. the 0.79 bps).

Note: the correct answer as per their answers is 1 bps (i.e. the first method I present underneath question C, but methodology 2 as per the answer to question B), which to me is inconsistent with the way they approach it in part B of the same question.

In this specific example the difference is miniscule so it doesn’t matter, but the question on exam day might be a different story…

Thanks for any help.

*The number in the question text ($25.40) is rounded, so just to stay consistent with their answers for parts A and B, I am using the exact weighted average here. Inexplicably, their answers to C switch to using the $25.40 number as per the question text, so I am using that in my part C again to stay consistent with their answers. So frustrating, but anyway…

I think it would be clearer if you differentiate between part B and part C.

Part B: you can understand by using this formula

IS (in bps) = (Paper return - Actual return) / Paper cost

The problem in this part is to explain why you cannot achieve the paper return (because of delay cost, trading cost, opportunity cost and fees). Hence, the denominator should be paper cost (your initial state) and the answer is methodology 1.

Part C: now go to the market-adjusted cost. Here, the initial state is different because it try to explain why your final cost is not the arrival cost (because of market movement). The focus is now on actual trading, not paper cost.