Why Transaction Costs Are Often Estimated at Half the Bid-Ask Spread

# Half of the bid-ask spread as transaction cost


# Half of the bid-ask spread as transaction cost












I am currently reading "Deviations from Covered Interest Rate Parity" by Du et al. When establishing deviations from CIRP they consider transaction costs as follows.

"We assume that the transaction cost for each step of the arbitrage strategy is equal to one-half of the posted bid-ask spread."

The transaction costs they are referring to here are calculated in this way for a forward and spot contract as well as a U.S. dollar repo. My understanding of bid-ask spread was that it is to be interpreted as transaction costs in its entirety. Following the logic that price takers buy at the ask price and sell at the bid price but the market maker buys at the bid price and sells at the ask price.

Hence my question is, whether this is common practice and if there is an explanation for taking half of the posted bid-ask spread. To me, this seems quite arbitrary.

Paper:

https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12620

Page 930, line 31.

## Answer by Dimitri Vulis (score 6, accepted)

https://quant.stackexchange.com/a/47058

The idea of assuming that the transaction cost is one half of the bid-offer spread comes from several assumptions:

- the positions are marked-to-market at mid;

- you can actually execute at bid or ask (that your trade isn't large enough to impact the market);

- there are no other fees or costs.

For example:

Bid-Ask Spreads: Measuring Trade Execution Costs in Financial Markets by Hendrik Bessembinder and Kumar Venkataraman

> Execution costs for a single trade are often measured as half the spread, described on a percentage basis by equation (1): Quoted half-spread = $QS_{it} = 100 * (Ask_{it} – Bid_{it}) / (2*M_{it})$ (1) where $A_{it}$ and $B_{it}$ are the posted ask price and bid price for security $i$ at time $t$, respectively, and $M_{it}$, the quote midpoint or mean of $A_{it}$ and $B_{it}$, is a proxy for the true underlying security value.

I.e., you can buy some security at price $Ask$ and then mark it at $Mid$ (recognizing only half of the b-o spread in your P&L initially) rather than mark at $Bid$ (the price you would get if you were to unwind), although you could only unwind at $Bid$ (recognizing the other half of the b-o spread in your P&L only when you unwind).

Another example:

Transaction Costs by Ed Tricker, Saurabh Srivastava, Marci Mitchell

> At a minimum, the transaction is immediately out of the money by half the amount of the bid-ask spread and the total cost may increase further if the order that is placed cannot be satisfied with the current volume that is associated with the current bid/ask price quoted.

Whether it is too optimistic depends on the intended audience of your papers. If you're just trying to publish in a peer-reviewed academic journal, it may be good enough, because clearly other authors do it, but if you're trying to convince someone (even yourself) that some strategy would be profitable, then you may want to be even more conservative.

In particular, my personal belief, with which many authorities disagree, is that, since you cannot execute at mid, neither should you mark at mid. In my opinion, the fair value should be what one would receive (or pay) to unwind.

## Answer by MaPy (score 0)

https://quant.stackexchange.com/a/63257

Let stock A traded at 109/111, let's assume I want to simultaneously buy and sell stock A and recorded buy at the best ask and sell at the best bid, the resulting portfolio will incur a loss due to the spread. (i.e. buy at 111 and sell at 109 therefore loss of 2).

But it is more realistic that since I bought at 111 then the latest traded price will be 111 and therefore the new bid/ask will recalibrate taking into account the latest transaction. If we oversimplify things and assume that always bid ask has size of 2 and it is symmetric the new bid ask will be 110/112. Therefore if I need to sell I will sell at new best bid i.e. 110 (note that this is the original mid-price) and I will have a Loss of 1 (since I bought at 111 and I sold at 110) which is equal to half-the spread. In that sense we can assume that Cost is half the spread and not full the spread.