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.

• This assumes that a. There are no additional costs, b. The average of the bid and ask really is the fair value, and c. There is enough size on the bid/ask for your strategy.
– will
Aug 10 '19 at 11:38
• a) I think the point behind only considering bid-ask spreads is that the arbitrageur in this example is considered to be an institutional investor and hence not largely affected by further transaction costs. b) could you elaborate on that? i don't quite understand what you mean by fair value in this case. Aug 10 '19 at 11:56
• A. If youre including trading costs in your analysis, why make the arbitrary decision to ignore other costs? B. If the bid/offer is 100/102, what is the real value? How about if its 0/2?
– will
Aug 10 '19 at 11:59
• a) I was just trying to figure out what the authors reasoning might have been, not implying that I believe it was done appropriatly. B) I see, however I do not see the relevance of this here, assuming I have to pay ask and get bid. Aug 10 '19 at 12:07
• I agree it might be implying better execution for what is, in this case, very liquid markets. Even then I think it's probably better to use the actual bid ask prices. For instance, you can arbitrage combing c & p strips and reconstituting into treasury notes and bonds but the prices of the strips need to observe bid ask or you will see arbitrage that is not transact-able. Dealers however can often buy the pieces cheaper implying better execution. Apr 7 '21 at 14:31

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:

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.

• On the other side of the optimism coin, if you're justifying the costs of a trading strategy to a potential client, you can use half the bid/offer and put the rest of the costs to zero and assume no market impact. Although in reality you might even assume less than half the bid/offer, saying you can target mid and nearly get it.
– will
Aug 10 '19 at 17:00
• Let's make up a numerical example for concreteness. Suppose some illiquid stock trades just 200 shares per day. Suppose it is quoted 23-23.5 (for 100 shares). Suppose you buy 2000 shares (10x daily volume; using a client's funds). Suppose that at the end of the day, perhaps because of the market impact of your trades, it is quoted 23.25-23.75 (for 100 shares), so the mid is 23.5. It is "acceptable" to say that the "fair value" is 23.5, but really if you were to unwind now, you're not likely to get even 23.25, which makes me sad. Aug 10 '19 at 17:15
• But you shouldn't expect to be able to get mid with an order 10x adv, this is the case where you talk to your client and say "I will execute over x days, and pass through the fill, because we expect it to be better than dumping it all into the market in 1d". Or you tell them that you can get it done in a more efficient (ie less impactfull) way, because this is where you have the expertise, and it's one of the services they pay you for...
– will
Aug 10 '19 at 17:35
• Some people claim they can systematically beat a vwap. I'm dubious (excluding deliberate impact). Definitely dubious when it's in size.
– will
Aug 10 '19 at 20:36
• If you want to do 1x adv and hope not to have impact, what we care about here is the spare capacity - in some markets there is a lot of extra volume lurking with no interest to cross - of course getting it done at mid is not necessarily easy. Some markets have liquid tas markets though, which can greatly increase your ability to fill "at mid", thought its of course more complicated when you include tas.
– will
Aug 10 '19 at 20:41

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.

• I've been following this thread quietly. Just one question if you don't mind. In your argument, did you not show that the total round trip transaction cost is the full spread and not half the spread ? You bought at 111 and lost a dollar ( the half spread was a dollar ) and then you later sold at 110 and lost another dollar. So, that's 2 dollars so the cost was the full spread which was 2 dollars. I'm just checking that I understand correctly. Thanks. Apr 8 '21 at 2:45
• Think about it as: at t0 I have 111 dollars, at t1 (the time that I unwinded the position) I have 110 dollars. Therefore, that buy and sell cost me 1$– MaPy Apr 8 '21 at 9:10 • thanks. I'll read it again. and probably again :). Apr 9 '21 at 2:25 • right but at t0$ you bought at 111 when the mid price was 110, so don't you lose a dollar there also ? Apr 9 '21 at 15:11
• That is the only dollar that I lost. Note that I sold the stock at the initial mid price i.e. 110. I started with an inventory of 0 stocks and 111 dollars and I end up with 0 stocks and 110 dollars, therefore my loss is 1 dollar.
– MaPy
Apr 9 '21 at 15:54