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ScilabGuru
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Transaction costs - concave or convex function?

January 22nd, 2004, 9:49 pm

I found in some paper the following claim: transaction costs is concave function of the value of trade since commission are not linear and for large trades they achieve somehow some saturation level. It does not seems me completely correct. Moreover, for high-frequency trading it seems me completely incorrect. Why? My logic is the following: for high frequency trading bid-ask spread starts to play very essential role, may be even more that other commissions. Bidask-spead term simply is modeled as ~coeff(current price) |trade_volume|.But it seems me a common knowledge to say that when you buy/sell more then actual bidask spead grows for you, because of liquidity issues. That means that this term should be somehow be even more convex than just |trade_volume|. Your opinions please.
Last edited by ScilabGuru on January 21st, 2004, 11:00 pm, edited 1 time in total.
 
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Johnny
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Transaction costs - concave or convex function?

January 23rd, 2004, 7:59 am

I agree with you but I also agree with the claim in the paper. Let's break transaction costs into two parts:1. Commissions: many common commission structures are concave. Two examples:a) fixed element plus constant ticket costb) no fixed element, but ticket cost decreases with size2. Bid-ask spread and/or slippage: convex as spread/slippage increases with size of tradeSo overall you have a concave element through the commission structure and a convex element through spread/slippage. Which effect will dominate will depend on circumstances.
 
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nono
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Transaction costs - concave or convex function?

January 23rd, 2004, 8:15 am

You guys should read "Optimal Trading Strategies" by Kissell & GlantzThere are also papers by Almgren & Chris on the same topic where you should be able to find what you look for.HTH
 
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adannenberg
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Transaction costs - concave or convex function?

January 23rd, 2004, 12:16 pm

The claim of concavity is for market impact alone, not for market impact plus commission. So it's still very weird.
 
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Johnny
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Transaction costs - concave or convex function?

January 23rd, 2004, 1:12 pm

QuoteOriginally posted by: adannenbergThe claim of concavity is for market impact alone, not for market impact plus commission. So it's still very weird.In that case I don't understand this: "I found in some paper the following claim: transaction costs is concave function of the value of trade since commission are not linear .." in SG's original post.
 
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ScilabGuru
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Transaction costs - concave or convex function?

January 23rd, 2004, 1:16 pm

QuoteOriginally posted by: adannenbergThe claim of concavity is for market impact alone, not for market impact plus commission. So it's still very weird.No, at least, the explanations were about broker commissions, etc. Market impact, can be modeled via bidask spread somehow at least this is my view, and then this term is convex - not concave.
 
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ScilabGuru
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Transaction costs - concave or convex function?

January 23rd, 2004, 1:26 pm

Many thanks, Nono, for the reference, the paper is great (may be becasue it correlates with my view )
 
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kr
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Transaction costs - concave or convex function?

January 23rd, 2004, 1:46 pm

I don't think it makes sense to separate upfront commision from slippage. In a way, block traders are doing a one-directional gamma bet: charge upfront to cover the expected slippage, and hope that your execution strategy leaves you something to take home when you're done. Actual performance, like dynamic hedging of an option, will be different, so there is a risk/return dimension to the problem. It's also like d.h. in that it need not be a one-shot control theory problem - i.e. in any realistic model, the block trader doesn't just dump all the shares on the market at once.
 
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Johnny
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Transaction costs - concave or convex function?

January 23rd, 2004, 2:10 pm

QuoteOriginally posted by: krI don't think it makes sense to separate upfront commision from slippage. In a way, block traders are doing a one-directional gamma bet: charge upfront to cover the expected slippage, and hope that your execution strategy leaves you something to take home when you're done. Actual performance, like dynamic hedging of an option, will be different, so there is a risk/return dimension to the problem. It's also like d.h. in that it need not be a one-shot control theory problem - i.e. in any realistic model, the block trader doesn't just dump all the shares on the market at once.It makes perfect sense to separate out commission from slippage. The question was whether the overall effect of transaction costs was concave or convex. By separating "transaction costs" into two constituents, it quickly becomes clear that there is a convex effect and a concave effect, with no a priori reason to say which one should dominate.Naturally, if you want to ask a much bigger question about all the effects that transaction costs have on your trading, you need to widen the discussion. But the question here is quite small and specific, no?
 
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ScilabGuru
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Transaction costs - concave or convex function?

January 23rd, 2004, 2:18 pm

QuoteBut the question here is quite small and specific, no? Well, the question was quite technical, but of course, if this is interesting we can proceed the discussion. The commissions and bid-ask speard vary pretty much with repsect to the market, institution, volume, broker and trading strategy. So everyone has to estimate it for himself and to deside what he is going to neglect and what to keep. For instance making with some security few trades in a week one cannot neglect bidask-spread. Making trade once in a week - this is the different story.
Last edited by ScilabGuru on January 22nd, 2004, 11:00 pm, edited 1 time in total.
 
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Johnny
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Transaction costs - concave or convex function?

January 23rd, 2004, 2:37 pm

ScilabGuruI was responding to kr's post. That's why I quoted it.
 
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adannenberg
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Transaction costs - concave or convex function?

January 23rd, 2004, 3:21 pm

Take a look at Farmer's "How storing supply and demand affects price diffusion", and references therein. It presents the overly simple logic as to why market impact should by a convex function of size, it gives references to the empirical studies showing that that market impact in fact appears to be a concave function of size, and most importantly it gives a detailed and reasonable model in which market impact is concave(!). That still doesn't mean you should just drop large order bombs on a specialist, though!
 
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ScilabGuru
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Transaction costs - concave or convex function?

January 23rd, 2004, 3:37 pm

QuoteOriginally posted by: adannenbergTake a look at Farmer's "How storing supply and demand affects price diffusion", and references therein. It presents the overly simple logic as to why market impact should by a convex function of size, it gives references to the empirical studies showing that that market impact in fact appears to be a concave function of size, and most importantly it gives a detailed and reasonable model in which market impact is concave(!). That still doesn't mean you should just drop large order bombs on a specialist, though!Hmm, I've looked there. It seems we are talking about a bit different setting. Impact function affects the price in the future. I pretty hard understand how we can estimate this impact since too many agents are on the market. So assume for the sake of simplicity that your trade does not make any impact. But still you have bidask-spread and other commissions. And still there is a difference in bidask-prices if you want to buy/sell 1 or 1000 shares. Am I wrong here? I am not sure that it works like in a supermarket buy more - pay less per unit. Any way I will read this paper deeper, thanks ....
 
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zerdna
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Transaction costs - concave or convex function?

January 23rd, 2004, 8:01 pm

here is the way i understand this. For large trades, and we are talking about very large trades when the cost function becomes concave, there are different market mechanics of execution. These are trades that were negotiated upstairs and mostly brokered, or sometimes went through POSIT, etc, in any case didn't go though a specialist or a limit-order book like ordinary trades. Still, they are printed on the tape in same way as ordinary trades and participate alongside them in empirical studies.
 
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adannenberg
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Transaction costs - concave or convex function?

January 23rd, 2004, 8:25 pm

That makes sense. So they cross blocks inside the spread and the market-impact curve which was rising suddenly shows a dip - hence the concavity.