Formula For Market Impact

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Anyone interested,

I found a formula for market impact of a trade: Link Here

I also attached the image of the formula.

There are other articles and this is used by in the Bloomberg Terminal for their Transactional Cost Analysis (TCA), for example.

The formula is in this one too with a lot of calculus that I did not wade through:Page 16. I found the sage advice of old traders interesting: “this formula is consistent with the trader rule-of-thumb that says that it costs roughly one day’s volatility to trade one days’ volume.” Trade a whole days volume? Wow!!! And I am just worried about increasing my trade size by $5,000.

This last article does say there is evidence that this formula holds for trading sizes in the 1% to 25% of daily volume range.

I researched this because I want to increase the amount of money in one of my ports without impacting the slippage too much. Can I? If so how much more can I put into this port?

So a hypothetical example with round numbers (somewhat close to my situation). Say each trade in my port is $5,000 and my ADT is $1,000,000 for the bottom 20% of liquidity. Can I increase my trades to $10,000 for each trade?

5,000/1,000,000 is the same as Q/V * (stock price/stock price). I.E., I can multiply Q/V by 1 and use trade cost/ADT in the equation.

The constant in the equation is generally about 1/2 in most articles (see the graph in the link).

Using ShowVar I find generally my daily volatility or the standard deviation of the daily percent change in my stock price is 3% or below for the last year. Using this variable converts the equation into the percent change in price rather than the absolute change in price. This is in essence dividing both sides of the equation by the price of the stock and multiplying by 100.

So the percent change in price (slippage due to market impact) is: 1/2 * 3 * sqrt(5,000/1,000,000) = 0.106%

If I increased my trades to $10,000 per trade the calculations come to 0.15% or a difference in slippage of 0.044%. The BID/ASK (spread cost) would be the same for either trade size.

This seems low. But the calculation is conservative considering this is calculated for just the bottom 20% of my liquidity. Presumably there would be little difference in market impact for the S&P 500 stocks in my port. Even if I am off by a factor of 3 it would mean that I should have tried this a long time ago. Of course, if I do increase my trade size I will keep track of the result as best I can. I get that a formula and a lot of hand waving proves nothing: trust the papers and the better experts but verify.

Any ideas, experience in the market or corrections welcome.

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You have a good understanding of this. That formula appears to be perfectly reasonable. It may be on the conservative side (estimating high) if you’re using algorithmic execution and good routing.

The only thing I’ll add is that I think you’re over-analyzing impact given your size as a % of ADV. These formulas and ideas are important when regularly dealing with larger orders, like 5%-25% of ADV, but for 1% adv orders using algorithmic execution your impact should be incredibly small.

My standard advice is to use either vwap or volume participation algorithms and attempt to always add liquidity with your orders (don’t cross the spread). Over a large sample I would be amazed if you saw anything worse than 5 basis points compared to arrival price at 1% adv with that strategy.

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Andrew,

Thank you so much!!! Your informed input is always helpful!!!

I was thinking the above is likely myself. But I would not have realized it without the article and your input. I certainly intend to test it with higher % of ADV in the future.

Again, much appreciated.

Regards,

Jim

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Jim -

If I’m using these calculations correctly, the market impact of large orders of microcaps and nanocaps is still very low. Let’s say I buy $100,000 worth of shares in FSI (market cap of 18 million, ADT of $90,000), to use a rather extreme example. That’s more than an entire day’s worth. This is a very volatile stock too, with a 3-month daily average pctdev of 5%. So I need to buy 64,500 shares, and the avgvol(90) is 58,000 shares. The market impact then computes to 0.55sqrt(64.5/58), or 2.64%.

That’s not negligible, but is it correct? I would have guessed that the market impact would be a lot higher–but that’s just a guess. I have no experience in placing trades this large, so I have no idea. But other people writing for this forum avoid trading more than 5% of the ADT, and this formula seems to imply that that volume of trading would be almost completely harmless.

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Yuval,

Your calculations look correct. Don’t forget that with the formula you would add the BID/ASK spread but I’m not sure that really works with more modern trading and dark pools. But other than that your formula looks good.

Note that if you double your trade size for a port the total market impact should end up being 2^(1/2) or 1.4 bigger for the new larger port (associative and commutative properties). I have the same port on 2 different days. One trades 3 times as much volume. My bigger port seems to be doing even better than this formula would suggest compared to the smaller port. This is the little real experience I would have to offer.

Bottom line: SUpirate1081 has a lot of actual experience with this kind of thing–not to mention some real skills when it comes to math–and he says I have been worrying about market impact too much. So far he seems to be right about that.

Regards,

Jim

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Yuval, I believe you’re doing the math correctly. It’s possible this concept breaks down a little bit when you’re talking about making trades larger than the adv. If you were to do that the only reasonable course would be to execute over several days (maybe 4 or 5). And doing that I would still expect to impact the price by around the 2-3% mark suggested by the formula.

The major thing I’ll point out is that 2.64% on one leg of a trade is absolutely not “almost completely harmless”. If it costs me 2.5% to get in to the position, and then 2.5% to get out of it, then I’ve lost 5% of any potential gains already. If the position is being held for years or decades then maybe we can consider that acceptable, but even holding something for 1 year and having that much market impact is a huge. If you intend to only hold it for weeks or months then you have virtually no chance of consistently beating that slippage.

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Oh, I agree! 2.5% each way is a high price to pay indeed. The “absolutely harmless” remark was about trading more than 5% of the ADT. If you’re trading 10% of the ADT and the standard deviation is 3%, the formula gives you a market impact of 0.47%, which seems pretty harmless to me.

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Ah I see. On that point I agree. And as I suggested earlier with intelligent execution I don’t believe the reality is even that high in most cases. With current software/brokerages available to practically every trader slippage is only a real concern for extremely high turnover or high volume traders.

But if people are still using limit orders and such then it can be a problem still.