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I found this power point and this paper to be an excellent source on this topic. Here is a quote from the paper: A square-root singularity for small traded volumes is highly non-trivial, and certainly not accounted for in Kyle’s classical model of impact [11], which predicts a linear impact ∆ ∝ Q. A concave impact function is often thought of as a ...


6

Let me try to answer: I have seen how equity trades are executed at the order book level. Let's say the price of the stock is 100 (last traded price). Let's say the order book is as follows: Bids: Bid1 = 99 (size = 10,000), Bid2 = 98 (size = 20,000), Bid3 = 97 (size = 25,000), Bid4 = 96 (size = 30,000), Bid5 = 95 (size = 40,000): total size = 125,000 stocks. ...


6

My understanding (devoid of any mathematical grounding) is as follows. v = Turnover PER UNIT TIME n = Shares you need to execute therefore n/v = Number of units of time required to execute your size at the normal turnover rate Realized vol follows a SQRT(T) heuristic. Given that we can now rewrite the transaction cost formula purely in terms of vol ...


6

There are a number of price impact models which seek to predict the bias induced on prices by trading. There are also issues with some of these models (which I will mention later). Models Probably the earliest and most-known model is that by Torre and Ferrari (1997) which estimates the impact to be a multiple of the square root of trade size over average ...


4

The reference papers for market impact decay are: Waelbroeck, H., and Gomes, C. (2013). Is market impact a measure of the information value of trades? market response to liquidity vs. informed trades. Social Science Research Network Working Paper Series. URL http://ssrn.com/abstract=2291720 Brokmann, X., Serie, E., Kockelkoren, J., and Bouchaud, J. P. (2014)...


4

In practice all impact models are sub-linear. Despite this is fact (seen in many academic publications, commercial and proprietary models), there is an interesting argument for using a linear impact models (other than being careful and pessimistic). Would anyone try to build a model, this approach would be also more parsimonious with less parameters to fit. ...


3

There is no official definition of market depth (this is only a qualitative concept), only the cost of a roundtrip for a given number of shares of contracts. Take $V$ shares, on average, knowing the shape of the book at time $t$, what is the cost of buying and selling them immediately? You obtain a cost $C(V,t)$. Then you need to average or to choose an ...


3

I’m by no means an “expert”, though I’ve spent a fair amount of time studying this and writing quant software. There are three important starting places to study this question, in this order: 1 dark pools ( see https://squeezemetrics.com/monitor/dix ) 40% to 60% of large trades are now done in dark pools. 2 the “closing auction” at 4pm 3 the “on balance ...


3

There are multiple models for price impact and the one you have listed here is not the latest. You can see a writeup of a few of the most popular and recent models in this answer. We can think of a few reasons why price impact is considered linear in the bid-ask spread. First, you want the trade to be completed (implied by most of these models). You may be ...


2

The square root law is a quite simple and popular model for price impact estimation: $$\Delta p = Y\sigma\sqrt{\frac{Q}{V}}$$ where: $\Delta p$ is the price impact, $Y$ is a constant (needs to be calibrated). $\sigma$ daily volatility of the returns $Q$ daily trading volume. There are a lot of papers around this model (e.g Gomes and Walbroeck 2015, Zarinelli ...


2

Please note that my answer is primarily opinion/experience based. If it is not appropriate I will take it down or edit accordingly. How should I begin to think about optimal execution given a choice of execution methods? What simplifying assumptions or heuristic frameworks could be useful in identifying quasi-optimal execution strategies? I think optimal ...


1

I will attempt to elaborate on this from risk management perspective. scenario analysis approach: An example of this is stress testing that Fed mandates for investment banks. Fed gives stress variables to various fundamental macro variables. For example, a certain market stress scenario will be rates down 100bps, volatility up 30%, curve flatter by 30bps, ...


1

A lot of the literature relies on estimating impacts of large orders (n), typically from major funds, that are split into child orders and executed over some period. Usually this data is proprietary and difficult to replicate. The metaorders used in this paper https://arxiv.org/pdf/1412.2152.pdf are one example (see footnote 3). This paper explains their ...


1

IMHO there is a general shift toward algorithmic execution for institutionz over the last 5 to 10 years, and depending on your method of execution the price impact can vary, so I am not certain whether you will get meaningful results using long histories. Some older papers look at tickets data and aggregate impact of large tickets as proxy for ...


1

This is a difficult problem, especially since estimating the volatility faces a number of issues: the classic "pollution" of realized variance by bid-ask bounce when using intraday data (cf Aït-Sahalia, Mykland, and Zhang); including overnight gap effects if using daily or less frequent data; volatility changing (hence the utility of GARCH and ...


1

See Kandel and Pearson (1995) and Kim and Verrecchia (1991, 1994, 1997).


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The easiest way ,i suppose, would be to analyze the market depth. If there is a 20 cent gap between each 100 shares on the bid then to sell 1000 shares instantly would have an impact of $2. Your average price is the midpoint. There are more complicated formulations, but this seems to be how it works on simple examples such as bitcoin exchanges.


1

This is actually a deceptively good question because, as we all know, estimates of variance are extremely sensitive to sampling frequency, sampling intervals, and lags. This is because not all stock prices perfectly adhere to Brownian Motion (i.e., the variance doesn't adhere strongly to the root time rule). It is also not entirely clear from the paper how ...


1

I can suggest a simple way that is not perfect but is reasonable and not too difficult. Transaction Costs Will Change the Optimal Portfolio What you want to do is account for the transactions costs of trading. Note that Engle and Ferstenberg (2007) have shown that including transactions costs shifts the efficient frontier down and to the right (because there ...


1

Depending on how big is bid-ask spread, it may not matter at all. To start with I'd suggest that for each security you randomly pick either it's bid or ask price, and see whether the optimal weights differ much depending on your choice. If not, you can simply disregard such asymmetry. If not, I am not sure whether MPT will work nicely with your setting since ...


1

We will know the answer to this question when Navinder Singh Sarao is put on trial in the United States on charges of doing precisely this.


1

It's like a giant game of tug-of-war except there are many ropes and thousands of participants. The SPY tugs at the ES, which tugs at the SPY, which tugs at other ETFs. I suppose in theory you could manipulate the ES in a low volume setting by selling a huge block in the thinly-traded period before 12AM PST, selling enough to make the price fall 1/2 -1% ...


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