# Market Impact proportional to the bid-ask spread

Quantitative Finance Asked by mbz0 on November 12, 2020

Empirical studies have shown that market impact can be linked to the following parameters:

$$mathcal{I}(Q) = kappa . sigma . (frac{Q}{V})^gamma + alpha . psi_{BA}$$

where $$psi_{BA}$$ is the bid-ask spread.

Can anyone explain the linear relationship in the spread? Why having a narrower spread implies lesser impact?

Thanks!

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 unable to wait for your price to be taken; you will need to switch from a price maker to a price taker, cross the spread, and trade at the far side fo the market. In that case, you pay the bid-ask spread to guarantee execution. However, that is not certain to occur, so $$alpha$$ accounts for that probability.

Second, suppose you trade in dark pools (or other ATSs using occasional auctions/matching at the midpoint). The imbalance of orders in a matching auction will bleed back out to the market and so instead of trading at mid-market when you entered your order, the price will shift a little. In that case, you again end up paying a price that is half the spread plus or minus some shift in that midpoint.

Third, market makers who take on a position when you trade with them eventually need to hedge. Doing that may require them to immediately get out of a position, so they pay the bid-ask spread to trade immediately. Their quotes will therefore reflect the spread to pass that cost on to you.

If you have not traded much, you might want to try doing so in a good simulator or (far better) with some real money. You will quickly see how often you need to consider crossing the spread and why that affects the price you pay.

You should also probably read up on permanent versus temporary (and decaying) price impact at the link above. That may help clarify the thinking of how the bid-ask spread affects prices.

Answered by kurtosis on November 12, 2020

## Related Questions

### Mapping One symbol’s Support/Resistance to another Symbol

1  Asked on February 4, 2021 by rc76

### Volatility of multimodal distribution of returns

0  Asked on February 3, 2021 by vivek-subramanian

### What is the importance of alpha, beta, rho in the SABR volatility model?

3  Asked on January 25, 2021 by user330060

### Is there any way to get a list of all trades that took place for a stock?

3  Asked on January 23, 2021 by dirtside

### Software for backtesting outside strategies (CSV transaction upload)

5  Asked on January 20, 2021 by dordal

### Pricing deep OTM and short expiry options with Monte Carlo methods

0  Asked on January 17, 2021 by ffbzona

### Obtain order level data for German stocks

0  Asked on January 15, 2021 by user49942

### How does Bloomberg calculate beta?

0  Asked on January 8, 2021 by friedrich

### Calculation of the Bid-Ask Spread on Bloomberg

1  Asked on January 7, 2021 by user45980

### Binomial Trees vs FDM

2  Asked on January 3, 2021

### Improving control variate for variance reduction

1  Asked on December 31, 2020 by lin-lex

### Modelling VWAP Slippage with HFT data

1  Asked on December 31, 2020

### Covariance, stochastic discount factor (SDF) and risk aversion

1  Asked on December 29, 2020 by question-anxiety

### delta neutral option cost

1  Asked on December 28, 2020 by roller

### Obtaining current list of companies in the FTSE 100 via an API

3  Asked on December 23, 2020 by thechubbypanda

### Continuity of a portfolio with two options with respect to the strikes

0  Asked on December 15, 2020 by user279687

### What’s the disadvantage of using linear programming for portfolio optimization?

3  Asked on December 15, 2020 by felix

### Relationship between asset volatility and debt and equity value

1  Asked on December 14, 2020 by dadude27

### Converting US Treasury CMT to Discount Yields

1  Asked on December 13, 2020 by mikerand

### How to calculate Greeks for leveraged Barrier options?

0  Asked on December 12, 2020 by twhale

### Ask a Question

Get help from others!