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There is a family of models that is so commonly used among practitioners that it can be almost regarded as standard. For a survey, check out Rob Almgren's entry in the Encyclopedia of Quantitative Finance. Check out also Barra, Axioma and Northfield's handbooks. In general, the impact term per unit traded currency is of the form MI \propto \sigma_n \cdot ...

10

Equity returns have persistent negative skewness and excess kurtosis[1] over longer periods. So yes you're right: a majority of the daily returns is positive and small and a minority of the returns is negative and larger. This can be quite extreme, for example Black Monday. I don't have the data right now but you can get returns on major indices freely. ...

8

I don't believe that there is a "standard" model (per say); in fact, there are many considerations around market impact models, so you would need to be more specific. At the most basic level, you might define market as $P_{first fill} - P_{last fill}$ once your order in actually in the order book (e.g. not including other costs like "opportunity cost"). ...

7

This answers a slightly larger question than you're asking, but I highly recommend "An Engine, Not a Camera: How Financial Models Shape Markets" by Donald MacKenzie, which is part of the burgeoning field of "Social Studies of Finance". Some relevant links: http://socfinance.wordpress.com/ http://www.sociology.ed.ac.uk/finance/ Regarding your specific ...

6

Arbitrage absolutely does not prevent a derivative (option, future, or otherwise) driving the price of the underlying. In fact, arbitrage, or the elimination of it, is what causes the "tail wagging the dog" phenomenon of large trades in the derivative causing wild swings in the underlying. see the may 2010 flash crash that started with some large e-mini ...

5

This isn't exclusive to VWAP; any assumed trade price (NBBO, Arrival Price, etc) has the same vulnerabilities. Many shops often lump market impact with slippage and transaction costs when modeling the difference between the ideal price and the realized price. To model the impact during a backtest for a given trade price, assess a penalty: This penalty can ...

3

The blog post "A slice of S&P 500 skewness history" http://www.portfolioprobe.com/2012/01/16/a-slice-of-sp-500-skewness-history/ has a bit of data on this question. It appears that log returns might have some negative skew, but symmetry is a possibility.

3

To get a feel for it think about an extreme scenario. Suppose I have an order to buy \$100bln VWAP in IBM over the course of one day. My "cost" relative to VWAP will be near zero, b/c I will be on the buy side of every trade that day. However, my market impact will be extremely high b/c IBM will fall like a rock the next day, leaving me with huge losses. ...

3

Bootvis accurately describes the math - Skew plus Kurtosis. What's interesting is that many of the efficient market theorists (example: Eugene Fama) observed this phenomenon too. I consider two intuitive reasons for this: 1) Behavioral - According to prospect theory, the mental benefit of gaining a dollar is lower than the fear of losing a dollar. This ...

3

Markets adjust with the impact of incoming orders. A large buyer will send the price up in any market. Don't let the mini in the name fool you, the emini S&P is one of the most liquid futures contracts in the world. The futures market often has more volume available in the best couple ticks than the equity markets that it is based on.

2

I have attended a number of conferences, and the percentage of asset under management by quantitative funds is consistently quoted between 17% and 23%; these statistics are usually based on aggregates from eVestments, SEC, and European stop that, like Frankfurt, ask the sender of an order to specify the way it was created. It is likely that the percentage ...

1

There is an ongoing trend in GARCH modeling that seeks explain the why of this phenomena. Some economic explanations iv'e read revolve around the effects of leveraged positions and flights to liquidity. The GARCH model derivatives used are usually classified as asymmetric power models I believe.

1

If it wasn't quant it would be something else. I rather think that the effect is due to real time which can allow manipulation more easily and so huge moves. In fact a Nobel Economist Maurice Allay did advocate to forbid real time and one quotation per day if the goal was to stabilize the effect of stock market on Economy. But of course no way that will ...

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