Arrival Price

The arrival price strategy attempts to minimize risk-adjusted costs using the arrival price benchmark.

Arrival price optimization is the most sophisticated and popular of the commonly used algo trading strategies.

The ideal user of arrival price strategy has the following characteristics:

- he is benchmarked to the arrival price

- he is risk averse and knows his risk aversion parameter

- he has high positive or high negative alpha

- he believes that market impact is minimized by maintaining a constant rate of trading over the maximum execution period while keeping trade size small.

Most implementations are based on some form of the risk-adjusted cost minimization introduced by Almgren and Chriss.

An arrival price strategy evaluates a series of trade schedules to determine which one minimizes risk-adjusted costs relative to the arrival price benchmark.

Parameters of arrival price optimization:

- Start time

- End Time

- # shares to execute

- Alpha

- Risk aversion parameter

For buyers (sellers), positive (negative) alpha encourages faster trading, while market impact costs encourage slower trading.

For traders with positive alpha, the feasible region of trade schedules lies between the immediate execution of total target quantity and a constant rate if trading thoughout the execution period.

A more general form of arrival price optimization allows for both the buyers and sellers to have either positive alpha or negative alpha.

Example:

Assumption: negative alpha

--> Shares held long and scheduled for liquidation are expected to go up in price over the execution period.

--> This would encourage a trader to delay execution or stretch out trading.

Hence, the feasible region of solutions that account for both positive and negative alpha includes back-weighted as well as front-weighted trade schedules.

Other factors that necessitate back-weighted trade schedules in an arrival price optimization are:

- expected changes in liquidity

- expected crossing opportunities

A variant of the basic arrival price strategy is adaptive arrival price.

A favorable execution may result in a windfall in which an accumulation of a large number of shares takes place at a price significantly below the arrival price.

This can happen by random chance alone.

Almgren and Lorenz demonstrated that a risk-averse trader should use some of this windfall to reduce the risk of the remaining shares.

He does this by trading faster and thus incurring a higher market impact.

Hence, the strategy is adaptive in that it changes its behaviour based on how well it is performing.