Typically, a strategy is motivated by a theme or style of trading.

The objective is to minimize either absolute or risk-adjusted costs relative to a benchmark

For strategies with mathematically defined objectives, an optimization is performed to determine how to best use the strategy to maximize a trader's or ptf manager's utility.

A trade schedule (or trajectory) is planned for strategies with a target quantity of shares to execute.

The order placement engine (= the microtrader) translates from a strategy's broad objectives to individual orders.

User-defined input parameters control the trade schedule and order placement strategy.

VWAP

It used to represent the bulk of algo trading activity. Currently it is second in popularity only to arrival price.

- easy to compute

- intuitively accessible

Typical parameters of a VWAP execution:

- start time

- end time

- # shares to execute

Additionally, optimized forms of this strategy require a choice of risk aversion.

The most basic form of VWAP trading uses a model of the fractional daily volume pattern over the execution period.

A trade schedule is calculated to match this volume pattern.

Example:

Assumption: Execution period is one day and 20% of a day's volume is expected to be transacted in the first hour.

--> Trader using this basic strategy would trade 20% of his target in the first our of the day.

-->Trader's VWAP pattern will have the same shape as the daily volume pattern.

VWAP is an ideal strategy for a trader with the following criteria:

- His trading has little or no alpha during the execution period

- He is benchmarked against the VWAP

- He believes that market impact is minimized when his own rate of trading represents the smallest possible fraction of all trading activity

- He has a set number of shares to buy or sell

Deviation from these criteria may make VWAP strategies less attractive.

The period of a VWAP execution is most typically a day or a large fraction of a day.

Several variations of the basic VWP strategy are common.

The ideal VWAP user can lower his expected costs by increasing his exposure to risk relative to the VWAP benchmark.

For example, assuming an alpha of zero, placing limit orders throughout the execution period and catching up to a target quantity with a market order at the end of the execution period will lower the expected cost while increasing risk --> highest risk strategy

Continuously placing small market orders in the fractional volume pattern is the lowest risk strategy, but has a higher expected cost.

For a particular choice of risk aversion, somewhere between the 2 extremes is a compromise optimal strategy that perfectly balances risk and costs.

For market participants with a positive alpha, a frequently used rule-of-thumb optimization is compressing trading into a shorter execution period.

In another variant of VWAP - guaranteed VWAP - a broker commits capital to guarantee his client the VWAP price in return for a predetermined fee.

TWAP = Time Weighted Average Price

It attempts to minimize market impact costs by maintaining an approximately constant rate of trading over the execution period.

With only a few parameters - start time, end time, and target quantity - TWAP has the advantage of being the simplest execution strategy to implement. As with VWAP, optimized forms of TWAP may require a choice of risk aversion. Typically, the VWAP or arrival price benchmarks are used to gauge the quality of a TWAP execution.

The most basic form of TWAP breaks a parent order into small child orders and executes these child orders at a constant rate.

An ideal TWAP user has almost the same characteristics as an ideal VWAP user, except that he believes that the lowest trading rate - not the lowest participation rate - incurs the lowest market impact costs.

TWAP users can benefit from the same type of optimization as VWAP users by placing market orders less frequently, and using resting limit orders to attempt to improve execution quality.

Participation

This strategy attempts to maintain a constant fractional trading rate --> its own trading rate as a fraction of the market's total trading rate should be constant throughout the execution period.

If the fractional trading rate is maintained exactly, participation strategies cannot guarantee a target fill quantity.

The parameters of a participation strategy are the start time, end time, fraction of market volume the strategy should represent, and max number of shares to execute. If the max number of shares is specified, the strategy may complete execution before the end time. Along with VWAP and TWAP, participation is a form of nonoptimized strategies, though some improvements are possible with optimization.

Typically, the VWAP or arrival price benchmarks are used to gauge the quality of a participation strategy execution. The VWAP benchmark is particularly appropriate because the volume pattern of a perfectly executed participation strategy is the market's volume pattern during the period of execution.

An ideal user of participation strategies has all the same characteristics as an ideal user of VWAP strategies, except that he is willing to forego certain execution to maintain the lowest possible fractional participation rate.

Participation strategies do not use a trade schedule. The strategy's objective is to participate in volume as it arises. Without a trade schedule, it cannot guarantee a target fill quantity.

The most basic form waits for trading volume to show up on the tape, and follows this volume with market orders.

Example: if the target fractional participation rate is 10%, and an execution of 10.000 shares is shown to have been transacted by other market participants, a participation strategy would execute 1000 shares in response.

Unlike a VWAP strategy, which for a given execution may experience large deviations from an execution period's actual volume pattern, participation strategies can closely track the actual - as opposed to the predicted - volume pattern.

However, close tracking has a cost. In the previous example, placing a market order of 1000 shares has a larger expected market impact than slowly following the market's trading volume with smaller orders.

An optimized form of the participation strategy amortizes the trading shortfall over some period of time. The result is a lower expected shortfall, but a higher dispersion of shortfalls.

Market-on-close

It is a popular strategy for market participants who either want to minimize risk-adjusted costs relative to the closing price of the day or want to manipulate the close to create the perception of a good execution (gaming).

The ideal market-on-close user is benchmarked to the close of the day and has low or negative alpha.

The parameters of a MOC execution are the start time, end time, and the number of shares to execute.

Optimized forms of this strategy require a risk-aversion parameter.

When MOC is used as an optimized strategy, it is similar in its formulation to an arrival price strategy. However, with MOC, a back-weighted trade schedule incurs less risk than a front-weighted one.

As with arrival price optimization, positive alpha increases urgency to trade and negative alpha encourages delayes execution.

Gaming the close is achieved by executing rapidly near the close of the day. The trade print becomes the closing price or very close to it, and hence shows little or no shortfall from the closing benchmark. The true cost of the execution is hidden until the next day when temporary impact dissipates and prices return to a new equilibrium.

Arrival Price

The arrival price strategy (= the implementation shortfall 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.

In the most general terms, an arrival price strategy evaluates a series of trade schedules to determine which one minimizes risk-adjusted costs relative to the arrival price benchmark.

The parameters in an arrival price optimization are alpha, number of shares to execute, start time, end time, and risk aversion parameter.

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.

For example: under the assumption of 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 and 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.

Crossing

The idea behind crossing networks is that large limit orders are not adequately protected in a public exchange. Simply displaying large limit orders in the open book of an electronic exchange may leak too much info about institutional traders' intentions. The info is used by prospective counterparties to trade more passively in the expectation that time constraints will force traders to replace some or all of the large limit orders with market orders. In other words, information leakage encourages gaming of large limit orders.

Crossing networks are designed to limit information leakage by making their limit books opaque to both their clients and the general public.

A popular form of cross is the midquote cross, in which 2 counterparties obtain a midquote fill price. Regulations require that the trade is then printed to a public exchange to alert other market participants that it has taken place. The cross has no market impact but both counterparties pay a fee to the crossing network. These fees are tyically higher than the fees for other types of algo trading because the market impact savings are significant while the fee is contingent on a succesfull cross.

More recently, crossing networks have offered their clients the ability to place limit orders in the crossing networks' dark books. This makes crossing networks much more like traditional exchanges, with the important difference that their books are opaque to market participants.

To protect their clients from price manipulation, crossing networks implement antigaming logice. Opaqueness is itself a form of antigaming, but there are other strategies.

For example: some crossing networks require orders to be above a minimum size or to remain in the network longer than a prespecified minimum time. Other networks will cross only orders of similar size. This prevents traders from pinging --> sending small orders to the network to determine which side of its book has an order imbalance.

There are several different kinds of crossing networks.

A continuous crossing network constantly sweeps through its book in an attempt to match buy orders with sell orders.

A discrete crossing network specifies points in time when a cross will take place, say every half hour. This allows market participants to queue up in the crossing network just prior to a cross instead of committing resting orders to the network for extended periods of time.

In automated crossing networks, resting orders are matched according to a set of rules, without direct interaction between the counterparties.

In negotiated crossing networks, the counterparties first exchange indications of interest, then negotiate price and size.

Some traditional exchanges not allow the use of invisible orders, resting orders that sit in their order books but are not visible to market participants. These orders are also referred to as dark liquidity. The difference between these orders and those placed in a crossing network is that traditional exchanges offer no special antigaming protection.

Private dark pools are collections of orders that are not directly available to the public.

For example: a bank or pension manager might have enough order flow to maintain an internal order book that, under special circumstances, is exposed to external scraping by a crossing network or crossing aggregator

A crossing aggregator charges a fee for managing a single large order across multiple crossing networks. Order placement and antigaming rules differ across networks, making this task fairly complex. A crossing aggregator may also use info about historical or real-time fills to direct orders.

For example: failure to fill a small resting buy order in a crossing network may betray info of a much larger imbalance in the network's book. This makes the network a more attractive destination for future sell orders.

Crossing lends itself to several optimization strategies. Longer exposure to a crossing network not only increases the changes of an impact-free fill, but also increases the risk of a large and compressed execution if an order fails to obtain a fill. Finding an optimal exposure time is one type of crossing optimization.

A more sophisticated version of this approach is solving for trade-out, a schedule for trading shares out of the crossing network into the open markets. As time passes and a cross is not obtained, the strategy mitigates the risk of a large, compressed execution by slowly trading parts of the order in the open markets.

Other Algos

Liquidity seeking is an algo where the objective is to soak up available liquidity. As the order book is depleted, trading slows down. As the order book is replenished, trading speeds up.

Financed trading: the idea behind it is to use a sale to finance the purchase of a buy with the objective of obtaining some form of hedge.

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