Execution or trading?

Unfortunately the terms are often used loosely: think of 'portfolio trading' or 'optimal trading strategy'. Here we focus on execution, in keeping with the services offered by banks and brokers. However, it is best defined as the opposite of trading, which:

In the above sense, trading is the responsibility of asset managers, proprietary traders and others who choose to take positions in assets. If they choose to use machines to exercise that responsibility, then the activity is perhaps more clearly labelled model based trading.

With algorithmic execution, as with all execution, we are looking at situations where only some discretion is left in completing the order, and the reward is commission or average efficiency in minimising the variance from executed prices and benchmarks.

Rules or strategies?

For many years, brokers have provided to their clients types of order beyond the limit orders offered by an exchange. The classic example is the stop order; a normal limit order which, once the market trades through a price, is automatically cancelled by the broker-dealer and replaced by a market order. These enhanced order types are still non-discretionary, just as if the investor had made the decision directly using publicly available information in real time. More are shown in the table below

Exchange ordersBroker-dealer orders
Stop loss: at the given price, submit the order as a market order.
Stop: at a given price, change the limit order into a market order.
Stop limit: at a given price, submit the order as a limit order.
Regular peg: keep the limit price equal to the best price on the same side.
Reverse peg: keep the limit price equal to the best price on the other side, less an offset.
Others: the FIX protocol has order types for pegging at the mid price, last traded price and VWAP; GL Tactics has a reversal order type, where for example, a buy order will be suspended on a price fall until the price has recovered a given amount.

The table is a necessary simplification of a complex world: for example, NASDAQ directly supports regular and reverse peg orders. Although some algorithmic execution systems include these enhanced order types, they are in essence rules rather than strategies for execution.

Algorithmic strategies automate all of the decisions on when to make prices or to take from the order book, and in what quanties, until the original order quantity is filled. VWAP strategies have been operating since the 1980s, throughout the period when VWAP was the dominant execution benchmark. Although banks seem to have overdone product branding, with dozens of strategies available, in essence there is a core family of single asset strategies:

Allocate the order quantity over time in proportion to expected market volume.
Allocate the order quantity equally over time. This could be regarded as a special case of VWAP, using an expectation of constant trading. However, strict TWAP would aim to trade at each change of quote.
Arrival Price
Allocate order quantity in decreasing proportion to expected market volume. The allocation may again be a special case of VWAP, with an exponentially declining expectation of market volume [1] , or it may follow Almgren [2] [3].
Execute whenever the asset trades in the market.

Further reading

1.Kissell and Glantz Optimal Trading Strategies, 2003
2.Almgren and Chriss Optimal Execution of Portfolio Transactions
3.Almgren Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
4.Gordon Baker and Shashi Tiwari Algorithmic Trading - Perceptions and Challenges, EDHEC Risk Newsletter 2004-11
Reproduced with the permission of EDHEC Risk.