7 Optimal trading strategies

7.1 Introduction

How do we go about determining the optimal trading strategy for a given order? We will start by examining an example trading decision framework, as described by Wayne Wagner(2006). This framework illustrates the process from the point of view of a buy-side trader:
Step

1. A portfolio manager initially notifies them of the order
2. If there are any specific restrictions then the trader must use the designated broker.
3. Otherwise, the trader must assess how difficult the order will be to trade.
   3.1 For orders that will provide much-needed liquidity to the markets, the trader should strive for the optimal price.
   3.2 Similarly, for the orders that are judged easy, the trader has a lot of leeway in how best to deal with them.
   3.3 Tough orders may be sub-categorized based on whether:
   • They are a large percentage of the average daily volume(ADV).
   • The asset is exhibiting significant trading momentum.

   • The investor has flagged the order as urgent.
     Depending on the perceived difficulty, the trader then must select the most appropriate method of trading. this may mean using trading algorithms, DMS, trying to cross the order, or negotiating a principal transaction with a dealer.

     
     
     A hierarchy of trading decisions

7.2 Assessing the difficulty of orders

Determining how difficult an order will depend on a range of properties. Wagner(2006) points out three such factors, namely large orders(relative to the ADV), unfavorable price momentum, and urgency. Conversely, the key feature that makes trading easy is liquidity.
One way of quantifying the potential order difficulty is based on historical results from transaction cost analysis(TCA). The following shows the results of a proprietary liquidity and impact cost analysis performed by Jacqueline King and Yan Yaroshevsky(2005) at Abel/Noser.

Realized costs for different asset groups

Order size, Liquidity, Volatility, Price momentum, Urgency, Trading horizon

7.3 Selecting the optimal trading strategy

Since the concept of the best execution revolves around achieving the investor's objectives, it is vital that these are considered:

• intended benchmark
• level of risk aversion
• desired trading goals
  These will have a significant impact on our choice of strategy
  The efficient trading frontier
  Trading strategies are generally more focused on cost, so Robert Almgren and Neil Chriss(2000) proposed the efficient trading frontier. They reasoned that rational traders would always seek to minimize expected costs for a certain level of risk. Hence, an optimal trading strategy was defined as one for which there were no alternatives with lower expected costs for the same degree of risk. The set of optimal solutions were termed the efficient trading frontier, consisting of a single solution for every possible level of risk.
  
  An efficient trading frontier
  
  Although the efficient trading frontier is an extremely useful theoretical concept, creating them can be time-consuming. To make things easier, Robert Kissell and Morton Glantz proposed an approximation by fitting an exponential decay curve to just a few specific strategies. More details may be found in Kissell and Glantz(2003)
  Choosing the benchmark
  The benchmark can have a substantial effect on the accuracy of performance measures. A similar result may be observed for the efficient trading frontiers, as highlighted in a study by Kissell and Malamut(2005b).
  
  The efficient trading frontier for a range of different benchmarks
  
  
  Benchmark expected costs and risks
  
  The cost consists of both temporary and permanent impacts. The permanent impact g() is based on the order size (X) whilst the temporary impact cost function h() also depends on the trader rate (α). The timing risk principally consists of the price volatility σ(), which in turn is based on an error factor (ε), this just represents random noise.
  Using a pre-trade benchmark (p_d) earlier than the arrival price means an additional price change (p₀ - p_d) must be considered. This corresponds to the delay cost. Therefore benchmarks based on previous closing or opening prices must incorporate this into their expected costs and risks. In terms of expected cost, the efficient trading frontier will be shifted by this amount. The direction depends on whether the order is a buy or sell.
  In comparison, using a post-trade benchmark based on future closing prices will reduce the expected cost. This is because the permanent market impact is already accounted for in the future benchmark price. Hence, the estimated cost is just the temporary market impact (assuming no real price trend). Thus, the efficient trading frontier is shifted downwards by an amount equal to the permanent market impact. Though, in terms of timing risk, it will be just like the arrival price benchmark (since the time periods are the same).
  Note that intraday benchmarks behave somewhat differently since they are based on prices throughout the day so they incorporate both temporary and permanent impact cost. Therefore, for a VWAP benchmark, it is possible to minimize both cost and timing risk by participating evenly with the day's volume.
  The benchmark choice can clearly affect the efficient trading frontier, and so it can later the optimal choice of trading strategy.
  Determining the level of risk aversion
  Risk aversion directly affects the aggressiveness of a trading strategy. A high level indicates that timing risk is not acceptable and so the strategy should be more aggressive to try to complete faster. This increases the expected cost due to the market impact. Alternatively, a low level suggests that minimizing market impact is more important.
  
  Risk aversion
  
  Kissell and Malamut(2005b) highlighted this relationship between the risk aversion parameter (λ) and trading style by plotting a normalized efficient trading frontier.
  Choosing a trading goal
• Minimize the expected cost for a given level of risk
• Achieve price improvement over a given level of cost
• Balance the trade-off between expected cost and risk
  Determining the optimal trading horizon
  
  Trading strategy optimization

7.4 Choosing between trading algorithms

Mapping algorithms to the efficient trading frontier

Differentiating algorithms using an efficient trading frontier