Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

the same vein as Markowitz’s portfolio optimisation framework, a very popular tool from classic finance theory. It shows the trade-off between risk and return in an investment portfolio: to achieve higher returns, investors must take on more risk. The same is true for the question at hand: to incur lower transaction costs, the trader must implement a riskier strategy. As in portfolio theory, this takes us to the notion of an efficient frontier. The notion of a trading frontier is explored in several academic and professional works that deal with execution optimisation. 26 It can be defined as the set of strategies that contain the lowest cost for the specified level of risk, in which strategies are determined through optimisation for all possible values of λ . Figure 11 shows a trading frontier. The cost curve is a convex function in which each points corresponds to a unique degree of risk aversion ( λ ). This function decreases over the range 0 ≤ ℜ ≤ t and increases when 0 ≤ ℜ ≤ t > . Strategy C ( θ (z,t) ) corresponds to the minimum cost of the frontier. Based on the above optimisation equation, this minimum cost will occur at frontier. Based on the above optimisation equation, this minimum cost will occur at λ =0 since risk is excluded. For positive values of λ , we obtain points with higher costs and lower risk than at the minimum cost point. For example, strategy A ( θ (y,s )) is on the curve to the left of C since sz. By contrast, points on the curve on the right of C are associated with negative values of λ . It is the case for strategy B whose cost profile is θ (y,u) . An important element here is that when λ <0 the optimisation is minimised at the value where the quantity of risk is maximised. This corresponds to a strategy wherein trading is spread over as long as possible a

period. However, we can observe situations in which the incremental price appreciation cost begins dominating the market impact cost reduction, resulting in an increase of total transaction costs. It is for this reason that optimisation with negative risk aversion is not really relevant for investors.

Figure 11: Trading frontier

26 - See, for example, Almgren and Chriss (2000) and Nevmyvaka et al. (2005).

Like the efficient frontier in portfolio theory, the efficient trading frontier (EFT) is the set of all the dominating trading strategies, that is, the set of strategies that contain the lowest cost for the specified risk and the least risk for a specified cost. It is quite easy to see in figure 11 that only strategies on the curve to the left of C are optimal. Although A and B exhibit the same cost level ( y ), only A is a true optimal strategy because it contains less risk for the cost ( s

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