Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

U(X) estimates the cost expressed in monetary units for the total order size. To get the cost per share or in basis points, we simply divide U(X) by the order size (X) or the traded value at the beginning of trading ( XP 0 ). Because U(X) is a cumulative function, predicting the cost of price appreciation for a specific trade list that contains several orders and securities results in making the sum of cost estimates for each order and listed security. We can illustrate the method above with a small example. Consider an order of 170,000 shares to be executed over three trading periods. The current security price is € 50 and this price is expected to increase by € 0.10 per period. If the execution strategy involves trading 60,000, 60,000 and 50,000 shares in periods 1, 2 and 3; we estimate the cost of price appreciation as follows: (3) Market impact Market impact is the price shift caused by a particular trade. It can be broken down into short-lived impact that dissipates over time and long-term disturbances in the price trajectory. As with price appreciation, we need first a model that relates the market impact cost of past trades to a number of trade-specific, market-related, and security-specific variables. We then use the calibrated model to obtain cost estimates for the specified execution strategy. However, because market impact is a more complex cost component This cost of € 33,000 is equivalent to € 0.19 or 39bp per share.

than price appreciation and depends on elements such as imbalances, volatility, trading style and liquidity, the approach is more difficult and technical. We provide hereafter a summarised version of Kissell and Glantz’s market impact model and illustrate how it can be used to derive cost estimates for given trading strategies. (a) Market impact model As explained just above, market impact depends on several factors: • Order size and imbalances: market impact is positively related to order size and the liquidity supply-demand imbalances it causes; •  Volatility: higher volatility means greater price elasticity and higher transaction costs; •  Trading style: aggressive trading strategies lead to higher market impact than do passive strategies; • Market conditions: market impact is negatively related to the available liquidity over the trading horizon. Based on the previous factors, Kissell and Glantz (2003) model the total market impact cost as: MI = α I + (1 − α )I , where α is the percentage of temporary impact; (1- α ) is the percentage of permanent impact and I is the total market impact cost. The latter is expressed in monetary units and depends on both imbalance and volatility. Assuming that only liquidity demanders incur temporary impact costs 15 and that permanent impact is a function of the net imbalance, 16 the market impact cost expressed in monetary units per share is rewritten as: MI = α I V side + (1 − α )I Q where V side is the

15 - Liquidity demanders consume the available

liquidity by trading at market prices and contribute to the supply-demand imbalance. By contrast, liquidity providers supply liquidity to obtain better prices for trades that they would like to complete. Hence, only liquidity demanders pay temporary impact costs. 16 - Permanent impact is due to the net effect of all market participants and all market participants incur permanent impact costs. This assumption is valid if (i) all trades convey some information to the market and the security current fundamental value is continuously assessed; (ii) the information content is proportional to the trade size and similar for buy orders and sell orders.

U( X ) = 60000 × 0.10 + 60000 × 2 × 0.10 + 50000 × 3 × 0.10 = 33000

U( X ) = 60000 × 0.10 + 60000 × 2 × 0.10 + 50000 × 3 × 0.10 = 33000

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An EDHEC Risk and Asset Management Research Centre Publication