Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

traded volume from liquidity demanders and Q is the net imbalance.

As previously explained, I is a function of both imbalance and volatility. By defining η = V side Q , the authors obtain the following market impact formulations: MI( Q ) = I( Q, σ ).( αη − 1 + (1 − α )) = I( Q, σ ).d( η ) MI bp = I bp ( Z , σ ).d( η ) The first equation specifies the total market impact cost in monetary units, the second in basis points, with imbalance stated as a percentage of average daily volume ( Z ). Both equations now present market impact as a product of two functions where d( η ) is the dissipation function and I(Z, σ ) is the instantaneous market impact function. The variables in each function have to be determined and the parameters have to be jointly estimated with advanced regression techniques. We report below what the authors propose given their own analyses. 17 Variables The instantaneous market impact function is built on two variables, Z and σ . The first represents the imbalance expressed as a percentage of average daily trading volume and is computed as follows:

In this top-down approach, the market impact cost for an order of X shares is then given by: MI( X ) = X α I V side + (1 − α )I Q ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ . As we may observe, if the order size is equal to the imbalance and accounts for all liquidity demand ( X= Q= V side ), the total market impact cost incurred by the investor is I . Hence, the market impact cost for a specific trading strategy MI(x k ) can be derived according to the following principles. First, the percentage of temporary impact in any trading period k is equal to the percentage of the imbalance in that period. The total temporary impact cost can then be allocated to each trading period based on the percentage of imbalance in each period ( q k Q where q k is the net imbalance in period k ). Next, by applying an average permanent impact cost across all trades, allocation of total permanent impact across periods is not necessary. The cost of market impact for the trading strategy x k is therefore calculated as follows:

17 - The results reported by Kissell and Glantz (2003) are based on numerous analyses on various sample sizes, volatility, participation rates and mixed data samples.

Q ADV × 100

Z =

q

α I

(1 − α )I Q

⎡

⎤

n ∑

,

MI( x k

) =

x

k

+

⎢

⎥

k

V

Q

⎣

⎦

where

k = 1

side

n ∑

Q =

sign( v i

)

(b) Parameter estimation To calibrate their model, Kissell and Glantz (2003) start with the total cost of market impact over an entire trading day when X=Q :

i = 1

with sign(v i

) equal to the signed trade size

and

ADV = 1 T

T ∑

v

t

t = 1 with T usually equal to thirty trading days. The second variable σ refers to the price volatility factor and corresponds to the close-to-close measure of the volatility of logarithmic price change

MI( X = Q ) = Q α I V side ⎡ ⎢

(1 − α )I Q

⎤ ⎦ ⎥ = α IQ V side

+ (1 − α )I

+

⎣

45 An EDHEC Risk and Asset Management Research Centre Publication