Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

P Q

⎛ ⎝⎜

⎞ ⎠⎟ × 10 4

ϕ Q = sign( Q )

− 1

for the previous T trading days (most of the time T =30). Mathematically, we have

.

P 0

1 T − 1

T ∑

Parameter estimates For the parameter α in the dissipation function, the authors found in almost all their regressions that it is about 95%; this estimate is not dependent on time and size. We can then rewrite the dissipation function as: d( η ) = 0.95 η − 1 + 0.05 . Since α refers to the temporary impact, Kissell and Glantz’s findings suggest that temporary impact cost is by far the largest part of total market impact cost. Kissell and Glantz (2003) investigate three possible structures for the instantaneous market impact function: the linear function, the non-linear function and the power function. Each requires i parameters termed a i . We present below each possible function with both the general formulation and the formulation including the estimated parameters. 18

( g t

g) 2 , where

σ =

−

t = 1

g t

= ln P

t P

.

t − 1

The dissipation function relies on the variable η that represents the participation number. It is used as a proxy of trading style and is calculated as the number of equal size orders executed in the market over the same trading period as the investor’s order.

η = V

.

side

Specifically, we have

Q

18 - According to Kissell and Glantz (2003), the three functions yield fairly consistent results across size and volatility. However, the non-linear and power functions exhibit smaller regression errors, suggesting that the true relationship between cost and size is non-linear.

Taking the absolute value of Q is required to ensure that the participation rate is positive. The lower the participation number is, the shorter the trading time horizon is, and the more aggressive the strategy is. Finally, estimation of the various parameters of the market impact model requires an additional variable that represents the trading cost associated with the imbalance Q . This cost expressed in monetary units is computed according to the following equation:

•  Linear function: I bp

( Z , σ ) = a 1

Z + a

2 σ + a 3

I bp ( Z , σ ) = 8Z + 0.3 σ + 90

• Non-linear function: I bp

( Z , σ ) = a 1 Z a 2 + a 3 σ + a 4

∑

x

p

− XP 0

= XP Q − XP 0

= X ( P Q − P 0

)

ϕ Q =

j

j

I bp ( Z , σ ) = 35 Z 0.65 + 0.3 σ + 15

where P 0 is the market price at the beginning of trading and P Q is the volume-weighted average price for shares on the same side as the imbalance, that is:

• Power function: I bp

( Z , σ ) = a 1 Z a 2 σ a 3

I bp ( Z , σ ) = 25 Z 0.38 σ 0.28

∑ ∑

p i

v

i

P Q =

(c) Forecasting market impact cost The forecast of market impact cost for an order K(X) and a particular trading strategy K(x k ) is based on the following equations:

for i ∈ Q .

v

i

The cost of imbalance expressed in value per share and in basis points is given by ϕ Q = sign( Q ) P Q − P 0 ( ) and

46

An EDHEC Risk and Asset Management Research Centre Publication