Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

We finally obtain that the market impact cost (in monetary units) for an order of X shares implemented over n -trading periods following strategy x k is:

K( X ) = I( 0.95 η − 1 + 0.05 )

K( x k n ∑ To apply these equations, estimated values are needed for imbalance Q , liquidity demander volume by period v k,side and instantaneous cost I . Kissell and Glantz (2003) discuss two cases that require specific forecasting techniques. First case: the imbalance is equal to the order size This situation corresponds to the common assumption that Q= X and each x k =q k , since intentions of other market participants are hard to assess before trading begins. Under this assumption, instantaneous cost is determined as follows: I = I bp ( Z , σ )10 − 4 P 0 Q where As for liquidity demander volume, the expected volume on the day V(t) is first computed as: where DOW(t) is a day-of-week adjustment factor accounting for the weekly volume effect. 19 The percentage of volume in each trading period v k is then obtained by applying the security volume profile u k , which represents the percentage of the day’s total volume traded in each period: . Since the total imbalance is assumed equal to the order size, v k consists of an equal amount of buy and sell volume. Consequently, the liquidity demander volume v k,side will be equal to the imbalance in each period ( x k ) plus half of the market volume. We have thus v k ,side = x k + 0.5v k . K( x k ) = x i ,k k = 1 n ∑ i = 1 m ∑ ) = x k 0.95Iq k Qv k ,side + 0.05I Q k = 1 Z = X ADV 100 v k = V ( t )u k

0.95Ix k

) + 0.05I X

n ∑

K( x k

) =

x

k

X ( x k

+ 0.5v k

k = 1

Since market impact cost is a cumulative function, the market impact cost estimated for a list of m -securities traded over n -periods is simply the sum of costs for all orders. That is:

0.95I i

x

+ 0.05I i X i

m ∑

n ∑

i ,k

K( x k

) =

x

i ,k

X

( x

+ 0.5v

)

i = 1

k = 1

i

i ,k

i ,k

19 - Patterns of daily trading volumes are used to exhibit a day-of-week effect. A factor specifying the day’s historical percentage of the average daily volume can improve the daily volume forecast. 20 - This case is possible when investors can formulate realistic expectations about buying and selling pressure from other market participants. It often happens at times of public announcements or index reconstitution.

0.95I i

x

+ 0.05I i X i

i ,k

X

( x

+ 0.5v

)

i

i ,k

i ,k

Second case: there is an incremental imbalance due to other market participants This situation corresponds to the assumption that Q=X+Y , where Y is the expected net imbalance of other market participants. 20 Appropriate adjustments in the previous developments are necessary to incorporate this piece of information. Accordingly, the instantaneous market impact cost becomes

I = I

( Z , σ )10 − 4 P 0

X + Y , where

bp

X + Y ADV

Z =

100

with X or Y >0 for buys

and X or Y<0 for sells. Next, the liquidity demander volume in each trading period is now:

= x k

+ y

+ 0.5v k

v

k ,side

k

47 An EDHEC Risk and Asset Management Research Centre Publication

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