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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