Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

It is worth noting that the absolute value function is necessary to account for the cases when the investor’s order and the net imbalance of other market participants are on opposite sides. Furthermore, whenever the net imbalance of other market participants is larger and on the opposite side, the investor incurs a savings rather than a cost. To address this potential savings, the calculation must provide the investor with the correct sign for market impact cost. This is made through the following cost function: sign( k ) = sign( X ).sign( X + Y ) From all the previous adjustments, the market impact cost (in monetary units) for an order of X shares implemented over n -trading periods following strategy x k is:

+ y An investor has a buy order for 100,000 shares ( X ) on a particular security whose current market price is € 30 ( P 0 ), daily volatility is 200bp/day ( σ ) and average daily volume is 1,000,000 shares (ADV). The investor wants to execute the order over an entire day whose day-of-week adjustment factor is about 0.95 (DOW). Given the data at hand, how can he estimate the market impact cost for his order (in monetary units)? The following five steps lead to an answer: 1 express the imbalance as a percentage of ADV: Z = 100000 1000000 × 100 = 10 2. determine the market impact instanta- neous cost using the power function (for example): I = ( 25 × 10 0.38 × 200 0.28 ) × 10 − 4 × 30 × 100000 k + y k + 0.5v k ) + 0.05I X + Y ⎤ ⎦ ⎥ ⎥ x i ,k + y i ,k i ,k + y i ,k + 0.5v i ,k ) + 0.05I i X i + Y i ⎤ ⎦ ⎥ ⎥ assume that the parameter values obtained by the authors are suitable for our examples. However, pre-trade analysis assumes that the market impact of future orders can be predicted from the market impact of past orders. This assumption is valid when liquidity conditions do not change too much. So, we recommend to those interested in using this market impact model to determine their own calibration with their own recent data sample, since the data used by the authors may be not relevant for estimation on other markets, securities and periods. Example 1: Forecasting market impact for an order when the imbalance is equal to order size

0.95I x k

⎡

n ∑

K( x k

) = sign( k ).

x

⎢

k

X + Y ( x k

⎣ ⎢

k = 1

0.95I x k

+ y

⎤

⎡

) + 0.05I X + Y

n ∑

k

K( x k

) = sign( k ).

x

⎥

⎢

k

X + Y ( x k

+ y

+ 0.5v k

⎦ ⎥

⎣ ⎢

k = 1

k

For a list of m -securities traded over n -periods, the market impact cost forecasting equation becomes:

⎡

0.95I i

m ∑

n ∑

K( x k

) =

sign( k i

). x

⎢

i ,k

X

+ Y i

( x

⎢

⎣

i = 1

k = 1

i

⎤

⎡

0.95I i

x

+ y

0.05I i

m ∑

n ∑

i ,k

i ,k

K( x k

) =

sign( k i

). x

+

⎥

⎢

i ,k

X

+ Y i

X

+ Y i

( x

+ y

+ 0.5v

)

⎥

⎢

⎦

⎣

i = 1

k = 1

i

i

i ,k

i ,k

i ,k

(d) Illustration We now present a set of examples to illustrate how Kissell and Glantz’s (2003) market impact model can, once it is calibrated, be used for easy cost estimates. For convenience, we change nothing and

I = ( 25 × 10 0.38 × 200 0.28 ) × 10 − 4 × 30 × 100000 = 79314

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An EDHEC Risk and Asset Management Research Centre Publication