Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

3. compute the expected volume on the day: V = 0.95 × 1000000 = 950000 4. calculate the participation number: η = 100000 + 0.5 × 950000 100000 = 5.75 5. determine the expected market impact cost: Example 2: Forecasting market impact for an order when there is an incremental imbalance Suppose a situation similar to the previous example, except that the investor believes now that there will be an additional imbalance of 100,000 shares ( Y ) on the same side as his order. Given the data at hand, how can he estimate the market impact cost for his order? Now the following six steps lead to an answer: 1. express the imbalance as a percentage of ADV: Z = 100000 + 100000 1000000 × 100 = 20 K( X ) = + 206429 ×

4. calculate the participation number: η = 100000 + 100000 + 0.5 × 950000 100000 + 100000

= 3.38

5. determine the sign: sign(100000 ) × sign(100000 + 100000 ) = + × +

sign(100000 ) × sign(100000 + 100000 ) = + × + = +

6. compute the expected market impact cost: K( X ) = + 206429 × 100000

K( X ) = 79314 × ( 0.95 × 5.75 − 1 + 0.05 ) = 17070

100000 + 100000 × ( 0.95 ×

K( X ) = 79314 × ( 0.95 × 5.75 − 1 + 0.05 ) = 17070

100000 100000 + 100000 × ( 0.95 × 3.38 − 1 + 0.05 ) = 34214

Example 3: Forecasting market impact for a given strategy when the imbalance is equal to order size An investor has a buy order for 200,000 shares ( X ) and wants to execute 40,000 shares ( x i ) in each of the coming five periods. Forecasts for expected market volume in each period are 250,000 ( v 1 ), 200,000 ( v 2 ), 100,000 ( v 3 ), 200,000 ( v 4 ) and 250,000 ( v 5 ). If the instantaneous market impact cost is estimated at € 150,000 ( I ), how can he compute the cost related to his strategy?

0.95 x k

I

⎤ ⎦ ⎥ = 150000 200000

⎡

n ∑

K( x k

) =

x

+ 0.05

⎢

k

x

+ 0.5v k

X

⎣

k = 1

k

2. determine the market impact instanta- neous cost using the power function (for example): I = ( 25 × 20 0.38 × 200 0.28 ) × 10 − 4 × 30 × 200000 = 206429 X k x k + 0.5v k + 0.05 ⎣ ⎢ ⎦ ⎥ = 150000 200000 k = 1 5 ∑ k = 1 n ∑ x k 0.95 x k x k + 0.5v k + 0.05 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = 150000 200000 0.95 x k 2 x k + 0.5v k + 0.05 x k ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ k = 1 5 ∑ K( x k ) = I x 0.95 x k ⎡ ⎤

0.95 x k 2

⎡

⎤

+ 0.05 x k

= 50271

⎢

⎥

x

+ 0.5v k

⎣

⎦

k

I

n ∑

K( x k

) =

= 50271

X

k = 1

I = ( 25 × 20 0.38 × 200 0.28 ) × 10 − 4 × 30 × 200000 = 206429

Example 4: Forecasting market impact for a given strategy when there is an incremental imbalance An investor has a buy order for 200,000 shares ( X ) and wants to execute 40 000 shares ( x i ) in each of the coming five periods. Forecasts for expected market volume in

3. compute the expected volume on the day: V = 0.95 × 1000000 = 950000

49 An EDHEC Risk and Asset Management Research Centre Publication