Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

each period are 250,000 ( v 1 ), 200,000 ( v 2 ), 100,000 ( v 3 ), 200,000 ( v 4 ) and 250,000 ( v 5 ). Furthermore, the investor believes that there will be an incremental market imbalance of 100,000 shares ( Y ). Incremental imbalances allocated to each period are 35,000 ( y 1 ), 30,000 ( y 2 ), 20,000 ( y 3 ), 10,000 ( y 4 ) and 5,000 ( y 5 ) respectively. If the instantaneous market impact cost is estimated at € 300,000 ( I ), how can he determine the cost related to his strategy?

cost for the security, Δ p is the expected price trend per period for the security, X is the order size, x k is the number of shares to trade in period k and v k the expected volume for the security in period k . Hence, the uncertainty surrounding the transaction cost estimate can be computed as the standard deviation of the previous equation, that is: ℜ ( φ ) = E( φ 2 ) − E( φ ) [ ] 2 Assuming that volume and price movement are independent 21 simplifies the calculation and allows the following equation: ℜ ( φ ) = σ 2 U( x k ) [ ] + σ 2 K( x k ) [ ] where timing risk is obtained through a simple combination of price risk and liquidity risk. (a) Price risk The most common measure of price risk is the standard deviation of price returns. For trading purposes, price return volatility must be converted into monetary units per share as follows: 1. assuming that  p is not much different from each p t , we can write: 22

0.95 x k

+ y

I X + Y

n ∑

k

K( x k

) = sign( k )

x

+ 0.05

k

x

+ y

+ 0.5v k

⎦ ⎥

⎣ ⎢

k = 1

k

k

0.95 x k

x

+ y

300000 200000 + 100000

5 ∑

k

k

K( x k

) = +

+ 0.05 x k

= 83350

x

+ y

+ 0.5v k

⎦ ⎥

⎣ ⎢

k = 1

k

k

(4) Timing risk Timing risk is related to the uncertainty associated with price movements and cost estimates. It can be broken down into price risk, which consists of price volatility, and liquidity risk, the result of fluctuations in market conditions. Price risk affects price appreciation estimates ( U(x k ) ) while liquidity risk affects market impact estimates ( K(x k ) ). Here again, we will refer to Kissell and Glantz’s material to document how timing risk components can be modelled and forecasted. Consistent with what we have seen earlier, we can write the following transaction cost estimate equation:

21 - There is a negligible degree of correlation between price changes and market volume, but the absolute value of price changes and that of volume are correlated. This means that the presence of high volume does not indicate the direction of price movement. 22 - Natural log of price returns can also be used. Both calculations deliver very similar results for normal market conditions.

= p t

≅ p t

− p

− p

= 1

r t

p Δ p t

t − 1

t − 1

p

p

t − 1

2. since  p is a constant: σ 2 ( r ) = 1

p 2 σ 2 ( Δ p t

)

2 I

0.95 x k

⎡ ⎣ ⎢

⎤ ⎦ ⎥ + ⎣ ⎢

k ∑

k ∑

X ( x k 3. for short time periods ( ≤ 5 days) and with E( r ) ≤ 50% and σ ( r ) ≤ 75% on a yearly basis, the current security price p 0 may be substituted for  p with little loss of accuracy: σ 2 ( r ) ≅ 1 p 0 2 σ 2 ( Δ p t ) + 0.5v k ) + 0.05I ⎦ ⎥

φ ( x

) = U( x k

) + K( x k

) =

x

k Δ p

k

k

2 I

0.95 x k

⎡ ⎣ ⎢

⎤ ⎦ ⎥ + ⎣ ⎢

k ∑

k ∑

φ ( x

) = U( x k

) + K( x k

) =

x

k Δ p

) + 0.05I

k

k

X ( x k

+ 0.5v k

,

where I is the instantaneous market impact

50

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