Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

Table 3: Expected market conditions over the trading horizon

Table 5: Expected market conditions over the trading horizon

Expected volume

VWAP strategy

10% participation strategy

Expected volume

Trading period

Trading period

Executed shares

Residual shares

Buy

Sell

Executed shares

Residual shares

Buy

Sell

1

200,000 200,000 24,000 120,000

1

200,000 200,000 40,000 120,000

2

150,000 150,000 18,000 96,000

2

150,000 150,000 30,000 80,000

3

100,000 100,000 12,000 78,000

3

100,000 100,000 20,000 50,000

4

50,000 50,000

6,000

66,000

4

50,000 50,000 10,000,

30,000

5

50,000 50,000

6,000

60,000

5

50,000 50,000 10,000 20,000

6

100,000 100,000 12,000 54,000

6

100,000 100,000 10,000 10,000

7

150,000 150,000 18,000 42,000

7

150,000 150,000

0

0

8

200,000 200,000 24,000 24,000

8

200,000 200,000

0

0

To determine the cost profile for this VWAP strategy, we must compute the expected price appreciation cost, market impact cost and timing risk. For the latter, we focus on price risk alone. The final results are presented in table 4 and some helpful details for each calculation are noted below.

Table 6: Cost profile of the 10% participation strategy Implicit costs

Risk

PA*

MI** Costs***

linear growth

Total euros ( € ) Euros/ share ( € / share) Basis points (bp/share)

77.500 76.972 30.350 107.850 53.343

0.90 0.44

0.65 0.64 0.25

Table 4: Cost profile of the VWAP strategy Implicit costs

Risk

112 56

81

80

32

PA*

MI** Costs***

linear growth

* price appreciation, ** market impact, *** total costs with the linear model

Total euros ( € ) Euros/ share ( € / share) Basis points (bp/share)

135,000 134,607 22,768 157,768 70,310

Comparing tables 4 and 6, we observe now that θ bp ( VWAP ) = (164.73 ) and θ bp (10%) = (112.56 ) . So, the second strategy is clearly less costly and risky than the first. In fact, given expected market conditions, the 10% participation strategy offers the lowest risk and cost because it completes trading at the sixth period and does not expose the order to adverse price movements over the entire trading day. (1) Optimisation formulation In uncertain market conditions, the preservation of asset value is essential for most investors and we can define the ultimate goal of implementation as asset value preservation in the presence of risk.

1.31 0.59

1.13 1.12 0.19

164 73

141 140

24

* price appreciation, ** market impact, *** total costs with the linear model

Note: As for price appreciation, the linear model delivers a constant price change of 0.25 per trading period while the growth model provides an exponential price change of 0.0031. Concerning timing risk, the stock variance per trading period (1,800bp) is estimated from daily volatility. To express it in monetary units, we multiply it by the square root of the current stock price. With the same method, we are also able to determine the cost profile of an alternative strategy such as a 10% participation strategy (see tables 5 and 6).

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An EDHEC Risk and Asset Management Research Centre Publication

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