Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

III. Measuring Transaction Costs with Post-Trade Analysis

time and the actual trade price, it actually delivers a nearly complete measure of implicit costs. Indeed, in this formulation, Perold’s market impact includes costs resulting from spread, market impact, operational delay and market timing delay. Therefore, the opportunity cost component refers only to the missed trade opportunity cost, i.e. , to the cost related to unfilled or partially filled orders. The mathematical notations for measuring the implementation shortfall for a given trade in a particular security can be presented as follows. X = total quantity to execute (total trade size) x i = number of shares executed at price i X , x i > 0 for a buy; X , x i < 0 for a sell P 0 = quotation midpoint at the time of the investment decision P T = quotation midpoint at the end of trading P i = execution price of i th trade EC = all the explicit costs associated with the trade

Figure 10: Principle of the implementation shortfall

30%

Potential Return

25%

20%

Implementation Shortfall (TotalTransaction Costs)

15%

Return

10%

Realised Return

5%

0.0

-10 -5 -2

1 2 3 5 10 15 20 30 Security Purchase Date

Days after Security Purchase Date

Days Prior to Security Purchase Date

5 - If an investor simultaneously buys and

Potential Return Realised Return

sells shares in a security and recorded buys at the best ask and sells at the best bid, the resulting paper portfolio will incur a loss due to the spread.

Research Period (Manager conducts research and develops a sound investment strategy whithin an optimal environment)

Source: Plexus Group

Much as with the benchmark comparison, the key here is the choice of price for valuing the paper portfolio. Perold’s definition requires that all executions occur at the spread midpoint prevailing on the market at the time of the investment decision. This specific valuation is necessary to avoid charging the paper portfolio with one-half the spread cost on average. 5 Calculated with the decision spread midpoint, transactioncosts are thendivided into what the author terms execution costs and opportunity costs . Execution costs cover all the costs that can be put down to the actual trade, such as explicit costs and market impact. However, as market impact is here measured by the difference between the market price at the decision

When the trade is completed, the implementation shortfall is:

⎡

⎤

N ∑

⎛ ⎝⎜

⎞ ⎠⎟ − EC

XP T

IS = XP T ⎡⎣

− XP 0

x i

P i

−

⎤⎦ −

⎢

⎥

⎣

⎦

i = 1

N ∑

IS =

x i

P i

− XP 0

+ EC

i = 1

When the trade is not completed, the implementation shortfall becomes:

N ∑

x i i = 1 N ∑ P 0

N ∑

⎤ ⎦ ⎥ + X − ⎛ ⎝⎜

⎞ ⎠⎟ P T (

⎡ ⎣ ⎢

) +

IS =

x i

P i

− P 0

x i

−

i = 1

i = 1

N ∑

x i i = 1 N ∑ P 0

N ∑

⎤ ⎦ ⎥ + X − ⎛ ⎝⎜

⎞ ⎠⎟ P T (

⎡ ⎣ ⎢

) + EC

IS =

x i

P i

− P 0

x i

−

i = 1

i = 1

30

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