Transaction Cost Analysis A-Z

Transaction Cost Analysis A-Z — November 2008

IV. Estimating Transaction Costs with Pre-Trade Analysis

I and timing risk provide very interesting material that, when we put all the pieces together, makes it possible to determine the cost profile of any trading strategy through simultaneous estimation of cost and risk. This combination of material is the foundation for the development of techniques to determine optimal trading strategies and to derive an efficient trading frontier. We address these points in the next subsection. The cost profile of a specific trading strategy x k summarises the cost and risk estimates associated with the strategy. It is expressed as θ k = ( φ ( x k ), ℜ ( x k )) , where θ k is the cost profile, φ (x k ) is the expected implicit transaction cost and θ k = ( φ ( x k ), ℜ ( x k )) ( k ) is the forecasted timing risk for the strategy x k . Based on cost profiles, comparisons of several strategies are easy to make. Consider a numerical example for an order to be executed and two possible strategies. We show below how we determine the cost profile of each strategy and how we can compare the findings. Let us first suppose a VWAP strategy for an order of 120,000 shares of XYZ stock. The market price is currently equal to € 80 and is expected to reach € 82 at the end of the trading day. Daily volatility is estimated at 120bp. The execution strategy and expected market conditions are summarised in table 3 and the instantaneous market impact cost for the stock is estimated at € 150,000. ⎞ ⎠⎟ 2 x j 4 σ 2 ( v j ) 4( x j + 0.5v j ) 4 j ∑ ⎞ ⎠ ⎟ = I X ⎛ ⎝⎜ ⎞ ⎠⎟ 2 x j 4 σ 2 ( v j ) 4( x j + 0.5v j ) 4 j ∑ 3. Optimisation and Efficient Trading Frontier

2

x

2

x ⎛ ⎝ ⎜

⎞ ⎠ ⎟

I

⎛ ⎝⎜

⎞ ⎠⎟

⎛ ⎝⎜

j ∑

j

σ 2 ( K( x )) =

σ 2

=

+ 0.5v j

X

X

j

σ ( K( x )) = σ 2 ( K( x )) 2 2

2

x

x

j 4 σ 2 ( v j

)

x ⎛ ⎝ ⎜

⎞ ⎠ ⎟

I

I

⎛ ⎝⎜

⎞ ⎠⎟

⎛ ⎝⎜

⎞ ⎠⎟

j ∑

j ∑

j

σ 2 ( K( x )) =

σ 2

=

+ 0.5v j

+ 0.5v j I 2

) 4

4( x j

X

X

x

2

x ⎛ ⎝ ⎜

⎛ ⎝⎜

⎞ ⎠⎟

j

j ∑

j

σ 2 ( K( x )) =

σ 2

+ 0.5v j

X

σ ( K( x )) = σ 2 ( K( x ))

j

σ ( K( x )) = σ 2 ( K( x ))

The liquidity risk for a trade list of several securities can be determined as above but by making an additional assumption of independence based on zero correlation of excess volumes 24 across securities and across periods for the same securities. So, assuming independence, the liquidity risk for a trade list is: σ 2 ( K( x )) = I i X i ⎛ ⎝⎜ ⎞ ⎠⎟ 2 i ∑ x ij 4 σ 2 ( v ij ) 4( x ij + 0.5v ij ) 4 j ∑ σ ( K( x )) = σ 2 ( K( x )) Now that we know how to compute both price and liquidity risk, and assuming that volume and price movement are independent, 25 we forecast the total timing risk for a given trade schedule through a simple combination of them, that is:

24 - Volume quantities above/ below the mean in each trading interval. 25 - 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 indeed correlated. This means that the presence of high volume does not indicate the direction of price movement.

2

x

ij 4 σ 2 ( v ij

)

I i

⎛ ⎝⎜

⎞ ⎠⎟

j ∑

i ∑

j ∑

ℜ ( x k

) =

r j

' Cr j

+

X

+ 0.5v ij

) 4

4( x

i

ij

It must be said that, in practice, the estimation and incorporation of liquidity risk into the timing risk term is complicated. It is for that reason that the timing risk of a strategy is often referred to only as the price risk of the strategy.

The estimation models and techniques for price appreciation, market impact

53 An EDHEC Risk and Asset Management Research Centre Publication