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In the text book on Risk Management by John Hull, The cost of liquidation is defined as one half of spread between bid price and ask price.

Investopedia justifies the one half factor by saying that we are concerned with only the sell part of the trade. This is not convincing.

I personally feel that The cost of liquidation should be plainly bid-ask spread without any factor. Can anyone please clarify.

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    $\begingroup$ If the cost of liquidating the position is "the bid ask spread" then what is the cost of acquiring the position, zero? The entering and exiting cost must add up to the bid ask spread. $\endgroup$
    – nbbo2
    Jun 16, 2017 at 20:15
  • $\begingroup$ @noob2 The cost of acquiring the position is the offer price; The cost of exiting the position is the negative of bid price. Both will add up to the spread. $\endgroup$
    – honeybadger
    Jun 16, 2017 at 20:22
  • $\begingroup$ You prefer to consider that there is only one transaction cost, Hull prefers to consider that there are two: half of it at the beginning (when you buy) and half when you sell. As long as you are consistent, you are both right. It is a convention. $\endgroup$
    – nbbo2
    Jun 16, 2017 at 20:28
  • $\begingroup$ @noob2 okay. That makes sense. Thank you $\endgroup$
    – honeybadger
    Jun 16, 2017 at 20:40
  • $\begingroup$ If only spreads were static :) $\endgroup$
    – amdopt
    Jun 17, 2017 at 0:55

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Cost of liquidation should include

  • the explicit costs: fees (brokers, exchanges, give-up, post trading, etc)
  • the implicit costs that you cannot know for sure a priori. They are themselves made of
    • slippage: linear costs mostly, a function of the bid ask spread. If you use a dumb trading algo, you will pay a full bid-ask spread, you are right. But if you use an algo that is a little smarter (for instance succeeding in being liquidity provider --ie in the book-- part of the time) you will pay less
    • and the market impact

Formulas are explained in Market microstructure in practice, but in short you need a market impact of the shape

$$\eta(q) = a \,\psi + \kappa\,\sigma\sqrt{\frac{q}{\bar V}}$$

where $q$ is your traded quantity, $\psi$ the bid-ask spread, $\sigma$ the volatility, $\bar V$ the average daily volume, and $a$ and $\kappa$ are parameters you need to fit on your data. It is important to use your own data because it will capture your trading habits (types of algo you use --see Chap 3 of the book-- for instance).

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