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The liquidity diversification can be measured by the liquidity score, defined here as the ratio between the pure market P&L CVaR and the market+liquidity P&L CVaR.

I have tried to reproduce the results in Meucci's paper A fully integrated liquidity and market risk model, for which the code is available in Matlab, more precisely Example 3 of the paper, the liquidity diversification. One would expect that with the same initial capital, varying the number of stocks (1, 5, 50 for example), the liquidity score increases, albeit not greatly because liquidity is less diversifiable than market risk. When I compute the liquidity score however, I don't get an increase but a decrease of the liquidity score. Did someone try his hands on this ? The first picture is for the portfolio with one stock, the second with 20 equally-weighted stocks. You can already see on the plots that the liquidity score for the portfolio of 20 stocks (LS = 0.4) will be lower than the portfolio with one stock (LS = 0.6). If you need the code for computing the liquidity score (not provided in Meucci's code), I can share it ! 1 stock 20 stocks

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The reason is because the parameter alpha (commissions + half the bid-ask spread) has to be changed for each portfolio ! For a same initial (and high) capital, the bid-ask spread estimate is going to be much higher for a highly concentrated portfolio with one stock than with a portfolio with 20 stocks. That means the expected impact on the P&L is going to be more negative than what was shown in the previous plot, and we thus get a lower liquidity score.

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Thanks for your very interesting post, a question :regarding the alpha, did you change the commision part or only the bid-spread component ? if yes, which proxy did you used ?(because we may think that commissions fees are smaller for a concentred portfolio than for a well diversified portfolio.. ) ps :i will be please if, as you propose, you could send me your code (adress in my profil). –  Malick Jan 20 at 1:49
    
I'm really interested in your proposal of sharing the code for computing the liquidity score. If you could send the script to samy9263@gmail.com, it would be great! Thanks in advance. Samy –  user8119 May 22 at 18:16
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