Liquidity Diversification and Portfolio-Specific Transaction Cost Assumptions
Summary
The document discusses a liquidity score defined as the ratio of pure market profit-and-loss conditional value at risk to market-plus-liquidity profit-and-loss conditional value at risk. In an attempt to reproduce an example from a liquidity and market risk model, the author finds that the score falls when moving from a single-stock portfolio to a portfolio of equally weighted stocks, contrary to the expected diversification effect.
The response attributes the result to the need to adjust the liquidity-cost parameter, which incorporates commissions and half the bid-ask spread, for each portfolio. With the same initial capital, a concentrated position in one stock is expected to have a larger estimated spread than a diversified portfolio. That changes the expected liquidity impact on profit and loss and can alter the score. The exchange gives a qualitative explanation rather than a full reproduction procedure, and its conclusion depends on estimating transaction costs consistently for each portfolio.
Key ideas
- The liquidity score compares market-only risk with risk that includes liquidity effects.
- Portfolio comparisons require liquidity-cost assumptions that reflect each portfolio’s composition.
- The cost parameter discussed includes commissions and half the bid-ask spread.
- A concentrated position may have a higher estimated spread impact than an equally capitalized diversified portfolio.
- Changing cost assumptions can affect the measured liquidity diversification score.
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Full text
# Liquidity diversification # Liquidity diversification 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 ! ## Answer by Bytesize (score 1) https://quant.stackexchange.com/a/8928 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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