# How to calculate average liquidity of a portfolio with multiple assets and weights?

I have a weighted portfolio with several assets and weights.

Liquidity of my assets varies from low to high and concentration of assets in the portfolio change from one asset to another, for example asset 1 may represent 5% of the portfolio with volume = 1.000.000,00 USD when asset 2 has 40% of the portfolio with volume = 200.000.000,00 USD over the same period.

How can I measure the average liquidity of my portfolio to compare it's traddability with another portfolios with differents assets and weights ?

My first idea is simply to mean the all assets volume over a given period but unfortunatly it doesn't takes into account weights of every single assets in the portfolio.

Second idea is to weight trading volume by it's corresponding asset's weight. For example liquidity of asset 1 would be $1.000.000 * 0.05 =$50.000 and liquidity of asset 2 would be 200.000.000,00 * 0.4 = $80.000.000 Is this consistent with a measure of the average liquidity of a weighted portfolio ? Thank you, ## 1 Answer Sounds like you need a liquidity metric per asset - do you have publically available trading volumes for all your assets so that in addition to the portfolio weight you can ascribe a liquidity number to each asset? If you don't have such a metric for all assets you may want to consider interpolating the assets over a liquidity grid (created using assets for which you do have a number) using some underlying property of the assets (eg for bonds you could consider ECB haircuts / cds-bond basis as proxies for 'liquidity' metrics - however these latter will be dynamic which may or may not be desirable). Once you have a liquidity grid in which discretely, or continuously to bucket your assets, then the notional weighted liquidity measure would give you a metric to compare the liquidity of your portfolio to that of another, or indeed to those of assets that define your liquidity grid. Then: $$Portfolio \; average \;liquidity\;\Lambda(\Pi)=\frac{\sum\limits_iN_i\cdot w_i\cdot \lambda(A_i)}{\sum\limits_iN_i\cdot w_i}$$ where$\lambda(A_i)=\phi(x_{i_1},...,x_{i_n}, G)$is the individual asset liquidity metric where$\phi$is some possibly mutivariate interpolation scheme that associates with each asset, based on asset attributes$\{x_{i_k}\}$and a grid$G\$ of reference assets whose liquidities are known vs those same attributes, a liquidity number. It might also be wise to make the asset liquidity a function of volume in your portfolio (eg if your quantity is several times the daily trading volume then it makes sense to attenuate the liquidity number. This is pretty general, you could make things a lot more straightforward with simplifying assumptions, the simplest being if you assets themselves had accessible trading data and so in a sense are themselves reference assets for your interpolation. my 2 cents' anyway - let me know if barking up wrong tree!

• Hi, thanks for your proposition. Yes I have publically available trading volumes for all the assets. Portfolios are composed with cryptocurrencies so trading volumes are expressed in BTC. I'm not familiar with the meaning of greek letters when applied to science (except sigma ∑i) and it will take some time for me to fully understand to above formula. – Florent Nov 27 '16 at 11:43
• Because I have trading volume for every single assets I understand I have no need to interpolate volumes. Thus portfolio average liquidity with 3 assets will be something like (weight1 * vol1 + weight2 * vol2 + weight3 * vol3) / (weight1 + weight2 + weight3), is my understanding correct ? – Florent Nov 27 '16 at 11:49