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I have a data set with 4000 companies and I have calculated a liquidity measure of each of the company in the dataset as

enter image description here

Where, Turnover is the monthly average ratio of daily volume to shares outstanding for a given stock. Liquidity (measured by this ratio) Liquidity is highly persistent. And my analysis shows that in these indiviual companies in my dataset depict strong first order autocorrelation. So, as suggested by literature I should transform this liquidity measure of each indiviual company by AR(2). By following AR(2) process equation

enter image description here

Where, Ct i is a measure of liquidity for stock i at month t, x is the number of lags included in the autoregressive process, and ut i is the residuals in liquidity for stock i at month t.

Part where is need help most. enter image description here Where,β1 is similar to the market beta of the CAPM except for additional term that is realted to the trading cost in the denominator. The remaining systematic risk components are associated with liquidity. β2 represents liquidity commonality, that is, the co-movement between individual stock liquidity and market liquidity.β3 measures the co-movement between stock returns and market liquidity.β4 captures the co-movement between individual liquidity and market returns.

Calculating liquidity betas for indiviual betas for indiviual stocks based on eqs. 3 to 6 could increase the power of test by providing ample observations but cost of doing so is that betas estimated at indiviual stock level have higher level of noise. To mitigate the measurement error problem calcute betas at portfolio level and then assign these portfolio betas to indiviual stocks to cross sectional regressions at the indiviual stock level (Fama and French,1992).

So, beginning of each year in our sample period ten portfolios are formed according to their level of liquidity(measured by ratio mentioned above).

I would really appreciate if you help me understand this decile portfolio formation part. I'm using R. Link to the paper that presented this model http://pages.stern.nyu.edu/~lpederse/papers/liquidity_risk.pdf

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  • $\begingroup$ Can you please provide reference the paper on which your model is based ? $\endgroup$ – Neeraj Jan 23 '16 at 19:10
  • $\begingroup$ The LCAPM model was developed by Acharya and Pedersen (2005) but the portfolio formation strategy that I have described is based on the methodology in "Empirical tests on the liquidity adjusted capital asset pricing model" by Vu et al (2014) $\endgroup$ – Aquarius Jan 23 '16 at 19:22
  • $\begingroup$ If possible please provide entire link. $\endgroup$ – Neeraj Jan 23 '16 at 20:04
  • $\begingroup$ Paper by Vu et al. researchgate.net/publication/…. Actually this one I got through my university's portal $\endgroup$ – Aquarius Jan 23 '16 at 20:13
  • $\begingroup$ None of your paper is getting dowloaded. Without your paper it is difficult to grasp the context. Lets hope somebody else has worked on it or have access to these paper. $\endgroup$ – Neeraj Jan 23 '16 at 20:28

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