Skip to content
All library documents

Forming Liquidity-Sorted Portfolios to Estimate Asset Pricing Betas

Article Quant Q&A · Author: Aquarius
Read the original

Summary

The document describes a proposed liquidity-adjusted asset pricing analysis using monthly turnover, defined as average daily volume relative to shares outstanding. Because the measure is persistent, the author plans to model each stock's liquidity with an autoregressive process and use residual liquidity changes in a set of systematic-risk measures. These include market return exposure, commonality with market liquidity, and cross-movement between stock returns or liquidity and market conditions.

The main estimation issue is noisy stock-level beta estimates. The proposed remedy is to estimate betas for portfolios and assign those estimates to individual stocks for subsequent cross-sectional regressions. At the start of each year, the author intends to sort stocks into ten portfolios by liquidity. The document asks how to implement that decile formation in R but does not give code or clarify details such as breakpoints, ties, missing observations, or portfolio rebalancing. The method is outlined, but implementation choices need specification.

Key ideas

  • Monthly turnover, measured relative to shares outstanding, is used as a stock liquidity measure.
  • An autoregressive model is proposed to account for liquidity persistence and isolate liquidity innovations.
  • The asset pricing setup considers exposures to market returns, market liquidity, and their co-movement with stock liquidity and returns.
  • Portfolio-level beta estimates are proposed to reduce noise before assigning estimates to stocks for cross-sectional analysis.
  • Stocks are to be sorted into ten liquidity groups at the start of each year, though the implementation details remain unspecified.

Tags

EquitiesFactor investingStatisticsPortfolio construction
Full text
# Liquidity Adjusted Asset Pricing Model


# Liquidity Adjusted Asset Pricing Model












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

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

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. 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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.