Liquidity Risk and Expected Stock Returns
Title, authors, journals (These sections are skipped: IIC, IIIA4, IIIB, IIIC,
IIID)
Title: Liquidity Risk and Expected Stock Returns
Authors: Lubos Pastor, Robert F. Stambaugh
Journal: Journal of Political Economy
- This study investigates whether marketwide liquidity is a state variable important for asset
pricing.
- We find that expected stock returns are related cross-sectionally to the sensitivities of
returns to fluctuations in aggregate liquidity.
- Our monthly liquidity measure, an average of individual-stock measures estimated with daily
data, relies on the principle that order flow induces greater return reversals when liquidity is
lower.
- From 1966 through 1999, the average return on stocks with high sensitivities to liquidity
exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures
to the market return as well as size, value, and momentum factors.
- Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy
over the same 34-year period.
Hypothesis: Is marketwide liquidity indeed priced in securities?
This study investigates whether expected returns are related to systematic liquidity risk in returns, as
opposed to the level of liquidity per se.
Research Question + underlying intuition
Research Question: Is marketwide liquidity indeed priced?
- Specifically: Do investor demand extra return for bearing liquidity risk?
Underlying intuition: This study investigates whether marketwide liquidity is a state variable
important for asset pricing.
The authors found that expected stock returns are related cross‐sectionally to the sensitivities of
returns to fluctuations in aggregate liquidity.
, - Specifically: Stocks that are more sensitive to aggregate liquidity have substantially higher
expected returns, even after we account for exposures to the market return as well as size,
value, and momentum factors.
- Also: This study takes a step on this path by showing that the momentum strategy of buying
recent winning stocks and selling recent losing stocks becomes less attractive from an
investment perspective when portfolio spreads based on liquidity risk are also available for
investment.
The monthly liquidity measure, an average of individual‐stock measures estimated with daily data,
relies on the principle that order flow induces greater return reversals when liquidity is lower.
From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that
for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return
as well as size, value, and momentum factors.
Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the
same 34‐year period.
Main methodology
I. Introduction
II. Market wide Liquidity
A. Constructing a Measure
B. Empirical Features of the Liquidity Measure
- Table 1
C. Specification Issues
III. Is Liquidity Risk Priced?
- Table 2
A. Sorting by Predicted Liquidity Betas
1. Predicting Liquidity Betas
2. Postranking Portfolio Betas
- Table 3
3. Alphas
- Table 4
- Table 5
4. Estimating the Premium Using All 10 Portfolios
- Table 6
B. Sorting by Historical Liquidity Betas
- Table 7
- Table 8
C. Sorting by Size
- Table 9
D. Individual Stock Liquidity
IV. An Investment Perspective
- Table 10
- Table 11
V. Conclusions
Measuring liquidity by Pastor and Stambaugh:
, – Market level liquidity per month as the average of stock level liquidity
– Return reversal following a particular volume is negatively related to liquidity
-> price impact
– Using daily data within each month estimate
They construct a model:
- We construct a measure of market liquidity in a given month as the equally weighted
average of the liquidity measures of individual stocks on the New York Stock Exchange (NYSE)
and American Stock Exchange (AMEX), using daily data within the month.
Detail Article Description
I. Introduction
Liquidity is a broad and elusive concept that generally denotes the ability to trade large quantities
quickly, at low cost, and without moving the price
We find that stocks’ “liquidity betas,” their sensitivities to innovations in aggregate liquidity, play a
significant role in asset pricing. Stocks with higher liquidity betas exhibit higher expected returns.
- In particular, between January 1966 and December 1999, a spread between the top and
bottom deciles of predicted liquidity betas produces an abnormal return (“alpha”) of 7.5
percent per year with respect to a model that accounts for sensitivities to four other factors:
o the market, size,
o and value factors of Fama and French (1993)
o and a momentum factor.
- The alpha with respect to just the three Fama-French factors is over 9 percent per year.
- The results are both statistically and economically significant, and similar results occur in
both halves of the overall 34-year period.
,II. Marketwide Liquidity
A. Constructing a Measure
- Liquidity has many dimensions.
- This study focuses on a dimension associated with temporary price changes accompanying
order flow.
- We construct a measure of market liquidity in a given month as the equally weighted
average of the liquidity measures of individual stocks on the New York Stock Exchange (NYSE)
and American Stock Exchange (AMEX), using daily data within the month.
- Specifically, the liquidity measure for stock i in month t is the ordinary least squares estimate
of in the regression
Class
-
Interpretation
High volume is accompanied by lower return in the future due to reversed returns if the stock is not
perfectly liquid.
- If the stock is not perfectly liquid, volume pushes price up too much -> should be followed by
reversal next period
The lower the stock´s liquidity, the greater the expected reversal in price for a given volume.
- is the return on stock i on day d in month t
- is the return on the CRSP value-weighted market return on day d in month t
Dependent variable
, - is the dollar volume for stock i on day d in month t
- A stock’s liquidity is computed in a given month only if there are more than 15 observations
with which to estimate the regression (1) ( D> 15), and we exclude a stock for the first and
last partial month that it appears on the CRSP tape.
- The daily observations are not required to be consecutive (except that each observation
requires data for two successive days).
- Stocks with share prices less than $5 and greater than $1,000 at the end of the previous
month are excluded, and volume is measured in millions of dollars.
- The return on stock i on day d is given by:
- The first two terms on the right-hand side represent permanent changes in the price
- market wide factor
- is a stock- specific effect
- is intended to capture the liquidity-related effect arising from order flow
in the sense that both current and lagged order flow enter the return, but in the opposite
directions.
- the coefficient is negative and represents the stock´s liquidity.
- We use (2) to simulate returns on 10,000 stocks.
- represents an additional reversal effect that is independent of the order flow effect,
and this component of the return is best viewed as bid-ask bounce or a tick size effect.
, Figure 1
- It can essentially be viewed as an estimate of the liquidity cost, averaged across stocks at a
given point in time, of trading $1 million in 1962 “stock market” dollars (about $34 million at
the end of 1999).
- The average value of this liquidity measure over time is 0.03 (the median is 0.02), indicating
about a 2–3 percent cost for such a trade.
- Perhaps the most salient features of the liquidity series plotted in figure 1 are its occasional
downward spikes, indicating months with especially low estimated liquidity
Title, authors, journals (These sections are skipped: IIC, IIIA4, IIIB, IIIC,
IIID)
Title: Liquidity Risk and Expected Stock Returns
Authors: Lubos Pastor, Robert F. Stambaugh
Journal: Journal of Political Economy
- This study investigates whether marketwide liquidity is a state variable important for asset
pricing.
- We find that expected stock returns are related cross-sectionally to the sensitivities of
returns to fluctuations in aggregate liquidity.
- Our monthly liquidity measure, an average of individual-stock measures estimated with daily
data, relies on the principle that order flow induces greater return reversals when liquidity is
lower.
- From 1966 through 1999, the average return on stocks with high sensitivities to liquidity
exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures
to the market return as well as size, value, and momentum factors.
- Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy
over the same 34-year period.
Hypothesis: Is marketwide liquidity indeed priced in securities?
This study investigates whether expected returns are related to systematic liquidity risk in returns, as
opposed to the level of liquidity per se.
Research Question + underlying intuition
Research Question: Is marketwide liquidity indeed priced?
- Specifically: Do investor demand extra return for bearing liquidity risk?
Underlying intuition: This study investigates whether marketwide liquidity is a state variable
important for asset pricing.
The authors found that expected stock returns are related cross‐sectionally to the sensitivities of
returns to fluctuations in aggregate liquidity.
, - Specifically: Stocks that are more sensitive to aggregate liquidity have substantially higher
expected returns, even after we account for exposures to the market return as well as size,
value, and momentum factors.
- Also: This study takes a step on this path by showing that the momentum strategy of buying
recent winning stocks and selling recent losing stocks becomes less attractive from an
investment perspective when portfolio spreads based on liquidity risk are also available for
investment.
The monthly liquidity measure, an average of individual‐stock measures estimated with daily data,
relies on the principle that order flow induces greater return reversals when liquidity is lower.
From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that
for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return
as well as size, value, and momentum factors.
Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the
same 34‐year period.
Main methodology
I. Introduction
II. Market wide Liquidity
A. Constructing a Measure
B. Empirical Features of the Liquidity Measure
- Table 1
C. Specification Issues
III. Is Liquidity Risk Priced?
- Table 2
A. Sorting by Predicted Liquidity Betas
1. Predicting Liquidity Betas
2. Postranking Portfolio Betas
- Table 3
3. Alphas
- Table 4
- Table 5
4. Estimating the Premium Using All 10 Portfolios
- Table 6
B. Sorting by Historical Liquidity Betas
- Table 7
- Table 8
C. Sorting by Size
- Table 9
D. Individual Stock Liquidity
IV. An Investment Perspective
- Table 10
- Table 11
V. Conclusions
Measuring liquidity by Pastor and Stambaugh:
, – Market level liquidity per month as the average of stock level liquidity
– Return reversal following a particular volume is negatively related to liquidity
-> price impact
– Using daily data within each month estimate
They construct a model:
- We construct a measure of market liquidity in a given month as the equally weighted
average of the liquidity measures of individual stocks on the New York Stock Exchange (NYSE)
and American Stock Exchange (AMEX), using daily data within the month.
Detail Article Description
I. Introduction
Liquidity is a broad and elusive concept that generally denotes the ability to trade large quantities
quickly, at low cost, and without moving the price
We find that stocks’ “liquidity betas,” their sensitivities to innovations in aggregate liquidity, play a
significant role in asset pricing. Stocks with higher liquidity betas exhibit higher expected returns.
- In particular, between January 1966 and December 1999, a spread between the top and
bottom deciles of predicted liquidity betas produces an abnormal return (“alpha”) of 7.5
percent per year with respect to a model that accounts for sensitivities to four other factors:
o the market, size,
o and value factors of Fama and French (1993)
o and a momentum factor.
- The alpha with respect to just the three Fama-French factors is over 9 percent per year.
- The results are both statistically and economically significant, and similar results occur in
both halves of the overall 34-year period.
,II. Marketwide Liquidity
A. Constructing a Measure
- Liquidity has many dimensions.
- This study focuses on a dimension associated with temporary price changes accompanying
order flow.
- We construct a measure of market liquidity in a given month as the equally weighted
average of the liquidity measures of individual stocks on the New York Stock Exchange (NYSE)
and American Stock Exchange (AMEX), using daily data within the month.
- Specifically, the liquidity measure for stock i in month t is the ordinary least squares estimate
of in the regression
Class
-
Interpretation
High volume is accompanied by lower return in the future due to reversed returns if the stock is not
perfectly liquid.
- If the stock is not perfectly liquid, volume pushes price up too much -> should be followed by
reversal next period
The lower the stock´s liquidity, the greater the expected reversal in price for a given volume.
- is the return on stock i on day d in month t
- is the return on the CRSP value-weighted market return on day d in month t
Dependent variable
, - is the dollar volume for stock i on day d in month t
- A stock’s liquidity is computed in a given month only if there are more than 15 observations
with which to estimate the regression (1) ( D> 15), and we exclude a stock for the first and
last partial month that it appears on the CRSP tape.
- The daily observations are not required to be consecutive (except that each observation
requires data for two successive days).
- Stocks with share prices less than $5 and greater than $1,000 at the end of the previous
month are excluded, and volume is measured in millions of dollars.
- The return on stock i on day d is given by:
- The first two terms on the right-hand side represent permanent changes in the price
- market wide factor
- is a stock- specific effect
- is intended to capture the liquidity-related effect arising from order flow
in the sense that both current and lagged order flow enter the return, but in the opposite
directions.
- the coefficient is negative and represents the stock´s liquidity.
- We use (2) to simulate returns on 10,000 stocks.
- represents an additional reversal effect that is independent of the order flow effect,
and this component of the return is best viewed as bid-ask bounce or a tick size effect.
, Figure 1
- It can essentially be viewed as an estimate of the liquidity cost, averaged across stocks at a
given point in time, of trading $1 million in 1962 “stock market” dollars (about $34 million at
the end of 1999).
- The average value of this liquidity measure over time is 0.03 (the median is 0.02), indicating
about a 2–3 percent cost for such a trade.
- Perhaps the most salient features of the liquidity series plotted in figure 1 are its occasional
downward spikes, indicating months with especially low estimated liquidity
