Liquidity measures how easily an asset can be traded without significant price impact. Less liquid assets tend to have higher expected returns to compensate investors for bearing illiquidity risk. The liquidity literature distinguishes between the level of illiquidity (a stock characteristic) and liquidity risk (sensitivity to market-wide liquidity fluctuations).
Two types of liquidity
- Market liquidity: the ease of trading a particular security (bid-ask spread, market depth, price impact)
- Funding liquidity: the ease of obtaining financing to hold positions (TED spread, repo rates, margin requirements)
The Amihud ILLIQ measure
Amihud (2002) proposed the most widely used illiquidity measure:
The average daily ratio of absolute return to dollar volume, capturing price impact per dollar of trading (Kyle’s lambda concept). Despite being coarser than microstructure-based measures, ILLIQ correlates well with them (R-squared ~0.30 cross-sectionally) and is practical for long-horizon, cross-market studies.
Cross-sectional results (NYSE, 1964-1997): in Fama-MacBeth regressions, the ILLIQ coefficient is 0.162 (t=6.55), positive and significant after controlling for beta, size, volatility, dividend yield, and past returns. ILLIQ is strongly negatively correlated with size (rho=-0.614), consistent with size proxying for liquidity.
Time-series results: expected market-wide illiquidity positively predicts future stock excess returns. Unexpected increases in illiquidity contemporaneously depress prices. Both effects are monotonically stronger for small stocks: the coefficient on expected illiquidity ranges from 19.5 (small decile) to -0.4 (large decile). This differential sensitivity explains time-variation in the size premium and constitutes an illiquidity risk factor.
Key insight: the equity premium should be interpreted as compensation for both risk and illiquidity, not risk alone.
Liquidity as a systematic risk factor
Pastor and Stambaugh (2003) demonstrated that market-wide liquidity is a priced state variable:
Liquidity measure: for each stock-month, estimate the OLS coefficient (gamma) from regressing next-day excess returns on signed volume. The idea: order flow induces greater return reversals when liquidity is lower (more negative gamma). Aggregate liquidity is the cross-sectional average.
Liquidity beta: a stock’s sensitivity to innovations in aggregate liquidity, estimated alongside the three Fama-French factors. Predicted using seven observable characteristics (historical beta, stock-level liquidity, volume, cumulative return, volatility, price, shares outstanding).
Key results (NYSE/AMEX/NASDAQ, 1966-1999):
- Q10-Q1 spread by predicted liquidity beta: four-factor alpha of 7.5%/year (t=3.42)
- FF3 alpha: 9.2%/year (t=4.29)
- Robust across both halves of the sample
- Smallest stocks have the highest liquidity betas; their size-related abnormal returns are fully explained by liquidity risk exposure
Interaction with other factors: liquidity innovations correlate 0.36 with market returns (0.52 in down markets), 0.23 with SMB, and only 0.01 with momentum. Adding the liquidity-risk spread to an investment universe cuts momentum’s alpha roughly in half and can eliminate it in some subperiods.
Crisis episodes: months of severe liquidity drops coincide with flight-to-quality patterns and major financial events (1987 crash, 1973 oil embargo, 1998 LTCM crisis).
Funding liquidity and factor returns
Asness, Moskowitz, and Pedersen (2013) find that funding liquidity risk partially explains the global factor structure of value and momentum: momentum is positively exposed to funding shocks (vulnerable to forced liquidation), while value is negatively exposed. Market liquidity measures show little relation to either strategy. A 50/50 value-momentum combination is essentially immune to funding shocks yet still earns large returns, so liquidity risk is at best a partial explanation.
Construction in MAC3
The MAC3 liquidity factor is a composite of three descriptors, all oriented so that positive exposure = higher liquidity:
Share Turnover (STO): EWMA of daily shares traded / shares outstanding.
Bid-Ask Spread (BAS): EWMA of -(ask - bid) / price. Sign is flipped from the natural definition. Based on Amihud and Mendelson (1986), who showed a positive relationship between bid-ask spread and expected returns.
Modified Amihud (AMH): EWMA of -(|return| / share turnover). MAC3 modifies the original Amihud (2002) measure to use share turnover instead of dollar volume, reducing collinearity with the size factor. Sign is flipped so positive = more liquid.
Role in factor models
Liquidity is not a standard factor in the FF3 or FF5 models, though Pastor and Stambaugh’s traded liquidity factor has become widely used as a control variable in empirical research. In commercial risk models like MAC3, liquidity is included because it explains significant cross-sectional variation in portfolio volatility and correlation structure.