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Amihud and Mendelson on Liquidity

 

Asset Pricing and Bid-Ask Spread
Amihud and Mendelson
JFE 1986

Executive Summary:

Investors require a premium for holding illiquid stocks (measured by bid-ask spread) and that there is a clientele effect whereby investors with longer holding periods will own assets with larger spreads. Implication is that by helping to increase liquidity, firms can lower their cost of capital.

The paper, an early microstructure paper, examines the effect on illiquidity (defined as the cost of immediate execution) on asset pricing. The bid-ask spread is one such cost. (Rather than wait for a trade inside the spread). The spread had already been found to be negatively correlated with volume and price continuity (Garbade (1982) and Stoll (1985). In this paper relative spread is used. This is the dollar spread divided by average of bid and ask prices.

The paper begins with a fairly rigorous model that shows “the spread-adjusted return on a portfolio increases with the expected holding period.”

 

This leads to Proposition I (clientele effect).
“Proposition I (clientele effect). Assets with higher spreads are allocated in equilibrium to portfolios with (the same or) longer expected holding periods.” A simple proof is also given, that basically shows the transaction costs will be amortized for a longer period.
“Proposition II (spread-return relationship). In equilibrium, the observed market (gross) return is an increasing and concave piece-wise linear function of the (relative) spread.”
Thus the slope decreases with holding period.

Empirical Section: Using monthly CRSP data, the authors test whether returns are increasing with spread.

The test uses three subperiods: Beta estimation period-60 month period Portfolio formation period-7 portfolios were formed on beta. and then 7 sub-groups based on spread. Test period As shown in Tables 4 and 6, the authors find that risk adjusted returns do increase with spread the slope is “positive and generally decreasing as we move to higher spread groups. This is consistent with the hypothesized concavity of the return-spread relation, reflecting the lower long-term portfolios to the spread.”

The authors then test whether this transaction cost approach could explain the small firm effect. Their findings suggest yes. When regressing return on beta, spread, and size, the size coefficient is insignificant. (Note this is challenged by Schultz (1983) but the authors suggest the difference is that Schultz did not look at long enough holding periods.)


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