Team member
Team manager: Lili Ma Speaker: Liang Gao Chuan Sun Technical support: Xiangyu Zheng
Zhewei Gu
The Effects of Beta ,Bid-Ask Spread ,Residual Risk ,and
Size on Stock Returns
YAKOV AMIHUD and HAIM MENDELSON
Background
(i) Merton's Model
According to the Capital Asset Pricing Model ,expected asset returns are determined solely by the systematic risk.
Inconsistencies between the dictum of
the theory and the empirical findings led Merton to suggest a more general model of asset pricing.
The expected return on each asset will be as follows:
(1) an increasing function of its systematic risk; (2) an increasing function of its residual risk (due to
imperfect diversification of this risk); (3) an increasing function of the fraction of the
market portfolio invested in the asset, which can be measured by the asset's value or size;
(4) a decreasing function of the fraction of all investors who buy the asset, reflecting public availability of information about the asset.
Expected return in Merton's Model
(ii) A-M's Model
An asset-pricing model which focuses on the role of
illiquidity, measured by the bid-ask spread, was suggested by Amihud and Mendelson.
In this model, assets have bid-ask spreads which reflect their transaction (or illiquidity) costs, and investors have heterogeneous liquidation plans or holding periods.
(iii) The Bid-ask spread
(1)The bid-ask spread is related to the number of investors holding the asset, by Merton, reflects the availability of information about it.
(2)The bid-ask spread is also related to the residual risk.
(iv) The Main Task
Carry out a well specified test of these relations jointly for all four explanatory variables .
2. Testing Hypothesis
Introduction to CAPM
Is the classical theory consistent with the empirical findings?
jtmtjjjt RR
Probably Related Variables
—Portfolio Beta —Portfolio Standard Deviation —Portfolio Average Spread —Average Market Value of Stocks in
Portfolio —Average Monthly Excess Return of
Portfolio
pn
pnpnS
pnSZ
pnR
Data & Methodology
Data Range: Monthly series over 1961—1980
Methods Using Pooled Cross-Section & Time-Series
Estimation
Steps
1) Estimate stock’s coefficients from previous data using market model
2) Form 49 ptfs according to spread and then according to the value of
3) Calculate probably related variables of each ptf
4) Estimate cross-sectional relation
pnpnpnpnpn RSSZ
Results 1—Correlation
Results 2—Regression
DYn—Dummy Variables ( denoting the differences between the years)
Results 2—Significance
OLS Results
Results 3
GLS Results
Results 3
Principal factors affecting asset returns are the Beta risk and Illiquidity (Bid-ask Spread)
The hypotheses on the effects of size and residual risk are not supported
Contributions
Joint Estimation of effects of all four variables are superior to those obtained when a partial set of variables is included.
Conclusion
Results support the hypotheses expected return is an increasing function of βand bid-ask spread
but do not support the hypotheses on
the effects of residual riskδand firm size
Conclusion
The effect of residual risk can be reduced by
investor because of diversification but the effect of illiquidity is nondissipative
because it is hardly eliminated by investors
firms have an incentive to increase the liquidity of their financial claims
Thanks for your attention! Thanks for our tutor- Peter N Smith! Thanks for the time we’ve been to
gether! Thank you!
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