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!