An Equilibrium Pricing Model with Decreasing Marginal Transaction Costs

By Kim, Moon K.; Ismail, Badr E. | Quarterly Journal of Business and Economics, Autumn 1990 | Go to article overview

An Equilibrium Pricing Model with Decreasing Marginal Transaction Costs


Kim, Moon K., Ismail, Badr E., Quarterly Journal of Business and Economics


An Equilibrium Pricing Model With Decreasing Marginal Transaction Costs

Abstract

The theoretical model developed in this study establishes that when

marginal transaction costs are decreasing, the expected rate of return on

a security is related positively to its systematic risk and its average

marginal transaction costs. The empirical part of the study relies on the

bid-ask price spread and a number of alternative transaction cost

measures based on firm size, share price, and trading activities. The

results of the test are consistent with the hypothesis that transaction

costs are an important additional factor explaining security returns.

Introduction

One of the underlying assumptions of the Markowitz[19] portfolio theory and the capital asset pricing model (CAPM) derived by Sharpe[28] and Lintner[18] is that security trading occurs with zero transaction costs. Several studies have examined the effect of nonzero transaction costs on the portfolio and the capital asset pricing theory. Brennan[9] finds that introducing transaction costs makes it economically infeasible to hold a perfectly diversified portfolio. Goldsmith[14] demonstrates that the fraction of a portfolio invested in risky securities is an increasing function of wealth when transaction costs exist. Milne and Smith[23] develop a pricing model by incorporating bid-ask price spreads as a measure of transaction costs and show that the equilibrium price of a security is bounded by its bid and ask prices. Levy[17] and Mayshar[20,21] establish that when transaction costs constrain the number of securities an investor is willing to hold, the variance of returns on a security is the major factor in determining the expected return and that the market price of risk is smaller than that specified by the traditional CAPM.

Recently, the validity of the CAPM has been questioned in light of the results obtained by Banz[3], Reinganum[24], and others showing that small firms have higher risk-adjusted abnormal returns than do large firms. One of the hypotheses offered in the literature to explain the small firm effect is the high costs of transacting small firms' securities.(1) In particular, faced with higher transaction costs and the resulting lower marketability, investors would require a higher return in order to trade in small firm securities.

Stoll and Whaley[32], using New York Stock Exchange firms, find that for holding periods between three months and one year, after-transaction-costs abnormal returns are not significantly different from zero. Under these conditions, Stoll and Whaley establish that the small firm effect is eliminated. Schultz[29], however, reports significant net-of-transaction-costs abnormal returns defined over shorter holding periods for American Stock Exchange firms. Although Schultz concludes that transaction costs do not fully explain the small firm effect, Amihud and Mendelson[1] confirm Stoll and Whaley's findings and suggest that firm size is a proxy for liquidity. Recently, Merton[22] develops the following theoretical rationale: When investors know about only a subset of securities due to the existence of information costs, securities with less information available to investors and with smaller investor base will have larger rates of return.

This paper develops an equilibrium pricing model in which decreasing marginal transaction costs are considered explicitly. Although decreasing marginal transaction costs are more realistic, previous studies assume either constant or proportional transaction costs (Milne and Smith[23]). The theoretical analysis of this study is similar in spirit to that of Levy[17], Mayshar[20,21], and Merton[22] in the broad set of issues bearing upon the pricing effects of transaction costs. Whereas Levy and Mayshar are primarily concerned with portfolio choice decisions, however, this paper addresses the ability of transaction costs in explaining the variations in security returns. …

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