Article1988

An Unconditional Asset-Pricing Test and the Role of Firm Size as an Instrumental Variable for Risk

246 citations0/0 files storedThe Journal of Finance

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Financial Markets and Investment Strategies Financial Analysis and Corporate Governance Financial Risk and Volatility Modeling

Abstract

ABSTRACT In an intertemporal economy where both risk (stock beta) and expected return are time varying, the authors derive a linear relation between the unconditional beta and the unconditional return under certain stationarity assumptions about the stochastic process of size‐portfolio betas. The model suggests the use of long time periods to estimate the unconditional portfolio betas. The authors find that, after controlling for the betas thus estimated, a firm‐size proxy, such as the logarithm of the firm size, does not have explanatory power for the averaged returns across the size‐ranked portfolios.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1973Risk, Return, and Equilibrium: Empirical Tests 1965The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets 1976The arbitrage theory of capital asset pricing 1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1973An Intertemporal Capital Asset Pricing Model 1981The relationship between return and market value of common stocks 1986

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