Chaptergreen2005

Realized Beta: Persistence and Predictability

Torben G. Andersen · Tim Bollerslev · Francis X. Diebold · Ginger Y. Wu

225 citations0/0 files storedAdvances in econometrics

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Financial Risk and Volatility Modeling Financial Markets and Investment Strategies Stochastic processes and financial applications

Abstract

A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management.

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References

1987Co-Integration and Error Correction: Representation, Estimation, and Testing 1993Common risk factors in the returns on stocks and bonds 1992The Cross-Section of Expected Stock Returns 1965The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets 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.]2012The Econometrics of Financial Markets 2003Modeling and Forecasting Realized Volatility 1987The Pricing of Options on Assets with Stochastic Volatilities

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