An Examination of Risk-Return Relationship in Bull and Bear Markets Using Time-Varying Betas

Son‐Nan Chen

98 citations0/0 files storedJournal of Financial and Quantitative Analysis

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Financial Markets and Investment Strategies Financial Risk and Volatility Modeling Risk and Portfolio Optimization

Abstract

Security behavior in bull and bear markets has received some attention in recent years. Fabozzi and Francis [5] first documented evidence that security betas are not influenced by the alternating forces of bull and bear markets. Their subsequent study of mutual fund betas also indicated that mutual funds generally respond indifferently to bull and bear market conditions. Using the concept of bull and bear market variations, Kim and Zumwa1t [9] developed and tested the risk premiums associated with the upside and the downside portions of returns variation. They concluded that investors expect to receive a risk premium for downside risk and pay a premium for upside variation of returns. From their results, Kim and Zumwalt [9] suggested that the down-market beta measuring downside risk (downside variation of returns) may be a more appropriate measure of portfolio risk than the single beta in the market model.

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References

1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*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.]1966Equilibrium in a Capital Asset Market 1969Risk, The Pricing of Capital Assets, and The Evaluation of Investment Portfolios 1962Economic Forecasts and Policy 1978Beta as a Random Coefficient 1977STABILITY TESTS FOR ALPHAS AND BETAS OVER BULL AND BEAR MARKET CONDITIONS 1971On the Short-Term Stationarity of Beta Coefficients

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