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Orthogonal Portfolios

Published online by Cambridge University Press:  06 April 2009

Richard Roll
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Extract

There is a false, but widely-held belief about orthogonal (“zero-beta”) portfolios: for a given market index, all zero-beta portfolios have the same expected return and the minimal-variance, zero-beta portfolio is unique. This is true only when the index is mean/variance efficient. Every nonefficient index possesses zero-beta portfolios at all levels of expected return. For a given index, minimal-variance zero-beta portfolios corresponding to different expected returns lie along an “orthogonal frontier” in the mean/variance space. The frontier has some unusual properties which turn out to be relevant for empirical work on asset pricing. It is functionally related to deviations about the “securities market line.”

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 15 , Issue 5 , December 1980 , pp. 1005 - 1023
Copyright
Copyright © School of Business Administration, University of Washington 1980

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References

REFERENCES

[1]Black, F. “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business, Vol. 45 (1972), pp. 444–454.CrossRefGoogle Scholar
[2]Black, F., and Scholes, M.. “The Effects of Dividend Yield and Dividend Policy on Common Stock Prices and Returns.” Journal of Financial Economics, Vol. 1 (1974), pp. 1–22.CrossRefGoogle Scholar
[3]Charest, G. “Split Information, Stock Returns and Market Efficiency – I.” Journal of Financial Economics, Vol. 6 (1978), pp. 265–296.CrossRefGoogle Scholar
[4]Fama, E. F.Foundations of Finance. New York: Basic Books (1977).Google Scholar
[5]Fama, E. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, Vol. 61 (1973), pp. 607–636.CrossRefGoogle Scholar
[6]Long, J. B. “Notes on the Black Valuation Model for Risky Securities.” Unpublished manuscript (1971). Rochester, New York: University of Rochester.Google Scholar
[7]Merton, R. C. “An Analytic Derivation of the Efficient Portfolio Frontier.” Journal of Financial and Quantitative Analysis, Vol. 7 (1972), pp. 1851–1872.CrossRefGoogle Scholar
[8]Morgan, I. G. “Prediction of Return with the Minimum-Variance Zero-beta Portfolio.” Journal of Financial Economics, Vol. 2 (1975), pp. 361–376.CrossRefGoogle Scholar
[9]Roll, R. “A Critique of the Asset Pricing Theory's Tests.” Journal of Financial Economics, Vol. 4 (1977), pp. 129–176.CrossRefGoogle Scholar
[10]Ross, S. “A Note on the Capital Asset Pricing Model (CAPM). Short-selling Restrictions and Related Issues.” Journal of Finance, Vol. 32 (1977), pp. 177–183.Google Scholar