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Risk Policy and Long–Term Investment

Published online by Cambridge University Press:  06 April 2009

Richard O. Michaud
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Extract

Empirical tests of the Sharpe [36]–Lintner [23]–Black [3] Capital Asset Pricing Model (CAPM) have generally concluded that there is a positive, approximately linear, trade-off between average return and systematic risk (beta) for portfolio returns of common stocks. Most of the empirical studies, however, have reported data for short, usually monthly, time intervals. Exceptions to this rule include Blume and Friend [8] and Sharpe [38, pp. 289–292]. Their data provide evidence that long-term wealth ratios are concave, possibly nonmonotonic, functions of beta. These data are surprising since, if returns are intertemporally independent and the linear return model of CAPM is correct, expected multiperiod terminal wealth is a convex, monotone increasing function of beta. The results of this paper provide a theoretical framework for interpreting the long-term empirical data which does not violate the notion of a monotone increasing expected terminal wealth-beta relationship.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 16 , Issue 2 , June 1981 , pp. 147 - 167
Copyright
Copyright © School of Business Administration, University of Washington 1981

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References

REFERENCES

[1]Aitchison, J., and Brown, J.A.C.. The Lognormal Distribution. Cambridge University Press (1957).Google Scholar
[2]Ball, R. “Anomalies in Relationships between Securities' Yields and Yield-Surrogates.” Journal of Financial Economics (06/09 1978).Google Scholar
[3]Black, F. “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business (07 1972).CrossRefGoogle Scholar
[4]Black, F.; Jensen, M.C.; and Scholes, M.. “The Capital Asset Pricing Model: Some Empirical Tests.” In Studies in the Theory of Capital Markets, Jensen, M., ed. New York: Praeger Publishers (1972).Google Scholar
[5]Block, F. “Elements of Portfolio Construction.” Financial Analysts Journal (05/June 1969).CrossRefGoogle Scholar
[6]Blume, M. “Unbiased Estimators of Long–Run Expected Rates of Return.” Journal of the American Statistical Association (09 1974).Google Scholar
[7]Blume, M., and Friend, I.. “A New Look at the Capital Asset Pricing Model.” Journal of Finance (1973).CrossRefGoogle Scholar
[8[Blume, M., and Friend, I.. “Risk, Investment Strategy and the Long–Run Rates of Return.” Review of Economics and Statistics (08 1974).CrossRefGoogle Scholar
[9]Breiman, L. “Investment Policies for Expanding Businesses Optimal in a Long Run Sense.” Naval Research Logistics Quarterly (1960).Google Scholar
[10]Fama, E. “Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance (05 1970).Google Scholar
[11]Fama, E.. “The Market Model and the Two–Parameter Model.” Journal of Finance (12 1973).Google Scholar
[12]Fama, E., and MacBeth, J.D.. “Risk, Return and Equilibrium: Empirical Tests.” Journal of Financial Economics (05 1974).Google Scholar
[13]Fisz, M.Probability Theory and Mathematical Statistics. New York: John Wiley & Sons, Inc. (1963).Google Scholar
[14]Hakansson, N. “Capital Growth and the Mean–Variance Approach to Portfolio Selection.” Journal of Financial and Quantitative Analysis (01 1971).Google Scholar
[15]Hakansson, N.. “Multi–Period Mean Variance Analysis: Toward a General Theory of Portfolio Choice.” Journal of Finance (09 1971),Google Scholar
[16]Hakansson, N.. “A Characterization of Optimal Multi–Period Portfolio Policies.” In Portfolio Theory, 25 Years After, Elton, N. and Gruber, M., eds. North Holland, N.Y. (1979).Google Scholar
[17]Hakansson, N., and Miller, B.C.. “Compound Return Mean–Variance Efficient Portfolios Never Risk Ruin.” Management Science (12 1975).Google Scholar
[18]Hogg, R.V., and Craig, A.T.. Introduction to Mathematical Statistics, 3rd ed.New York: The Macmillan Co. (1973).Google Scholar
[19]Ibbotson, R., and Sinquefield, R.. “Stocks, Bonds, Bills and Inflation: Historical Return (1926–1978).” The Financial Analysts Research Foundation (1979).CrossRefGoogle Scholar
[20]Jensen, M.C. “Capital Markets: Theory and Evidence.” Bell Journal of Economics and Management Science (1972).Google Scholar
[21]Kelly, J.L. “A New Interpretation of Information Rate.” Bell System Technical Journal (1956).Google Scholar
]22]Latane, H.A. “Criteria for Choice among Risky Ventures.” Journal of Political Economy (04 1959).Google Scholar
[23]Lintner, J. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” The Review of Economics and Statistics (02 1965).Google Scholar
[24]Lorie, J.H., and Hamilton, M.T.. The Stock Market: Theories and Evidence. Homewood, Illinois: Richard D. Irwin, Inc. (1973).Google Scholar
[25]Markowitz, H.M.Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons, Inc. (1959).Google Scholar
[26]Markowitz, H.M.. “Investment for the Long Run.” In Risk and Return in Finance, Friend, I. and Bicksler, J., eds. Cambridge, Mass.: Ballinger Publishing Co. (1977).Google Scholar
[27]Merton, R.C., and Samuelson, P.A.. “Fallacy of the Log–Normal Approximation to Optimal Portfolio Decision–Making over Many Periods.” Journal of Financial Economics (03 1974).CrossRefGoogle Scholar
[28]Michaud, R., and Monahan, J.. “Comparisons of Optimal versus Stationary Investment Policies over Time. Presented to: The Institute for Quantitative Research in Finance (05 1981).Google Scholar
[29]Rao, C.R.Linear Statistical Inference and Its Application. New York: John Wiley & Sons, Inc. (1965).Google Scholar
[30]Roll, R. “Ambiguity When Performance Measurement Is Measured by the Securities Market Line.” Journal of Finance (09 1978).CrossRefGoogle Scholar
[31]Rosenberg, B., and Ohlson, J.. “The Stationary Distribution of and Portfolio Separation in Capital Markets: A Fundamental Contradiction.” Journal of Financial and Quantitative Analysis (09 1976).Google Scholar
[32]Ross, S. “Return, Risk and Arbitrage.” In Risk and Return in Finance, Friend, I. and Bicksler, J., eds. Cambridge, Mass.: Ballinger Publishing Co. (1977).Google Scholar
[33]Samuelson, P.A. “The Fallacy of Maximizing the Geometric Mean in Long Sequences of Investing or Gambling.” Proceedings of the National Academy of Arts and Sciences (10 1971).Google Scholar
[34]Samuelson, P.A., and Merton, R.C.. “Generalized Mean Variance Tradeoffs for Best Perturbation Corrections to Approximate Portfolio Decisions.” Journal of Finance (03 1974).Google Scholar
[35],Sharpe, W.F. “A Simplified Model for Portfolio Analysis.” Management Science (01 1963).Google Scholar
[36]Sharpe, W.F.. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance (09 1964).Google Scholar
[37]Sharpe, W.F.. Portfolio Theory and Capital Markets. New York: McGraw–Hill Book Co. (1970).Google Scholar
[38]Sharpe, W.F.. Investments. New York: Prentice Hall (1978).Google Scholar
[39]Thomas, J.F.An Introduction to Applied Probability and Random Processes. New York: John Wiley & Sons, Inc. (1971).Google Scholar
[40]Thorp, E. “Portfolio Choice and the Kelly Criterion.” Reprinted in Investment Portfolio Decision Making, Bicksler, j.c. and Samuelson, P., eds. Lexington, Mass.: Lexington Books (1974).Google Scholar
[41]Williamson, J.P.Investments: New Analytic Techniques. New York: Praeger Publishers (1970).Google Scholar
[42]Young, W.E., and Trent, R.H.. “Geometric Mean Approximation of Individual Security and Portfolio Performance.” Journal of Financial and Quantitative Analysis (06 1969).Google Scholar