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Asset Pricing Under a Subset of Linear Risk Tolerance Functions and Log-Normal Market Returns

Published online by Cambridge University Press:  06 April 2009

Extract

The Capital Asset Pricing Model (CAPM) developed and popularized by Treynor [27], Sharpe [26], Lintner [16], Mossin [19], and Fama [6] is of the form

where

E is the expected return at time t for firm i (conditional on information available at time t); the subscript m denotes the analogous market variable; rf is the risk-free rate; and . Black [2] has developed a similar form with expected returns from a zero beta portfolio, , assuming the role of the risk-free rate.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1980

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References

REFERENCES

[1]Aitchison, J., and Brown, J. A. C.. The Lognormal Distribution. Cambridge, Mass.: Cambridge University Press (1957).Google Scholar
[2]Black, Fischer. “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business, Vol. 45 (07 1972), pp. 444454.CrossRefGoogle Scholar
[3]Blume, Marshall E.Unbiased Estimators of Long-Run Expected Rates of Return.” Journal of the American Statistical Association, Vol. 69 (09 1974), pp. 634638.CrossRefGoogle Scholar
[4]Conte, S. D., and de Boor, Carl. Elementary Numerical Analysis. New York: McGraw-Hill Book Co. (1972).Google Scholar
[5]Elton, Edwin J., and Gruber, Martin J.. “Maximization of the Geometric Mean with Lognormal Return Distribution.” Management Science, Vol. 21 (12 1974), pp. 483488.CrossRefGoogle Scholar
[6]Fama, E. F.Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance, Vol. 25 (05 1970), pp. 383417.CrossRefGoogle Scholar
[7]Fama, E. F.The Behavior of Stock Market Prices.” Journal of Business, Vol. 38 (01 1965), pp. 34105.CrossRefGoogle Scholar
[8]Feldstein, M.Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection.” Review of Economic Studies, Vol. 36 (01 1968), pp. 511.CrossRefGoogle Scholar
[9]Friend, Irwin, and Bicksler, James L.. Risk and Return in Finance. Ballinger Publishing Company (1977).Google Scholar
[10]Friend, Irwin, and Blume, Marshall E.. “The Demand for Risky Assets.” In Risk and Return in Finance, Friend, and Bicksler, (eds.). Ballinger Publishing Company, pp. 101139.Google Scholar
[11]Grauer, Robert R.The Inference of Taste and Beliefs from Bond and Stock Market Data.” Journal of Financial and Quantitative Analysis, Vol. 13 (06 1978), pp. 273297.CrossRefGoogle Scholar
[12]Hakansson, Nils H. “The Capital Asset Pricing Model: Some Open and Closed Ends.” In Risk and Return in Finance, Friend, and Bicksler, (eds.). Ballinger Publishing Company, pp. 245260.Google Scholar
[13]Jones, R. M., and Miller, K. S.. “On the Multivariate Lognormal Distribution.” The Journal of the Industrial Mathematics Society, Vol. 16 (1966), pp. 6376.Google Scholar
[14]Kraus, Alan, and Litzenberger, Robert H.. “Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility.” The Journal of Finance, Vol. 30 (12 1975), pp. 12131227.Google Scholar
[15]Levy, Haim. “Stochastic Dominance among Log-Normal Prospects.” International Economic Review, Vol. 14 (10 1973), pp. 601614.CrossRefGoogle Scholar
[16]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, Vol. 47 (02 1965), pp. 1337.CrossRefGoogle Scholar
[17]Mandelbrot, B.The Variation of Certain Speculative Prices.” Journal of Business, Vol. 36 (10 1963), pp. 394419.CrossRefGoogle Scholar
[18]Merton, Robert C.Optimum Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory, Vol. 3 (1971), pp. 373413.CrossRefGoogle Scholar
[19]Mossin, J.Equilibrium in a Capital Asset Market.” Econometrica, Vol. 34 (10 1966), pp. 768783.CrossRefGoogle Scholar
[20]Moore, Arnold B. “Some Characteristics of Changes in Common Stock Prices.” In The Random Character of Stock Market Prices, Cootner, Paul (ed.). Cambridge, Mass.: MIT Press (1964).Google Scholar
[21]Osborne, M. F. M.Brownian Motion in the Stock Market.” Operations Research, Vol. 7 (0304 1959), pp. 145173.CrossRefGoogle Scholar
[22]Roll, Richard. “Evidence on the ‘Growth Optimum’ Model.” The Journal of Finance, Vol. 28 (06 1973), pp. 551566.Google Scholar
[23]Ross, Stephen A.The Capital Asset Pricing Model (CAPM), Short Sale Restrictions and Related Issues.” The Journal of Finance, Vol. 32 (03 1977), pp. 177183.Google Scholar
[24]Rubinstein, Mark. “The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets.” The Journal of Finance, Vol. 31 (05 1976), pp. 551571.CrossRefGoogle Scholar
[25]Samuelson, Paul A., and Merton, Robert C.. “Generalized Mean-Variance Trade-offs for Best Pertubation Corrections to Approximate Portfolio Decisions.” The Journal of Finance, Vol. 29 (03 1974).Google Scholar
[26]Sharpe, W. F.Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” The Journal of Finance, Vol. 19 (09 1964), pp. 425442.Google Scholar
[27]Treynor, J. L. “Toward a Theory of Market Value of Risky Assets.” Unpublished manuscript (1961).Google Scholar
[28]Young, William E., and Trent, Robert H.. “Geometric Mean Approximations of Individual Security and Portfolio Performance.” Journal of Financial and Quantitative Analysis, Vol. 4 (06 1969), pp. 179199.CrossRefGoogle Scholar