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Stochastic Dominance with Riskless Assets

Published online by Cambridge University Press:  19 October 2009

Haim Levy  and
Yoram Kroll
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Extract

Investment decision making under conditions of uncertainty, and in particular portfolio selection, is carried out mainly in the Mean-Variance framework which has been developed by Markowitz [29], [30] and Tobin [42]. By assuming the lending and borrowing of money at a given riskless interest rate, Sharpe [39], [40], Lintner [27], [28], Mossin [34], and others derived and extended the Capital Asset Pricing Model, under which an equilibrium price of each risky asset is determined. However, though the mean variance rule is quite convenient to apply, its limitations are well known, i.e., one must assume either normal probability distributions with risk aversion or quadratic utility functions.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 11 , Issue 5 , December 1976 , pp. 743 - 777
Copyright
Copyright © School of Business Administration, University of Washington 1976

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References

REFERENCES

[1]Aitchison, J., and Brown, J. A. C.. The Lognormal Distribution. Cambridge University Press, 1963.Google Scholar
[2]Alexander, S. S. “Price Movements in Speculative Markets: Trends or Random Walks.” Industrial Management Review (1961), pp. 7–26.Google Scholar
[3]Arditti, F. D. “Risk and Required Return on Equity.” Journal of Finance, vol. 22 (1967), pp. 19–36.CrossRefGoogle Scholar
[4]Arditti, F. D. “Another Look at Mutual Fund Performance.” Journal of Financial and Quantitative Analysis,” vol. 6 (1971), pp. 909–912.CrossRefGoogle Scholar
[5]Arditti, F. D., and Levy, H.. “Portfolio Efficiency Analysis in Three Moments: the Multiperiod Case.” Journal of Finance, vol. 30 (1975), pp. 797–809.Google Scholar
[6]Cass, D., and Stiglitz, J.. “Risk Aversion and Wealth Effects on Portfolios with Many Assets.” Review of Economics Studies, vol. 39 (1972), pp. 331–356.CrossRefGoogle Scholar
[7]Cootner, P. H., ed. The Random Character of Stock Market Prices. Cambridge, Mass.: M.I.T. Press, 1964.Google Scholar
[8]Diamond, P. A., and Stiglitz, J.. “Increase in Risk and in Risk Aversion.” Journal of Economic Theory, vol. 8 (1974), pp. 337–360.CrossRefGoogle Scholar
[9]Fama, E. F. “Risk, Return and Equilibrium: Some Clarifying Comments.” Journal of Finance, vol. 23 (1968), pp. 29–40.CrossRefGoogle Scholar
[10]Feldstein, M. S. “Mean Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection.” Review of Economic Studies, vol. 37 (1969), pp. 5–12.CrossRefGoogle Scholar
[11]Fishburn, P. C.Decision and Value Theory. New York: Wiley, 1964.Google Scholar
[12]Fishburn, P. C. “Convex Stochastic Dominance with Continuous Distribution Functions.” Journal of Economic Theory, vol. 7 (1974), pp. 143–158.CrossRefGoogle Scholar
[13]Hadar, J., and Russell, W. R.. “Rules of Ordering Uncertain Prospects.” American Economic Review, vol. 59 (1969), pp. 25–34.Google Scholar
[14]Hadar, J., and Russell, W. R.. “Stochastic Dominance and Diversification.” Journal of Economic Theory, vol. 3 (1971), pp. 288–305.CrossRefGoogle Scholar
[15]Hadar, J., and Russell, W. R.. “Diversification of Interdependent Prospects.” Journal of Economic Theory, vol. 7 (1974), pp. 231–240.CrossRefGoogle Scholar
[16]Hammond, J. S. “Simplifying the Choices between Uncertain Prospects Where Preference Is Non-Linear.” Management Science, vol. 20 (1974), pp. 1047–1072.CrossRefGoogle Scholar
[17]Hanoch, G., and Levy, H.. “The Efficiency Analysis of Choices Involving Risk.” Review of Economic Studies, vol. 36 (1969), pp. 335–346.CrossRefGoogle Scholar
[18]Hanoch, G., and Levy, H.. “Efficient Portfolio Selection with Quadratic and Cubic Utility.” Journal of Business, vol. 43 (1970), pp. 181–189.CrossRefGoogle Scholar
[19]Levy, H. “Portfolio Selection and Optimal Capital Structure.” Unpublished Ph.D. Dissertation, Jerusalem (1969).Google Scholar
[20]Levy, H. “The Demand for Asset., under Conditions of Risk.” Journal of Finance, vol. 28 (1973), pp. 79–96.CrossRefGoogle Scholar
[21]Levy, H. “Stochastic Dominance, Efficiency Criteria, and Efficient Portfolios: The Multiperiod Case.” American Economic Review, vol. 63 (1973), pp. 986–994.Google Scholar
[22]Levy, H. “Stochastic Dominance among Log-Normal Prospects.” International Economic Review, vol. 3 (1973), pp. 602–614.Google Scholar
[23]Levy, H. “Multiperiod Stochastic Dominance with One-Period Parameters and Equilibrium in the Lognormal Case.” Forthcoming.Google Scholar
[24]Levy, H., and Paroush, J.. “Toward Multivariate Efficiency Citeria.” Journal of Economic Theory, vol. 7 (1974), pp. 129–142.CrossRefGoogle Scholar
[25]Levy, H., and Sarnat, M.. “A Note on Portfolio Selection and Investor Wealth.” Journal of Financial and Quantitative Analysis, vol. 6 (1971), pp. 639–642.CrossRefGoogle Scholar
[26]Levy, H.Investment and Portfolio Analysis. New York: Wiley, 1972.Google Scholar
[27]Lintner, J. “Security Prices, Risk and Maximal Gains from Diversification.” Journal of Finance, vol. 20 (1965), pp. 587–615.Google Scholar
[28]Lintner, J. “The Valuation of Risky Assets and Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economic Statistics, vol. 47 (1965), pp. 13–37.CrossRefGoogle Scholar
[29]Markowitz, H. M. “Portfolio Selection.” Journal of Finance, vol. 7 (1952), pp. 77–91.Google Scholar
[30]Markowitz, H. M.Portfolio Selection: Efficient Diversification of Investments.” New York: Wiley, 1959.Google Scholar
[31]Merton, R. C. “Optimum Consumption and Portfolio Rules in Continuous-Time Model.” Journal of Economic Theory, vol. 3 (1971), pp. 373–413.CrossRefGoogle Scholar
[32]Merton, R. C., and Samuelson, P. A.. “Fallacy of Log-Normal Approximation to Optimal Portfolio Decision Making over Many Periods.” Journal of Financial Economics, vol. 1 (1974), pp. 67–94.CrossRefGoogle Scholar
[33]Moore, J. B. “Some Characteristics of Changes in Common Stock Prices.” Abstract of Ph.D. Thesis (1960) in Cootner [2, pp. 39–161].Google Scholar
[34]Mossin, J. “Equilibrium in a Capital Asset Market.” Econometrica, vol. 34 (1966), pp. 768–783.CrossRefGoogle Scholar
[35]Osborne, M. F. M. “Brownian Motion in the Stock Market.” Operation Research, vol. 7 (1969), pp. 145–173, also in Cootner [7, pp. 100–128].CrossRefGoogle Scholar
[36]Quirk, J. P., and Saposnik, R.. “Admissibility and Measurable Utility Functions.” Review of Economics Studies, vol. 29 (1962), pp. 140–146.CrossRefGoogle Scholar
[37]Rothschild, M., and Stiglitz, J. E.. “Increasing Risk: I. A Definition.” Journal of Economic Theory, vol. 2 (1970), pp. 225–243.CrossRefGoogle Scholar
[38]Rothschild, M., “Increasing Risk: II. Its Economic Consequences.” Journal of Economic Theory, vol. 3 (1971), pp. 66–84.CrossRefGoogle Scholar
[39]Sharpe, W. F. “Capital Asset Prices: A Theory of Market Equilibrium under Condition of Risk.” Journal of Finance, vol. 19 (1964), pp. 425–442.Google Scholar
[40]Sharpe, W. F.Portfolio Theory and Capital Markets. New York: McGraw Hill, 1971.Google Scholar
[41]Sprenkle, C. M. “Warrant Prices as Indicators, of Expectations and Preferences.” Yale Economic Essays, vol. 1 (1961), pp. 178–231.Google Scholar
[42]Tobin, J. “Liquidity Preference as Behavior towards Risk.” Review of Economics Studies, vol. 25 (1958), pp. 65–87.CrossRefGoogle Scholar
[43]Tobin, J. “The Theory of Portfolio Selection.” In Theory of Interest Rates, edited by Hahn, F. H. and Brechling, F. P. R.. New York: Macmillan (1963).Google Scholar