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The Distribution of the Sample Minimum-Variance Frontier
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The Distribution of the Sample Minimum-Variance Frontier (2008)The Distribution of the Sample Minimum-Va…Optimal Portfolio Choice with Parameter Uncertainty (2007)Optimal Portfolio Choice with…Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach (2006)Portfolio Selection with Para…Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps (2003)Risk Reduction in Large Portf…Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003)Improved estimation of the co…The Statistics of Sharpe Ratios (2002)The Statistics of Sharpe Rati…Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps (2002)Risk Reduction in Large Portf…The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights (1999)The Sampling Error in Estimat…Assessing Specification Errors in Stochastic Discount Factor Models (1997)Assessing Specification Error…Common risk factors in the returns on stocks and bonds (1993)Common risk factors in the re…The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal? (1989)The Markowitz Optimization En…Bayes-Stein Estimation for Portfolio Analysis (1986)Bayes-Stein Estimation for Po…International Portfolio Diversification with Estimation Risk (1985)International Portfolio Diver…Performance Hypothesis Testing with the Sharpe and Treynor Measures (1981)Performance Hypothesis Testin…Estimation for Markowitz Efficient Portfolios (1980)Estimation for Markowitz Effi…An Analytic Derivation of the Efficient Portfolio Frontier (1972)An Analytic Derivation of the…A Simplified Model for Portfolio Analysis (1963)A Simplified Model for Portfo…The Risk of Expected Utility Under Parameter Uncertainty (2024)The Risk of Expected Utility …Lest We Forget: Learn from Out-of-Sample Forecast Errors When Optimizing Portfolios (2021)Lest We Forget: Learn from Ou…Bayesian mean-variance analysis: Optimal portfolio selection under parameter uncertainty (2018)Bayesian mean-variance analys…Diversification Benefits of REIT Preferred and Common Stock: New Evidence from a Utility‐based Framework (2016)Diversification Benefits of R…Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks (2014)Nonlinear shrinkage of the co…Solving norm constrained portfolio optimization via coordinate-wise descent algorithms (2013)Solving norm constrained port…Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations (2012)Risk index based models for p…Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk (2012)Performance Analysis and Opti…Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix (2012)Parameter uncertainty in port…High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: Risk underestimation (2010)High-dimensionality effects i…Jackknife Estimator for Tracking Error Variance of Optimal Portfolios (2009)Jackknife Estimator for Track…On the Fundamental Law of Active Portfolio Management (2008)On the Fundamental Law of Act…Econometrical analysis of the sample efficient frontier (2008)Econometrical analysis of the…Portfolio Performance Manipulation and Manipulation-proof Performance MeasuresOn estimating the expected return on the market (1980)The Econometrics of Financial Markets (1997)High Frequency Trading and the New-Market Makers (2012)The Econometrics of Financial Markets (2012)Can ChatGPT forecast stock price movements? Return predictability and large language models (2026)CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* (1964)Risk, Return, and Equilibrium: Empirical Tests (1973)The Cross-Section of Expected Stock Returns (1992)On Persistence in Mutual Fund Performance (1997)Illiquidity and stock returns: cross-section and time-series effects (2002)A five-factor asset pricing model (2014)An Empirical Evaluation of Accounting Income Numbers (1968)THE PERFORMANCE OF MUTUAL FUNDS IN THE PERIOD 1945–1964 (1968)Construct validity of an objective (entropy) categorical measure of diversification strategy (1993)CORPORATE DIVESTITURE INTENSITY IN RESTRUCTURING FIRMS: EFFECTS OF GOVERNANCE, STRATEGY, AND PERFORMANCE. (1994)Portfolio Selection: Efficient Diversification of Investments (1959)A Note on Uncertainty and Indifference Curves (1969)An Intertemporal Capital Asset Pricing Model (1973)A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory (1977)Theory of Financial Decision Making. (1988)The arbitrage theory of capital asset pricing (1976)The Determinants of Capital Structure Choice (1988)Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation (1991)Asset Pricing at the Millennium (2000)Efficiency and the Bear: Short Sales and Markets Around the World (2007)Shrinking the cross-section (2019)Portfolio Selection: Efficient Diversification of Investments. (1962)On the Predictability of Stock Returns: An Asset‐Allocation Perspective (1996)The Properties of Equally Weighted Risk Contribution Portfolios (2010)Industry costs of equity (1997)Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH (2001)International Stock Return Comovements (2005)High dimensional covariance matrix estimation using a factor model (2008)PORTFOLIO SELECTION* (1952)Honey, I Shrunk the Sample Covariance Matrix (2004)Chapter 4 Forecast Combinations (2006)A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms (2009)THE 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.] (1975)The Adjustment of Stock Prices to New Information (2003)An Engine, Not a Camera (2006)
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References

  • 1993Common risk factors in the returns on stocks and bonds26,615 cited
  • 1963A Simplified Model for Portfolio Analysis2,740 cited
  • 2003Improved estimation of the covariance matrix of stock returns with an application to portfolio selection1,634 cited
  • 2003Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps1,471 cited
  • 1989The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?1,333 cited
  • 1972An Analytic Derivation of the Efficient Portfolio Frontier1,039 cited
  • 1986Bayes-Stein Estimation for Portfolio Analysis960 cited
  • 1981Performance Hypothesis Testing with the Sharpe and Treynor Measures860 cited
  • 2002The Statistics of Sharpe Ratios842 cited
  • 1997Assessing Specification Errors in Stochastic Discount Factor Models768 cited
  • 2007Optimal Portfolio Choice with Parameter Uncertainty704 cited
  • 2006Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach690 cited
  • 1985International Portfolio Diversification with Estimation Risk672 cited
  • 1980Estimation for Markowitz Efficient Portfolios554 cited
  • 2002Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps535 cited

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  • 1999The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights472 cited
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    • 2012Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations63 cited
    • 2013Solving norm constrained portfolio optimization via coordinate-wise descent algorithms59 cited
    • 2012Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk57 cited
    • 2009Jackknife Estimator for Tracking Error Variance of Optimal Portfolios47 cited
    • 2018Bayesian mean-variance analysis: Optimal portfolio selection under parameter uncertainty47 cited
    • 2021Lest We Forget: Learn from Out-of-Sample Forecast Errors When Optimizing Portfolios43 cited
    • 2024The Risk of Expected Utility Under Parameter Uncertainty40 cited
    • 2008On the Fundamental Law of Active Portfolio Management34 cited
    • 2016Diversification Benefits of REIT Preferred and Common Stock: New Evidence from a Utility‐based Framework29 cited