The Distribution of the Sample Minimum-Variance Frontier

Raymond Kan · Daniel R. Smith

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Risk and Portfolio Optimization Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios.

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References

1993Common risk factors in the returns on stocks and bonds 1963A Simplified Model for Portfolio Analysis 2003Improved estimation of the covariance matrix of stock returns with an application to portfolio selection 2003Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps 1989The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?1972An Analytic Derivation of the Efficient Portfolio Frontier 1986Bayes-Stein Estimation for Portfolio Analysis 1981Performance Hypothesis Testing with the Sharpe and Treynor Measures

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