Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Minimum Variance Portfolios in the U.S Equity Market Abstract and Summary The minimum variance portfolio at the leftmost tip of the efficient frontier has the unique property that the optimal security weights are independent of expected security returns. Portfolios can be constructed based solely on the estimated security covariance matrix without reference to a model of equilibrium expected or actively forecasted returns. The empirical analysis of minimum variance portfolio return characteristics over time yields perspectives on the practical value of numerical portfolio optimization, competing security covariance matrix estimation techniques, the characteristics of low volatility stocks, and other issues of concern to quantitative portfolio managers. In this paper we conduct large-scale (1000 stock) minimum variance optimizations on the U.S. equity market at the beginning of each month over several decades (1968 to 2005) and examine the characteristics of the realized portfolio returns. To avoid ex-post data mining critiques of pre-specified factor models, we restrict ourselves to covariance matrix estimation using the security return data available at the beginning of each monthly optimization. Specifically, we use covariance matrixes calculated from monthly (prior five years) and daily (prior one year) security returns, structured to ensure matrix invertability using either principle components or Bayesian shrinkage. We find that the long-only minimum variance portfolio has about 25 percent less realized risk (standard deviation and beta) than the cap-weighted market portfolio. Despite the lower realized risk, the average return on the minimum variance portfolio over time approximately matches the average return on the market. We next impose constraints on the portfolio optimization with respect to the Fama/French factors of size, value, and momentum, using both stock characteristics and estimated stock sensitivities. The factor constraints ensure ex-ante neutrality with respect to these cross-sectional drivers of stock returns, and leads to only a modest reduction in the Sharpe ratios of minimum variance portfolios. However, despite the ex-ante neutrality constraints, we find a material ex-post exposure to the value factor in most time periods which explains much of the superior performance of minimum variance portfolios in the U.S. equity market.