Download Minimum Variance Portfolios in the U.S. Equity

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.