This paper introduces a new approach to constructing optimal mean-variance portfolios. The approach relies on a novel unconstrained regression representation of the mean-variance optimization problem combined with high-dimensional sparse-regression methods. Our estimated portfolio, under a mild sparsity assumption, controls for risk and attains the maximum expected return as both the numbers of assets and observations grow. The superior properties of our approach are demonstrated through comprehensive simulation and empirical analysis. Notably, using our strategy, we find that investing in individual stocks, in addition to the Fama-French three-factor portfolios, leads to substantially improved performance. Received October 6, 2014; editorial decision July 13, 2018 by Editor Andrew Karolyi.

We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of autocovariances and autocorrelations of the noise. Simulation studies demonstrate excellent performance of our estimators in the presence of jumps, irregular observation times, and even rounding. Empirical studies reveal (moderate) positive autocorrelations of microstructure noise for the stocks tested.

Using available return data, many multi-factor asset pricing models present impressive in-sample Sharpe ratios, significantly surpassing that of the market portfolio. Such a performance, however, contradicts the conventional wisdom in finance. Investors cannot realistically attain the in-sample Sharpe ratios. They obtain the out-of-sample Sharpe ratios, which are significantly lower. Estimation risk is one reason for this performance deterioration. We theoretically study the effect of estimation risk by obtaining the exact distributions of in-sample and out-of-sample Sharpe ratios, and argue that such effect needs to be considered in model comparisons.