We study information demand and supply at the firm and market level using data for 30 of the largest stocks traded on NYSE and NASDAQ. Demand is approximated in a novel manner from weekly internet search volume time series drawn from the recently released Google Trends database. Our paper makes contributions in four main directions. First, although information demand and supply tend to be positively correlated, their dynamic interactions do not allow conclusive inferences about the information discovery process. Second, demand for information at the market level is significantly positively related to historical and implied measures of volatility and to trading volume, even after controlling for market return and information supply. Third, information demand increases significantly during periods of higher returns. Fourth, analysis of the expected variance risk premium confirms for the first time empirically the hypothesis that investors demand more information as their level of risk aversion increases.

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.