Shrinking Against Sentiment: Exploiting Behavioral Biases in Portfolio Optimization

High sentiment predicts lower market returns, higher arbitrage returns, and lower transaction costs. We propose a shrinkage methodology that exploits this empirical evidence to construct mean-variance portfolios. Exploiting the eigenvalue decomposition of the covariance matrix of stock returns, we show that mean-variance portfolio performance is the sum of two components: a market and an arbitrage component. Shrinking the sample covariance matrix toward the identity in the construction of mean-variance portfolios gives more relevance to the market component as the shrinkage intensity increases. We time the exposure to each component byshrinking more (less) when sentiment is low (high), which provides sizable economic gains even net of transaction costs.