The first principal component of stock returns is often identified with a market factor. Empirical portfolios based on this principal component sometimes contain short positions. These portfolios are based on the dominant eigenvector of the correlation matrix. We analyze empirically how stock return correlations affect the signs of the dominant eigenvector. If all the correlations are positive the dominant eigenvector is positive and the portfolio has positive weights. This follows from the Perron Frobenius theorem. In practice some of the correlations are negative and in this case the dominant eigenvector may be positive or it may contain negative values. We analyze the characteristics of the correlation matrix that lead to negative weights in the dominant eigenvector and we show that this is driven by a few stocks. We document the characteristics of these stocks. We also explore the relationship more generally and manage to obtain a few analytic results.