On the weight sign of the global minimum variance portfolio

We investigate the one-to-one mapping between the global minimum variance portfolio and regression hedge coefficients. The analysis demonstrates that assets with a superior (inferior) regression hedged effect in terms of marginal return create a negative (positive) weight. The asset has a weight of zero when both the asset and regression hedge enjoy the same marginal return. In addition, we develop a modified information ratio to compare the magnitudes of two arbitrary weights of the global minimum variance portfolio. From the perspective of hedging, we determine that the asset with a higher modified information ratio yields a larger weight.