I'm calculating the weights of 10 securities in a portfolio for a course project, with the objective of maximizing the sharpe ratio. I'm getting both positive and negative results for weights. The course guide says that negative weights mean that the optimal portfolio contemplates short selling. The results looks like the image.
I have doubts in the interpretation of these results. What exactly does a negative weight means for the portfolio assets, and how it benefits from short selling with those weights? Also, the positive sum of weights is larger than 1. The model is restricted so the sum of all weights is equal to 1, so the sum of positive and negative weights is equal to 1. By taking the course test, the answers seems to be correct, but I still dont understand the logic behind the results. How could be positive weights greater than 1, and what is the logic behind it?