This is a new project for work that I am stuck on and looking for help:
If i am given a factor model (e.g. barra) and a equity portfolio we're trying to hedge, how can I come up with a hedge portfolio that will 1) reduce overall risk and 2) reduce large factor exposures? Assume we have factor exposures for a universe of all stocks, and short selling is allowed.
I don't know where to start! I have taken courses on standard portfolio optimization, but I don't know how to apply it on this problem since I need to first find the list of stocks to go in hedge portfolio then optimize the weights. Since barra gives factor exposures and factor covariance matrix, it seems I have all the inputs but I don't know how to go about finding the stocks to put in hedge portfolio and then find optimal weights.
Please give me any direction on how to approach this!