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Portfolio sector emposures The art-vector h denotes a portfolio of investments in n assets, with h:- the dollar value invested in asset i. We consider a set of m industrjg,r sectors, such as pharmaceuticals or consumer electronics. Each asset is assigned to one of these sectors. (More complex models allow for an asset to be assigned to more than one sector.) The exposure of the portfolio to sector 2' is dened as the sum of investments in the assets in that sector. We denote the sector exposures using the m-vector s, where 39; is the portfolio exposure to sector 1'. (When 31- = U, the portfolio is said to be neutral to sector 12} An investment advisor species a set of desired sector exposures, given as the m-vector ad\". Express the requirement 3 = 5\"!\" as a set of linear equations of the form Ah 2 b. (You must describe the matrix A and the vector b.) Remark. A typical practical case involves n = 1000 assets and m = 50 sectors. An advisor might specifysf'\" = 0 if she does not have an opinion as how companies in that sectorr' will do in the future; she might specify a positive value for sags if she thinks the companies i in that sector will do well (i.e., generate positive returns) in the future, and a negative value if she thinks they will do poorly