Industry or sector exposure. Consider a set of n assets or stocks that we invest in. Let f be an n-vector that encodes whether each asset is in some specific industry or sector, e.g., pharmaceuticals or consumer electronics. Specifically, we take fi = 1 if asset i is in the sector, and fi = 0 if it is not. Let the n-vector h denote a portfolio, with hi the dollar value held in asset i (with negative meaning a short position). The inner product f T h is called the (dollar value) exposure of our portfolio to the sector. It gives the net dollar value of the portfolio that is invested in assets from the sector. A portfolio h is called neutral (to a sector or industry) if f T h = 0.
A portfolio h is called long only if each entry is nonnegative, i.e., hi ≥ 0 for each i. This means the portfolio does not include any short positions. What does it mean if a long-only portfolio is neutral to a sector, say, pharmaceuticals? Your answer should be in simple English, but you should back up your conclusion with an argument.