A short position in a hedge improves as the basis of the hedge strengthens or increases unexpectedly. The basis is defined as the difference between the spot price of the asset to be hedged and the futures price of the contract used. An increase in the basis will improve the company's short position as the company will get a higher price for the asset after futures gains or losses are considered. In contrast, a decrease in the basis will worsen the company's short position as the company will pay a higher price for the asset after futures gains or losses are considered. A short hedge comprises a long position in the spot (underlying asset) and a short position in the futures contract, so the short hedge is +S - F. It follows that the short hedge profits whenever the basis increases: +B = +(S - F) because in this scenario, the basis 'matches' the two positions making up the short hedge which are (I) long the spot, +S, and short the futures, -F.

Choice B is incorrect. A strengthening basis does not necessarily improve the long positions of the firm. The basis is defined as the difference between the spot price and futures price of an asset. If the basis strengthens, it means that this difference is increasing, which could be due to either an increase in spot prices or a decrease in futures prices. Since the firm has a long position in spot market, an increase in spot prices would indeed improve its position; however, if it's due to a decrease in futures prices, this wouldn't affect its long position.

Choice C is incorrect. Contrary to what this option suggests, if the basis of hedge strengthens (i.e., increases), it will actually improve rather than worsen short positions of the firm. This is because when you are short on futures contracts and there's an increase in basis (spot price - future price), you stand to gain as you have committed to sell at higher future prices while current spot rates are lower.

Choice D is incorrect. As explained above for choices B and C, both positions will not necessarily improve with a strengthening hedge basis since it depends on whether this change was driven by changes in spot or futures prices.