A. The basis is always the near-future price minus the distant-future price; it narrows as it gets closer to zero it narrows, and widens as it gets farther from zero.
B. Interest rates and futures prices move inversely. Selling the near future and buying the distant future suggests that the investor is speculating that contract prices will move down. Considering that only one-fourth of the position is hedged, this is probably a strongly held belief.
A. Uncovered position: $93,750 (50 bps x $25 x 75 contracts). Hedged position is also positive because the speculator sold near future and bought distant future as the basis narrowed: $6,250 (10 bps x $25 x 25 contracts).
D. Gross margin is $100,000, per 3A. The amount invested is $966.65 ($96.6650 x 100 contracts x 10%) plus $241.68 ($96.6700 x 25 contracts x 10%) plus $100 ($50 x 2 trades)
C. A is false and the others are not necessarily true.
B. Pyramiding involves the incremental addition of futures positions in decreasing amounts in a rising market, not a falling one.