Stock index arbitrage is a trading strategy that seeks to exploit price discrepancies between a stock index and its corresponding futures contract. The correct answer to the question is D: "It involves selling a stock index futures contract and purchasing the portfolio of stocks underlying the index." This strategy is based on the principle that the price of the index should closely reflect the value of the stocks that make up the index. When there is a significant divergence between the two, an arbitrage opportunity arises.

In the context of stock index arbitrage, the trader would sell the futures contract if the index is trading at a price higher than the value of the underlying stocks, anticipating that the price will correct itself. Simultaneously, the trader would purchase the actual stocks that make up the index to hedge their position. This allows the trader to profit from the convergence of the index price and the value of the stocks, without taking a directional bet on the market.

The explanation provided in the file content clarifies why the other options (A, B, and C) are incorrect:

• Option A describes a long/short trade or a pairs trade, which is different from stock index arbitrage.
• Option B also refers to a long/short trade or a pairs trade, rather than stock index arbitrage.
• Option C is incorrect because if the portfolio underlying the index is not tradable, it is possible for the index price to diverge from the value of the underlying stocks.

The objective of stock index arbitrage is to ensure market efficiency by taking advantage of temporary mispricings between the index and its futures contracts, thus promoting a more accurate reflection of the underlying asset values in the financial markets.