The process described in the question is known as 'Rolling a hedge forward'. This is a common practice in futures trading, where an investor closes out their existing position as the futures contract approaches its maturity date, and replaces it with another futures contract that has a later delivery date or maturity. This strategy allows the investor to maintain their position in the market, while avoiding the delivery of the underlying asset. It is particularly useful in situations where the investor's primary interest is in the price movements of the asset, rather than in owning the asset itself. The new contract that replaces the old one is typically identical in all respects except for its delivery date. This process of 'rolling forward' can be repeated indefinitely, allowing the investor to maintain a continuous presence in the futures market.

Choice A is incorrect. Cross-over hedging refers to the practice of hedging a position in one asset by taking a position in another asset. This is not the same as closing out a futures contract and replacing it with another one, which is described as rolling a hedge forward.

Choice C is incorrect. Basis risk of hedging refers to the risk that the value of a futures contract will not move in line with that of the underlying asset, leading to ineffective hedging. This concept does not involve replacing an expiring futures contract with another one.

Choice D is incorrect. Reducing the beta of a portfolio involves adjusting its sensitivity to market movements, typically through diversification or using derivatives like options and futures for hedging purposes. However, this does not specifically refer to closing out an existing futures position and opening another one with later maturity.