By design, the Nikkei index futures attaches 500 (Yen) to each point of the Nikkei 225 share index. Suppose, in July, the Nikkei 225 index is at 25,000 and in the futures market the index level is at 25,500. (Yen) is the Japanese currency.

a.) A fund manager has invested 200 million in the Nikkei 225 index. Propose a strategy for this fund manager to hedge against the index volatility for the full amount of investment.

b.) Suppose, in December, the Nikkei 225 index drops to 22,000, and the level of its future drops to 23,500. Calculate the gains/losses in the futures market and the cash market respectively. Show your steps.

c.) Suppose, in December, the Nikkei 225 index rises to 28,000, and the level of its future increases to 27,500, calculate the gains/losses in the futures market and the cash market respectively. Show your steps.

Thank you in advance, your time is much appreciated!