Suppose you are holding a stock portfolio worth $20 million at current market prices. The stock portfolio has a beta of 1.3. You are given the following data: Todays date: September 2020 December NZSE10 futures expiration: Dec. 2020 (in exactly 3 months time from today) Current NZSE10 index: 1,950.00 December NZSE10 futures price (actual trade price): 1,989.00 Current 3-month risk-free interest rate: 6 percent per annum (continuously compounded) Dividend yield on NZSE10 index: 0.00 percent per annum (continuously compounded) Futures contract size: One futures contact is equal to $25 times the index value.

a. What is the theoretical price today for the December NZSE10 futures contract?

b. If the December NZSE10 futures is not at fair value as at todays date, what arbitrage trade should you do? Also calculate the arbitrage profit at maturity for one futures contract that you may trade.

c. You are worried that market may crash between now and December, when the futures contract on the NZSE10 index will expire. How many December NZSE10 futures contracts should you trade (indicate long or short) to reduce the overall portfolio beta of your current portfolio to 0.50. (Ignore basis risk between the NZSE10 futures and the cash index). In your calculations use the actual traded December NZSE10 futures price, rather than the theoretical futures price that you calculated in part a. of this question. That is, for this part of the question only you can assume the actual December NZSE10 futures price equals the theoretical futures price.