It is Sep 20 th , 2018. You are contemplating taking positions in Apple futures contracts (available here: http://www.onechicago.com/?

It is Sep 20th, 2018. You are contemplating taking positions in Apple futures contracts (available here: http://www.onechicago.com/?page_id=751) which expire on December 21st 2018 and March 22nd 2019. Use actual day counts and continuous compounding and that the rate is the same across all periods. Assume that contracts are settled at expiration by delivery of the actual stock. Ignore marking to market.

Based on historical dividend policy, you believe that the stock will pay a $0.73 dividend on Nov 10th 2018, February 10th 2019, May 11th 2019, and Aug 10th 2019.

The prices and rates quoted on September 20th are:

December futures: $230.85;

March futures: $231.75

Risk-free borrowing and lending rate: 2.31%

a)    Suppose you carry out an arbitrage involving a long December futures and short March futures contract (this is called a calendar spread). Construct a table showing the cash flows for each relevant date (assuming that you can borrow stock for a sale as long as you return it in the future and deal with dividends correctly), make sure you consider the following:

·      Do you ever purchase/sell the stock, do you need to short sell at any point?

·      Do you ever receive any dividends? Or pay any?

·      If you need any cash, you must borrow at the risk-free rate.

·      It you receive cash, you should invest at the risk-free rate

Calculate the size of your arbitrage profits (if any) in March.

b)    You are concerned that Apple's dividend policy may change between now and March, 2019. What would be the size of dividend (assume that all dividends are of the same size) that would reduce your arbitrage profits to zero?