Question

QUESTION 2 (6 points, 2 points per section) If you need additional help with this question, read Part I of Lecture Note #2 on Arbitrage. You must own 100 shares of NoteBook three months from today. NoteBook will not pay any dividends over the next 3 months. You have the money to buy the shares today, if you wish. There is a futures contract calling for delivery of 100 shares of NoteBook three months from today. The current futures price is $140 per share. The price of NoteBook on the delivery day is unknown today. The interest rate for the next 3 months is 1%, per 3 months. That is, for every dollar that you will have in the bank you will get $1.01 after 3 months. a) What are two strategies that will enable you to have shares of NoteBook three months from today? b) Suppose that the current spot price of NoteBook is also $140 per share. What is the best (that is, least costly) strategy TODAY that will enable you to have 100 NoteBook shares three months from today (which is also the futures delivery day)? Suppose that the current spot price of NoteBook is also $137 per share. What is the best (that is, least costly) strategy TODAY that will enable you to have 100 NoteBook shares three months from today (which is also the futures delivery day)? c)

Answer 1

a) The two strategies are

i) Purchase the 100 shares of Notebook today and carry them till 3 months. In this way, one can have the shares after 3 months. One has to forego the interest earned on the purchase amount as an opportunity cost.

ii) Buy the futures contract today for delivery after 3 months. There is no opportunity cost (except margin amount which is not under consideration in this scenario)

b) If the current spot price is $140 per share which is the same as the futures price, one is better off purchasing the futures contract of 100 shares at $140. In this manner, one can keep the money in the bank account and earn interest on the same.

Amount required to purchase the stock today = $140 *100 shares = $14000

Amount required to purchase the stock in futures contract = $140 *100 shares = $14000

Interest earned when futures buying is done = $14000* 1% =$140

Interest earned when buying is done today = $0

Net cost of Futures contract buying =$14000-$140 =$13860

c)

If the current spot price is $137 per share, one is better off purchasing the stock of 100 shares today at $137. In this manner, one can avoid paying a higher amount  $140 per share as per the futures contract

Amount required to purchase the stock today = $137 *100 shares = $13700

Amount required to purchase the stock in futures contract = $140 *100 shares = $14000

Interest earned when futures buying is done = $14000* 1% =$140

Net cost of Futures contract buying =$14000-$140 =$13860

Onviously, net cost of buying today ($13700) is less and hence buying the stock today and keeping it for 3 months is the least costly strategy in this case