Suppose that you have gathered the information from a financial broker who trade

Question

Suppose that you have gathered the information from a financial broker who trades on Lusaka Stock exchange about the shares of Lafarge, which is the underlying asset for a futures contract with settlement six months from now. You know the following about this financial asset and futures contract:

1. In the spot cash market, Lafarge is selling its shares for $1000 per share.

2. Lafarge pays $120 per year in four quarterly payments of $30 per share, and the next quarterly payment is due exactly three months from now.

3. The current interest at which funds can be loaned is 10% per annum and the borrowing rate is 18% per annum .

4. The contract is for six months

Answer the below questions:

a. What is the theoretical (or equilibrium) futures price? Based on the lending rate? Based on the borrowing rate?

b. What action would you take if the futures price is $900? Clearly indicate the position as to the asset , the futures contract and the related financing decision. What is the profit from this action?

c. What action would you take if the futures price is $1,200? Clearly indicate the position as to the asset, the futures contract and the related finacing decision. What the profit from this action?

d. If you know that you can reinvest any funds you received one month from now at 1% a month , what would the theoretical futures price for six month settlement be?

Explanation / Answer

a. Equilibrium futures price based on lending rate is:

Lending rate for 6 months = 10/2 = 5%. Hence the the futures price should be 1000*1.05 = 1050

Since you recieve 2 payent of $30 , which is 30 *2 = $60

Hence the price of the future contract should be 1050-60 =$990

Equilibrium futures price based on borrowing rate is:

Lending rate for 6 months = 18/2 = 9%. Hence the the futures price should be 1000*1.09 = 1090

Since you recieve 2 payent of $30 , which is 30 *2 = $60

Hence the price of the future contract should be 1090-60 =$1,030

b. If the futures is at 900, I would buy (or go long) it since price after 6 months would be either 990 or 1030 making a profit in both cases. I would make of profit of either $90 or $130

c. If the futures price is at 1200, I would sell (or go short) since the price would be only 990 or 1030 in either case. YOu can make a profit od $210 or $170

d. Yes the theorical price sill change. The new theorical futures price based on lending rates will be 1050 - 30*(1.03)-30 = 989.10 and the theoritical futures price based on borrowing rates will be 1090- 30*(1.03) -30 = 1029.10

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