Question1: Mechanism of futures markets
A company enters into a long futures contract to buy 1,000 units of a commodity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account?
Question2: Hedging strategies using futures
On March 1 the price of a commodity is $1,000 and the December futures price is $1,015. On November 1 the price is $980 and the December futures price is $981. A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity?
Question 3: Interest rate
The six-month zero rate is 8% per annum with semi-annual compounding. The price of a one-year bond that provides a coupon of 6% per annum semi-annually is 97. What is the one-year continuously compounded zero rate?
Question 4: Determination of forward and futures prices
A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.
a) What are the forward price and the initial value of the forward contract?
b) Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?