Posted: June 21st, 2016

Compute the minimum-variance hedge ratio.

(12 marks) Chococo Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 750 metric tons of cocoa in 3 months. The current spot price of cocoa is $2,645 per metric ton. The standard deviation of the value for the inventory is 0.15. Mr. Dulce, the CFO of the Chococo, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The volatility of the futures is 0.2. The covariance between the change in the spot and futures cocoa price is 0.027.

a. Compute the minimum-variance hedge ratio. (5 marks)

b. How many contracts she should trade? Long or short? (3 marks)

c. What is the estimated effectiveness of this minimum variance hedge?
(2 marks)

d. What is the correlation of the change in the spot and futures cocoa price?
(2 marks)

9. (15 marks) You manage a portfolio that is currently all invested in equities in companies in five major Canadian industries. The market value involved and beta for each industry are shown in the table below.

Industry MV Beta
Oil and Gas $1,000,000 1.2
Technology 600,000 1.5
Utilities 1,500,000 0.8
Financial 800,000 1.3
Pharmaceutical 1,300,000 1.1

You believe that the Canadian equity market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and reestablishing your equity position. Instead, you decide to hedge your portfolio with three-month S&P/TSX 60 index futures contracts for one month. Currently, the level of the S&P/TSX 60 index is 678.68, the three-month futures price of the S&P/TSX 60 is 665.60, and one contract is for $200 times the index. The annual simple risk-free rate of return is 1%.

a. How many futures contracts should you use? Long or short? (5 marks)

b. Suppose the return on the S&P/TSX 60 index is -5% in one month, and the S&P/TSX index futures price falls to 620 in one month. Calculate your net gain or loss on your hedged portfolio in part (a). (10 marks)