Finance 300 Financial Markets Lecture 25 © Professor J. Petry, Fall

2 Things To Do: VIII-2 Assume that in the previous example Nov 98 soybeans settled at 636. If a hurricane destroys the entire Illinois soybean crop and nobody is willing to sell soybean futures for less than 800, how many days will pass before trading resumes? Assuming that the broker marks to market at the theoretical limit on each day, calculate the daily and cumulative paper profit, deposit to margin, and equity position for both John Q. Investor (who bought 10 contracts at 636) and George Q. Farmer (who sold 10 contracts at 631) from day to day. Chapter VIII – Futures

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4 Things To Do: VIII-3 George Q. Farmer expects to harvest 50,000 bushels of soybeans in October, but there are no October futures in soybeans. Tofu, Inc wishes to buy 50,000 bushels of soybeans in October, but faces the same problem. The current spot price for soybeans is $6.20 and the price for November soybeans is 631. Initial margin is $1,125 per contract. A) Construct a hedge strategy for George and for Tofu Inc. B) In October the spot price for soybeans is $6.00 and the November futures price is 611. What is the basis on November soybeans? How do George and Tofu Inc. make out? How would George and Tofu made out had they not hedged? C) In October the spot price for soybeans is $7.00 and the November futures price is 714. Now how do George and Tofu make out? Why is this different than in Part B? Chapter VIII – Futures

5 Things To Do: VIII-3 Chapter VIII – Futures

6 Things To Do: VIII-3 Chapter VIII – Futures

7 Things To Do: VIII-3 Chapter VIII – Futures

8 Speculating on Basis: Basis: The difference between the futures price and the spot price. Basis Risk: Risk attributable to uncertain movements in the spread between a futures price and a spot price. If investors hold the contract to maturity, basis risk vanishes, as it is recognized beforehand that this basis will converge to zero by maturity of the futures contract. Some investors attempt to profit from changes in basis during the life of a contract. Generalizing from the last example, a long spot- short futures position will profit when the basis narrows. The converse must also be true. Chapter VIII – Futures

9 Speculating on Basis: –Example: Consider an investor holding 100 troy ounces of gold, who is short one gold futures contract (100 troy ounces). Gold today sells for $291 an ounce, and the futures price for June delivery is $296. Hence, basis is $5. Tomorrow, the spot price might increase to $294, while the futures price increases to $299 (basis still $5). The investors gains and losses are: –Gain on holdings of gold (per ounce)294 – 291 = $3.00 –Loss on gold futures position (per ounce)299 – 296 = $3.00 –Net gain (or loss) = $0.00 Now assume spot goes to 294, but futures to Gains/losses? And if spot goes to 296, futures to Gains/losses? And if spot goes to 294, but futures go to 300. Gains/losses? Chapter VIII – Futures

10 Determination of Futures Prices Futures prices are based on the following theorem: Spot-futures parity theorem (aka cost of carry relationship): Describes the theoretically correct between spot and futures prices. It states that the futures price reflects the spot price of the underlying asset plus the carrying charges (cost of borrowing, storage, insurance, etc) necessary to carry the underlying asset forward to delivery. Violation of the parity relationship gives rise to arbitrage opportunities (A risk-free profit requiring no initial investment. Arbitrage often involving the simultaneous purchase and sale of essentially the same asset). Chapter VIII – Futures

11 Determination of Futures Prices Ranges for futures prices can be easily established by calculating the points at which arbitrage profits become possible. Futures prices will not remain at these levels, as market participants quickly buy up these opportunities until prices adjust them away. Example: Suppose in January 1998 the spot price of gold is $370 and the January 1999 gold futures are trading at $400. The risk free rate of interest is 5%, storage & insurance cost $1.20 per ounce. CBT gold futures trade in contracts of 100 ounces, with an initial margin requirement of $1,800. –Abitrage opportunities exist in both of the following slides. In the first we use the assumptions given above. In the second, we change the futures price from 400 to 360. Chapter VIII – Futures

12 Determination of Futures Prices Chapter VIII – Futures

13 Determination of Futures Prices Chapter VIII – Futures

14 Things To Do: VIII-7 In the previous example, at what prices to the arbitrage opportunities disappear? A) What is the expected price range for gold futures? B) What is the expected price range for 12 month gold futures when the interest rate is 15%? C) What happens to the price range when the time horizon shortens? Answer this question by looking at 12, 6, 3, and 0 month futures. Calculate the expected price range for 6 month (July ’98) gold futures when the interest rate is 15%. Calculate the expected price range for 3 month (April ’98) gold futures. And if the delivery date is tomorrow (Jan ’98). Chapter VIII – Futures