Question

Instructions: Solve the following problem. To receive credit, readers must be able to follow your logic and you must explain each step in detail. Please label each step, identify each equation and variable, and explain your answer.

The management of a mutual fund plans to sell a basket of stocks in three months. The stocks are similar to the S&P 500. It seeks protection against a decrease in the price of the stocks. The current price of the S&P 500 Index is $2352.40. The futures price of index is $2397.80. The number of shares to be hedged is 1,000, and the number of shares per futures contract is 100. Therefore, 10 contracts will be hedged.

1.   Define the following:

1. Hedge
2. Speculation
3. Futures contract

2.   Describe in detail the hedge created by the mutual fund. That is, what action will the mutual fund take?

3.   Describe the outcome of this hedge in detail if the price of the index is $2304.20 per share and the price of the futures contract is $2349.60 per share when the hedge is lifted.

4.   Describe the outcome of this hedge in detail if the price of the index is $2392.50 per share and the price of the futures contract is $2437.90 per share when the hedge is lifted. Base your answer on the original information given, not your answer in 3 above.

Answer 1

(1) Hedge: A hedge involves taking a position opposite to the hedger's position in the underlying asset so as to successfully protect himself/herself against a fluctuation in the underlying asset's price. The underlying asset can be a commodity (e.g gold, crude oil, cotton, etc) or an intangible financial instruments such as the S&P 500 index in this case.

Speculation: A speculation is said to be executed when a person takes a position in the derivatives market of an underlying asset without a corresponding opposite position in the underlying asset's market, thereby attempting to benefit from the underlying asset's price (and hence its derivative's) price fluctuation in an expected direction.

Futures Contract: A futures contract is a derivative product which can be either sold or bought, thereby creating a corresponding obligation of selling or buying the future contract's underlying asset at a fixed price specified in the contract at a specified future date (hence the name futures contract). A futures contract can be used to hedge or speculate in the derivatives market.

(2) As the mutual fund is long on the underlying asset (S&P 500 in this case), it needs to go short on the underlying asset's futures contract so as to effectively hedge against price fluctuation's of the underlying asset. Any profit generated by a rise in S&P 500 price will be netted off against a corresponding loss in the derivatives position and vice-versa. The same will be more clear when one looks at the process being explained by means of numbers in part (3) and (4).

(3) Number of Shares to be Hedged = 1000, Shares per Contract = 100 and Number of Contracts Required = 1000 / 100 = 10

Current Index Price = 2352.4 and Futures Price = $ 2397.8

Upon lifting hedge:

Index Price = $ 2304.2 and Futures Price = $ 2349.6

Profit/Loss in Index Position = 2304.2 - 2352.4 = - $ 48,2 and Profit/Loss in Futures Position = 2397.8 - 2349.6 = $ 48.2

Hence, Net Profit/Loss = -48.2 + 48.2 = $ 0

(4) Initial Index Price = $ 2352.4 and Futures Price = $ 2397.8

Upon lifting hedge:

Index Price = $ 2392.5 and Futures Price = $ 2437.9

Profit/Loss in Index Position = 2392.5 - 2352.4 = $ 40.1 and Profit/Loss in Futures Postion = 2397.8 - 2437.9 = - $ 40.1

Hence, Net Profit = 40.1 - 40.1 = $ 0