FIN 353: Exercise Problems on Derivative Assets
1. Sample problem on Futures Hedging:
On July 1, an investor holds 50,000 shares of a certain stock.
The market price is
$30 per share. The investor is interested in hedging against movements in the
market over the next month and decides to use the September Mini S&P 500
futures contract.
The index is currently 1,500 and one contract is for delivery of
$50 times the index.
a. What strategy should the investor follow?
b. If in one month, the S&P index changes to 1,450, while the price of the stock
goes down to $28, what is the net hedging result?
Solution:
(a): A short hedge is needed by selling 20 S&P 500 futures.
20 contracts are
needed since ($30x50,000)/($50x1,500).
(b)
Spot
Futures
July 1: Hold 50,000 shares at $30/share
July 1: Sell 20 S&P 500
Futures at
1,500
Total value = $1,500,000
Total value = 20x$50x 1,500
= $1,500,000
August 1: Share price at $28/share
August 1:Buy back 20 futures
contracts
Total Value = $1,400,000
at 1,450
Total value = $20 x $50 x
1,450
= $1,450,000
Loss = $100,000
Gain = $50,000
This is an imperfect hedge because the stock price is moving faster and wider than
the S&P 500 index, that means the stock beta is greater than 1.
You need to buy
more contracts for a perfect hedge.
For this case, 40 contracts will be needed.
2. From Saunders and Cornett, Ch. 10, Solution to #14:
a.
Total profit = ($150  $136)  $5 = $9 per share.
b.
If the price of the underlying stock is $130 (less than the exercise price), you will not exercise
the option. Thus, your profit is $5 per share (the cost of the option).
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3. From Saunders and Cornett, Ch. 10, Solution to #15:
a.
If the price of the underlying stock is $40 (greater than the exercise price), you will not exercise
the option. Thus, your profit is $.50 per share (the cost of the option).
b. Total profit = ($38  $34)  $.50 = $3.50 per share.
4. From Saunders and Cornett, Ch. 10, Solution to #18:
The BlackScholes model examines five factors that affect the price of an option: 1) the spot price
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 Spring '11
 heler
 Derivative, Saunders, Cornett

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