1 Ariya anticipates that the S&P 500 index will increase to 4,200 by year end. The S&P 500 index is 3,900 currently. She wants to trade derivatives to make some money. However, she has no experience in derivatives trading. She is not comfortable with the idea of receiving margin calls. Can you help her design a strategy so that she can potentially make some money and not worry about receiving margin calls? Please clearly describe your strategy. In addition, please discuss the benefits of using this strategy (at least can help her make money and avoid significant downside risks) while pointing out at least one drawback of the strategy.
2 Rick thinks that US dollar will continue to depreciate relative to other major currencies. He believes that Japanese Yen will be a good currency to hedge the risk. The exchange rate is $0.0091 per yen. He needs to hedge $100 million. Please search the CME or ICE futures products and advise him which futures contract he should use. Please also determine whether he should long or short in the futures contract and how many contracts. How much does he gain or lose if the exchange rate at the end of the contract is (a) $0.01 per yen; (b) $0.008 per yen?
3. Courtney thinks that Apple’s stock is cheap at $120 a share. She can think of three trading strategies. She can buy the AAPL stock at $120. She can also buy April 23 call option contracts with a strike of $120 for $4.90 a share or $490 per contract. Alternatively, she can write put contracts with a strike price of $120 and an expiration date on April 23. The put price is $4.82. There is a margin requirement of $4.82+24=$28.82 per put or $2,882 per contract. She is given an initial fund of $10,000. She expect that the stock price can be either $132 or $108 on April 23. Assume that she will try to maximize her gains. However, no fractional shares or contracts are allowed. Please show the initial costs for each of the strategy. Use the following table to show how much she gain or lose using the strategies.
Initial cost for buying AAPL stocks:
Initial cost for buying AAPL options:
Please show profits or losses under the different strategies:
Stock price at $132 Stock price at $108
Buy Stock
Buy Call
Write Put (bonus, not required)
4 According to Coindesk, the price of bitcoin is currently at $58,311.80 (March 19 2021). According to the CME, the futures bitcoin price on December 17 2021 is $67,060 each. The borrowing cost for Jean is 3% per annum. Is there an arbitrage opportunity? What should Jean do to take advantage of the opportunity? Assume that the cost of storing a bitcoin is zero and that it provides no income.
https://www.coindesk.com/price/bitcoin
https://www.cmegroup.com/trading/equity-index/us-index/bitcoin_quotes_globex.html
5 The Volkswagen AG’s stock, with the ticker symbol of VOW, is traded on Xetra based in Frankfurt, Germany. The stock price is € 280.60 on March 19 2021. The same stock is also traded on the over-the-counter (OTC) market in the US under the ticker symbol of VLKAF. The stock price is $342.24 on the same day. The exchange rate is 1 Euro to 1.19 USD. Bob is interested in making money without bearing any risk. Please show him if there is such an opportunity. What should Bob do to take advantage of the opportunity?
6 A trader sells two December futures contracts on Bitcoin. Each contract is for delivery of 5 bitcoins. The current futures price is $31,340 per bitcoin, the initial margin is $300,000 per contract, and the maintenance margin is $200,000 per contract (or $40,000 per bitcoin). What’s the futures price that would lead to a margin call? Under what circumstances could $240,000 be withdrawn from the margin account?
7 Suppose an investor placed an order to take a long position in 10 March gold futures contracts on February 16. Assume that at the time the order was executed, the March gold futures price was 1,980 dollars per troy ounce. The size of each contract is 100 troy ounces. The broker required the investor to post an initial margin of $2,500 per contract. The broker also informed the investor that the maintenance margin is $1,000 per contract.
a) What was the balance of the margin account if the investor just had enough margin to open the 10 contracts?
b) The price of gold was $1,990 per ounce at the end of February 17. What was the balance of the margin account? How much could be withdrawn from the account?
c) The price of gold was $1,960 per ounce at the end of February 18. Assume the investor did not withdraw money from the account in previous days, would the investor receive a margin call? If there was a margin call, how much was needed to restore the account back to the initial margin balance?
d) If the investor decided to use forward contracts instead of futures contracts. Would the investor receive margin calls before the forward contracts expiration date?
8 Suppose a U.S. company knows that it will have to pay five million pounds in three months for goods it has purchased from a British supplier. The U.S. company would like to hedge its exposure to exchange rate risk.
Date Spot 1-mth 3-mth 6-mth
Forward Price ($/£) 1.8878 1.8885 1.8897 1.8906
a) Which forward contract should the firm trade? Should the firm buy or sell the forward contract?
b) What’s the gain or loss on the forward contracts (in dollars) on the expiration date? Suppose the pound spot exchange rate in three months is 1.9886 dollars per pound.
9 Theta Airlines wants to hedge its use of jet fuel. The airline is expected to purchase 3.9 million gallons of fuel in the spot market this year. The airline wants to use gulf coast jet fuel futures to hedge its risk. The futures contracts are based on the Jet Fuel Price Index published by S&P Global Platts. The size of one contract is 42,000 gallons or 1,000 barrels. The correlation between the futures price changes and the spot price changes is 0.91. The standard deviation of the futures price is $1.05/gallon while the standard deviation of the spot price is $0.84/gallon. What is the hedge ratio? Is it long or short hedge? How many contracts are needed?
10 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 fully 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 at 4,000 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow? Should the investor long or short the futures? How many contracts?
