Joan Tam, CFA, believes she has identified an arbitrage opportunity for a commodity as indicated by the information given in the following exhibit:
a. Describe the transactions necessary to take advantage of this specific arbitrage opportunity.
b. Calculate the arbitrage profit.
a. The strategy of reserve, cash and carry should be adopted.
To take advantage of the arbitrage opportunity, the strategy of reserve, cash and carry should be adopted.
This strategy results when the relationship F0t ≧ S0 (1 + C) doesn’t hold true.
If the future price is less than spot price plus transportation cost at a futures date, the arbitrage opportunity exists in the form of Reserve, Cash and Carry.
Opening transaction Now
Sell the spot commodity short
Buy the commodity futures expiring in 1 years
Contract to lend $120 at 8% for a year
Total cash flow
Closing transaction One year from Now
Accept delivery on expiring futures
Cover short commodity position
Collect on loan of $120
Total arbitrage profit
A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Jerry Harris sells one July silver futures contract at a price of $28 per ounce, posting a $6,000 initial margin. If the required maintenance margin is $2,500, what is the first price per ounce at which Harris would receive a maintenance margin call?.
a. Turn to Figure 17.1 and locate the contract on the Standard & Poor’s 500 Index. If the margin requirement is 10% of the futures price times the multiplier of $250, how much must you deposit with your broker to trade the September contract?
b. If the September futures price were to increase to 1,200, what percentage return would you earn on your net investment if you entered the long side of the contract at the price shown in the figure?
c. If the September futures price falls by 1%, what is the percentage gain or loss on your net investment?
In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $ D per share at the expiration date of the option.
a. What is the value of the stock-plus-put position on the expiration date of the option?
b. Now consider a portfolio consisting of a call option and a zero-coupon bond with the same expiration date as the option and with face value ( X + D ). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio, regardless of the stock price.
c. What is the cost of establishing the two portfolios in parts ( a ) and ( b )? Equate the cost of these portfolios, and you will derive the put-call parity relationship, Equation 16.3.
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