1. Suppose you notice that the April gold futures price is $1,518, while that fo
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Question
1. Suppose you notice that the April gold futures price is $1,518, while that for December is $1,535 (both prices are per ounce). Historically, this spread has been around $10. Suggest a trading strategy that you might set up in the hope that the spread would revert to its historical level next month.
2. A stock price is $50 today. It pays dividend of $1 after two months and $1.05 after five months. The continuously compounded interest rate is 4% per year. Transaction costs are $0.10 per stock traded, a $0.25 one-time fee for trading forward contracts, and no costs for trading bonds. If the six-month forward price is $51, demonstrate how to make arbitrage profits or explain why you cannot.
Explanation / Answer
1)The spread now=$1,535-$1,518=$17
Since the spread now=17>10, the historical spread therefore we should enter the positions looking at the fact that the spread should again narrow down to 10.Therefore we can say that the December golf futures are overpriced relative to the April gold futures therefore the price of December golf futures should drop relative to the April gold futures price such that the spread narrows down to the 10 between their prices.Therefore we should short December golf futures and long April gold futures such that we capitalize on the dropping price of December golf futures relative to the April gold futures.
2)If i buy stock today(include transaction costs of .10$) for $50.10 by borrowing $50.10 at 4% and receive dividends of $1 after two months and $1.05 after five months and deposit them at 4% for remaining period.And enter the forward contract to sell the stock at $51 after 6 months at cost 0.25$( borrowing $0.25 at 4%).
The future value after 6 month of all these cash flows
=(-50-0.10-0.25)*exp(.04*.5)(payback borrowings with interest)+1*exp(0.04*4/12)+1.05*exp(0.04*1/12)(dividends with interest)+The $51 from the short Forward
=(-50-0.10-0.25)*exp(.04*.5)+1*exp(0.04*4/12)+1.05*exp(0.04*1/12)+ $51
=$51-$49.300
=$1.7 is the arbitrage profit made after 6 months.
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