4. The price of gold is currently $1,200 per ounce. Forward contracts are availa

Question

4. The price of gold is currently $1,200 per ounce. Forward contracts are available to buy or sell gold at $1,400 per ounce for delivery in one year. An arbitrageur can borrow money at 10% per annum. Assume continuous compounding.

-Clearly outline the trading strategy to exploit the profitable arbitrage opportunity, if any. What is the profit (per ounce)?

- How does your answer change if storage costs of 2% per annum are incurred? What is the profit (per ounce)?

5. A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $1250 per ounce and sell gold for $1249 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year (assume continuous compounding).

- For what range of six-month forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid-offer spread for forward prices.

6. An 8-month forward contract on a stock is currently priced at $84. The stock currently sells for $80. Assume that the risk-free rate of interest (with continuous compounding) is 10% per annum. Assume that dividends of $0.90 per share are expected after 4 months and 6 months.

- Is there an arbitrage opportunity here?

- If so, how can you engage in a trading strategy to exploit this opportunity? What is the profit from this trading strategy?

Explanation / Answer

5)

Suppose that 0F is the one-year forward price of gold. If F0 is relatively high, the trader can borrow $1250 at 6%, buy one ounce of gold and enter into a forward contract to sell gold in one year for 0F. The profit made in one year is   

F0 - 1250 x1.06

This is profitable if F0 >1325. If 0F is relatively low, the trader can sell one ounce of gold for $1249, invest the proceeds at 5.5%, and enter into a forward contract to buy the gold back for F0. The profit (relative to the position the trader would be in if the gold were held in the portfolio during the year) is   

1249 x 1.055 - F0 = 1317.695 - F0 This shows that there is no arbitrage opportunity if the forward price is between $1317.695 and $1325 per ounce.

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