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Forward Price and Arbitrage Opportunity

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A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $450 per ounce and sell it for $449 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year (both interest rates are expressed with annual compounding). For what range of 1-year forward prices of gold does the trader have no arbitrage opportunities? Assume there is no bid-offer spread for forward prices.

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Solution Summary

Brief calculations to find the range of prices of gold a trader has no arbitrage opportunities for are shown and explained.

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Hello!
The forward price can't be higher than $477. If it were, then there would be the following arbitrage opportunity:

1) Borrow $450 today, buy one ounce of gold. Sell the forward contract.
2) At delivery date, hand over the gold, receive the forward price, and repay the debt, ...

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